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Jerome Cardan: A Biographical Study

by W. G. Waters · English · Gutenberg #19600 · 564,125 chars · public domain (US)

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Title: Jerome Cardan: A Biographical Study

Author: W. G. Waters


        
Release date: October 22, 2006 [eBook #19600]

Language: English

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JEROME CARDAN




[Illustration]




JEROME CARDAN

_A BIOGRAPHICAL STUDY_

BY

W.G. WATERS

"To be content that times to come should only know there was such a man,
not caring whether they knew more of him, was a frigid ambition in
Cardan."--SIR THOMAS BROWNE.

[Illustration]

LAWRENCE & BULLEN, Limited,

16 Henrietta Street, Covent Garden, London, MDCCCXCVIII.




  RICHARD CLAY & SONS, LIMITED,
  LONDON & BUNGAY.




PREFACE


No attempt is made in the following pages to submit to historical
treatment the vast and varied mass of printed matter which Cardan left as
his contribution to letters and science, except in the case of those works
which are, in purpose or incidentally, autobiographical, or of those which
furnish in themselves effective contributions towards the framing of an
estimate of the genius and character of the writer. Neither has it seemed
worth while to offer to the public another biography constructed on the
lines of the one brought out by Professor Henry Morley in 1854, for the
reason that the circumstances of Cardan's life, the character of his work,
and of the times in which he lived, all appeared to be susceptible of more
succinct and homogeneous treatment than is possible in a chronicle of the
passing years, and of the work that each one saw accomplished. At certain
junctures the narrative form is inevitable, but an attempt has been made
to treat the more noteworthy episodes of Cardan's life and work, and the
contemporary aspect of the republic of letters, in relation to existing
tendencies and conditions, whenever such a course has seemed possible.

Professor Morley's book, _The Life of Girolamo Cardano, of Milan,
physician_, has been for some time out of print. This industrious writer
gathered together a large quantity of material, dealing almost as fully
with the more famous of the contemporary men of mark, with whom Cardan
was brought into contact, as with Cardan himself. The translations and
analyses of some of Cardan's more popular works which Professor Morley
gives are admirable in their way, but the space they occupy in the
biography is somewhat excessive. Had sufficient leisure for revision and
condensation been allowed, Professor Morley's book would have taken a high
place in biographical literature. As it stands it is a noteworthy
performance; and, by reason of its wide and varied stores of information
and its excellent index, it must always prove a valuable magazine of
_mémoires pour servir_ for any future students who may be moved to write
afresh, concerning the life and work of the great Milanese physician.

An apology may be needed for the occurrence here and there of passages
translated from the _De Vita Propria_ and the _De Utilitate ex Adversis
capienda_, passages which some readers may find too frequent and too
lengthy, but contemporary opinion is strongly in favour of letting the
subject speak for himself as far as may be possible. The date and place of
Cardan's quoted works are given in the first citation therefrom; those of
his writings which have not been available in separate form have been
consulted in the collected edition of his works in ten volumes, edited by
Spon, and published at Lyons in 1663.

The author desires to acknowledge with gratitude the valuable assistance
in the way of suggestion and emendation which he received from Mr. R.C.
Christie during the final revision of the proofs.

_London, October 1898._




JEROME CARDAN




CHAPTER I


LIKE certain others of the illustrious personages who flourished in his
time, Girolamo Cardano, or, as he has become to us by the unwritten law of
nomenclature, Jerome Cardan, was fated to suffer the burden and obloquy of
bastardy.[1] He was born at Pavia from the illicit union of Fazio Cardano,
a Milanese jurisconsult and mathematician of considerable repute, and a
young widow, whose maiden name had been Chiara Micheria, his father being
fifty-six, and his mother thirty-seven years of age at his birth. The
family of Fazio was settled at Gallarate, a town in Milanese territory,
and was one which, according to Jerome's contention, could lay claim to
considerable antiquity and distinction. He prefers a claim of descent from
the house of Castillione, founding the same upon an inscription on the
apse of the principal church at Gallarate.[2] He asserts that as far back
as 1189 Milo Cardano was Governor of Milan for more than seven years, and
according to tradition Franco Cardano, the commander of the forces of
Matteo Visconti,[3] was a member of the family. If the claim of the
Castillione ancestry be allowed the archives of the race would be still
farther enriched by the name of Pope Celestine IV., Godfrey of Milan, who
was elected Pope in 1241, and died the same year.

Cardan's immediate ancestors were long-lived. The sons of Fazio Cardano,
his great-grandfather, Joanni, Aldo, and Antonio, lived to be severally
ninety-four, eighty-eight, and eighty-six years of age. Of these Joanni
begat two sons: Antonio, who lived eighty-eight years, and Angelo, who
reached the age of eighty-six. To Aldo were born Jacopo, who died at
seventy-two; Gottardo, who died at eighty-four; and Fazio, the father of
Jerome, who died at eighty.[4]

Fazio, albeit he came of such a long-lived stock, and lived himself to be
fourscore, suffered much physical trouble during his life. On account of a
wound which he had received when he was a youth, some of the bones of his
skull had to be removed, and from this time forth he never dared to remain
long with his head uncovered. When he was fifty-nine he swallowed a
certain corrosive poison, which did not kill him, but left him toothless.
He was likewise round-shouldered, a stammerer, and subject to constant
palpitation of the heart; but in compensation for these defects he had
eyes which could see in the dark and which needed not spectacles even in
advanced age.

Of Jerome's mother little is known. Her family seems to have been as
tenacious of life as that of Fazio, for her father Jacopo lived to be
seventy-five years of age. Of his maternal grandfather Jerome remarks that
he was a highly skilled mathematician, and that when he was about seventy
years of age, he was cast into prison for some offence against the law. He
speaks of his mother as choleric in temper, well dowered with memory and
mental parts, small in stature and fat, and of a pious disposition,[5] and
declares that she and his father were alike in one respect, to wit that
they were easily moved to anger and were wont to manifest but lukewarm and
intermittent affection for their child. Nevertheless they were in a way
indulgent to him. His father permitted him to remain in bed till the
second hour of the day had struck, or rather forbade him to rise before
this time--an indulgence which worked well for the preservation of his
health. He adds that in after times he always thought of his father as
possessing the kindlier nature of the two.[6]

It would seem from the passage above written, as well as from certain
others subsequent, that Jerome had little affection for his mother; and
albeit he neither chides nor reproaches her, he never refers to her in
terms so appreciative and loving as those which he uses in lamenting the
death of his harsh and tyrannical father. In the _Geniturarum Exempla_[7]
he says that, seeing he is writing of a woman, he will confine his remarks
to saying that she was ingenious, of good parts, generous, upright, and
loving towards her children. Perhaps the fact that his father died early,
while his mother lived on for many years, and was afterwards a member of
his household--together with his wife--may account for the colder tone of
his remarks while writing about her. She was the widow of a certain
Antonio Alberio,[8] and during her marriage had borne him three children,
Tommaso, Catilina, and Joanni Ambrogio; but when Jerome was a year old all
three of these died of the plague within the space of a few weeks.[9] He
himself narrowly escaped death from the same cause, and this attack he
attributes to an inherited tendency from his mother, she having suffered
from the same disease during her girlhood. There seems to have been born
to Fazio and Chiara another son, who died at birth.[10]

Jerome Cardan was born on September 24, 1501, between half-past six
o'clock and a quarter to seven in the evening. In the second chapter of
his autobiography he gives the year as 1500, and in _De Utilitate_, p.
347, he writes the date as September 23, but on all other occasions the
date first written is used. Before he saw the light malefic influences
were at work against him. His mother, urged on no doubt by the desire to
conceal her shame, and persuaded by evil counsellors, drank a potion of
abortive drugs in order to produce miscarriage,[11] but Nature on this
occasion was not to be baulked. In recording the circumstances of his
birth he writes at some length in the jargon of astrology to show how the
celestial bodies were leagued together so as to mar him both in body and
mind. "Wherefore I ought, according to every rule, to have been born a
monster, and, under the circumstances, it was no marvel that it was found
necessary to tear me from the womb in order to bring me into the world.
Thus was I born, or rather dragged from my mother's body. I was to all
outward seeming dead, with my head covered with black curly hair. I was
brought round by being plunged in a bath of heated wine, a remedy which
might well have proved hurtful to any other infant. My mother lay three
whole days in labour, but at last gave birth to me, a living child."[12]

The sinister influences of the stars soon began to manifest their power.
Before Jerome had been many days in the world the woman into whose charge
he had been given was seized with the plague and died the same day,
whereupon his mother took him home with her. The first of his bodily
ailments,--the catalogue of the same which he subsequently gives is indeed
a portentous one,[13]--was an eruption of carbuncles on the face in the
form of a cross, one of the sores being set on the tip of the nose; and
when these disappeared, swellings came. Before the boy was two months old
his godfather, Isidore di Resta of Ticino, gave him into the care of
another nurse who lived at Moirago, a town about seven miles from Milan,
but here again ill fortune attended him. His body began to waste and his
stomach to swell because the nurse who gave him suck was herself
pregnant.[14] A third foster-mother was found for him, and he remained
with her till he was weaned in his third year.

When he was four years of age he was taken to Milan to be under the care
of his mother, who, with her sister, Margarita, was living in Fazio's
house; but whether she was at this time legally married to him or not
there is no evidence to show. In recording this change he remarks that he
now came under a gentler discipline from the hands of his mother and his
aunt, but immediately afterwards proclaims his belief that the last-named
must have been born without a gall bladder, a remark somewhat difficult to
apply, seeing he frequently complains afterwards of her harshness. It must
be remembered, however, that these details are taken from a record of the
writer's fifth year set down when he was past seventy.[15] He quotes
certain lapses from kindly usage, as for instance when it happened that he
was beaten by his father or his mother without a cause. After much
chastisement he always fell sick, and lay some time in mortal danger.
"When I was seven years old my father and my mother were then living
apart--my kinsfolk determined, for some reason or other, to give over
beating me, though perchance a touch of the whip might then have done me
no harm. But ill-fortune was ever hovering around me; she let my
tribulation take a different shape, but she did not remove it. My father,
having hired a house, took me and my mother and my aunt to live with him,
and made me always accompany him in his rounds about the city. On this
account I, being taken at this tender age with my weak body from a life of
absolute rest and put to hard and constant work, was seized at the
beginning of my eighth year with dysentery and fever, an ailment which was
at that time epidemic in our city. Moreover I had eaten by stealth a vast
quantity of sour grapes. But after I had been visited by the physicians,
Bernabo della Croce and Angelo Gyra, there seemed to be some hope of my
recovery, albeit both my parents, and my aunt as well, had already bewept
me as one dead.

"At this season my father, who was at heart a man of piety, was minded to
invoke the divine assistance of San Girolamo (commending me to the care of
the Saint in his prayers) rather than trust to the working of that
familiar spirit which, as he was wont to declare openly, was constantly in
attendance upon him. The reason of this change in his treatment of me I
never cared to inquire. It was during the time of my recovery from this
sickness, that the French celebrated their triumph after defeating the
Venetians on the banks of the Adda, which spectacle I was allowed to
witness from my window.[16] After this my father freed me of the task of
going with him on his rounds. But the anger of Juno was not yet exhausted;
for, before I had fully recovered my health, I fell down-stairs (we were
then living in the Via dei Maini), with a hammer in my hand, and by this
accident I hurt the left side of my forehead, injuring the bone and
causing a scar which remains to this day. Before I had recovered from this
mishap I was sitting on the threshold of the house when a stone, about as
long and as broad as a nut, fell down from the top of a high house next
door and wounded my head just where my hair grew very thickly on the left
side.

"At the beginning of my tenth year my father changed this house, which had
proved a very unlucky one for me, for another in the same street, and
there I abode for three whole years. But my ill luck still followed me,
for my father once more caused me to go about with him as his _famulus_,
and would never allow me on any pretext to escape this task. I should
hesitate to say that he did this through cruelty; for, taking into
consideration what ensued, you may perchance be brought to see that this
action of his came to pass rather through the will of Heaven than through
any failing of his own. I must add too that my mother and my aunt were
fully in agreement with him in his treatment of me. In after times,
however, he dealt with me in much milder fashion, for he took to live with
him two of his nephews, wherefore my own labour was lessened by the amount
of service he exacted from these. Either I did not go out at all, or if we
all went out together the task was less irksome.

"When I had completed my sixteenth year--up to which time I served my
father constantly--we once more changed our house, and dwelt with
Alessandro Cardano next door to the bakery of the Bossi. My father had two
other nephews, sons of a sister of his, one named Evangelista, a member of
the Franciscan Order, and nearly seventy years of age, and the other Otto
Cantone, a farmer of the taxes, and very rich. The last-named, before he
died, wished to leave me his sole heir; but this my father forbad, saying
that Otto's wealth had been ill gotten; wherefore the estate was
distributed according to the directions of the surviving brother."[17]

This, told as nearly as may be in his own words, is the story of Cardan's
birth and childhood and early discipline, a discipline ill calculated to
let him grow up to useful and worthy manhood. It must have been a wretched
spring of life. Many times he refers to the hard slavery he underwent in
the days when he was forced to carry his father's bag about the town, and
tells how he had to listen to words of insult cast at his mother's
name.[18] Like most boys who lead solitary lives, unrelieved by the
companionship of other children, he was driven in upon himself, and grew
up into a fanciful imaginative youth, a lover of books rather than of
games, with an old head upon his young shoulders. After such a training it
was only natural that he should be transformed from a nervous hysterical
child into an embittered, cross-grained man, profligate and superstitious
at the same time. Abundant light is thrown upon every stage of his career,
for few men have left a clearer picture of themselves in their written
words, and nowhere is Cardan, from the opening to the closing scene, so
plainly exhibited as in the _De Vita Propria_, almost the last work which
came from his pen. It has been asserted that this book, written in the
twilight of senility by an old man with his heart cankered by misfortune
and ill-usage, and his brain upset by the dread of real or fancied
assaults of foes who lay in wait for him at every turn, is no trustworthy
guide, even when bare facts are in question, and undoubtedly it would be
undesirable to trust this record without seeking confirmation elsewhere.
This confirmation is nearly always at hand, for there is hardly a
noteworthy event in his career which he does not refer to constantly in
the more autobiographic of his works. The _De Vita Propria_ is indeed ill
arranged and full of inconsistencies, but in spite of its imperfections,
it presents its subject as clearly and effectively as Benvenuto Cellini is
displayed in his own work. The rough sketch of a great master often
performs its task more thoroughly than the finished painting, and Cardan's
autobiography is a fragment of this sort. It lets pass in order of
procession the moody neglected boy in Fazio's ill-ordered house, the
student at Pavia, the youthful Rector of the Paduan Gymnasium, plunging
when just across the threshold of life into criminal excess of
Sardanapalean luxury, the country doctor at Sacco and afterwards at
Gallarate, starving amongst his penniless patients, the University
professor, the famous physician for whose services the most illustrious
monarchs in Europe came as suppliants in vain, the father broken by family
disgrace and calamity, and the old man, disgraced and suspected and
harassed by persecutors who shot their arrows in the dark, but at the same
time tremblingly anxious to set down the record of his days before the
night should descend.

Until he had completed his nineteenth year Jerome continued to dwell under
the roof which for the time being might give shelter to his parents. The
emoluments which Fazio drew from his profession were sufficient for the
family wants--he himself being a man of simple tastes; wherefore Jerome
was not forced, in addition to his other youthful troubles, to submit to
that _execrata paupertas_ and its concomitant miseries which vexed him in
later years. To judge from his conduct in the matter of Otto Cantone's
estate, Fazio seems to have been as great a despiser of wealth as his son
proved to be afterwards. His virtue, such as it was, must have been the
outcome of one of those hard cold natures, with wants few and trifling,
and none of those tastes which cry out daily for some new toy, only to be
procured by money. The fact that he made his son run after him through the
streets of Milan in place of a servant is not a conclusive proof of
avarice; it may just as likely mean that the old man was indifferent and
callous to whatever suffering he might inflict upon his young son, and
indisposed to trouble himself about searching for a hireling to carry his
bag. The one indication we gather of his worldly wisdom is his
dissatisfaction that his son was firmly set to follow medicine rather than
jurisprudence, a step which would involve the loss of the stipend of one
hundred crowns a year which he drew for his lectureship, an income which
he had hoped might be continued to a son of his after his death.[19]

Amidst the turmoil and discomfort of what must at the best have been a
most ill-regulated household, the boy's education was undertaken by his
father in such odds and ends of time as he might find to spare for the
task.[20] What with the hardness and irritability of the teacher, and the
peevishness inseparable from the pupil's physical feebleness and morbid
overwrought mental habit, these hours of lessons must have been irksome to
both, and of little benefit. "In the meantime my father taught me orally
the Latin tongue as well as the rudiments of Arithmetic, Geometry, and
Astrology. But he allowed me to sleep well into the day, and he himself
would always remain abed till nine o'clock. But one habit of his appeared
to me likely to lead to grave consequences, to wit the way he had of
lending to others anything which belonged to him. Part of these loans,
which were made to insolvents, he lost altogether; and the residue, lent
to divers persons in high places, could only be recovered with much
trouble and no little danger, and with loss of all interest on the same. I
know not whether he acted in this wise by the advice of that familiar
spirit[21] whose services he retained for eight-and-thirty years. What
afterwards came to pass showed that my father treated me, his son, rightly
in all things relating to education, seeing that I had a keen
intelligence. For with boys of this sort it is well to make use of the bit
as though you were dealing with mules. Beyond this he was witty and
diverting in his conversation, and given to the telling of stories and
strange occurrences well worth notice. He told me many things about
familiar spirits, but what part of these were true I know not; but
assuredly tales of this sort, wonderful in themselves and artfully put
together, delighted me marvellously.

"But what chiefly deserved condemnation in my father was that he brought
up certain other youths with the intention of leaving to them his goods in
case I should die; which thing, in sooth, meant nothing less than the
exposure of myself to open danger through plots of the parents of the boys
aforesaid, on account of the prize offered. Over this affair my father and
my mother quarrelled grievously, and finally decided to live apart.
Whereupon my mother, stricken by this mental vexation, and troubled at
intervals with what I deem to have been an hysterical affection, fell one
day full on the back of her neck, and struck her head upon the floor,
which was composed of tiles. It was two or three hours before she came
round, and indeed her recovery was little short of miraculous, especially
as at the end of her seizure she foamed much at the mouth.

"In the meantime I altered the whole drift of this tragedy by a pretended
adoption of the religious life, for I became for a time a member of the
mendicant Franciscan brotherhood. But at the beginning of my twenty-first
year[22] I went to the Gymnasium at Pavia, whereupon my father, feeling my
absence, was softened towards me, and a reconciliation between him and my
mother took place.

"Before this time I had learnt music, my mother and even my father having
secretly given me money for the same; my father likewise paid for my
instruction in dialectics. I became so proficient in this art that I
taught it to certain other youths before I went to the University. Thus he
sent me there endowed with the means of winning an honest living; but he
never once spake a word to me concerning this matter, bearing himself
always towards me in considerate, kindly, and pious wise.

"For the residue of his days (and he lived on well-nigh four more years)
his life was a sad one, as if he would fain let it be known to the world
how much he loved me.[23] Moreover, when by the working of fate I returned
home while he lay sick, he besought, he commanded, nay he even forced me,
all unwilling, to depart thence, what though he knew his last hour was
nigh, for the reason that the plague was in the city, and he was fain that
I should put myself beyond danger from the same. Even now my tears rise
when I think of his goodwill towards me. But, my father, I will do all the
justice I can to thy merit and to thy paternal care; and, as long as these
pages may be read, so long shall thy name and thy virtues be celebrated.
He was a man not to be corrupted by any offering whatsoever, and indeed a
saint. But I myself was left after his death involved in many lawsuits,
having nothing clearly secured except one small house."[24]

Fazio contracted a close intimacy with a certain Galeazzo Rosso, a man
clever as a smith, and endowed with mechanical tastes which no doubt
helped to secure him Fazio's friendship. Galeazzo discovered the principle
of the water-screw of Archimedes before the description of the same,
written in the books of the inventor, had been published. He also made
swords which could be bent as if they were of lead, and sharp enough to
cut iron like wood. He performed a more wonderful feat in fashioning iron
breast-plates which would resist the impact of red-hot missiles. In the
_De Sapientia_, Cardan records that when Galeazzo perfected his
water-screw, he lost his wits for joy.

Fazio took no trouble to teach his son Latin,[25] though the learned
language would have been just as necessary for the study of jurisprudence
as for any other liberal calling, and Jerome did not begin to study it
systematically till he was past nineteen years of age. Through some whim
or prejudice the old man refused for some time to allow the boy to go to
the University, and when at last he gave his consent he still fought hard
to compel Jerome to qualify himself in jurisprudence; but here he found
himself at issue with a will more stubborn than his own. Cardan writes:
"From my earliest youth I let every action of mine be regulated in view of
the after course of my life, and I deemed that as a career medicine would
serve my purpose far better than law, being more appropriate for the end I
had in view, of greater interest to the world at large, and likely to last
as long as time itself. At the same time I regarded it as a study which
embodied the nobler principles, and rested upon the ground of reason (that
is upon the eternal laws of Nature) rather than upon the sanction of human
opinion. On this account I took up medicine rather than jurisprudence, nay
I almost entirely cast aside, or even fled from the company of those
friends of mine who followed the law, rejecting at the same time wealth
and power and honour. My father, when he heard that I had abandoned the
study of law to follow philosophy, wept in my presence, and grieved amain
that I would not settle down to the study of his own subject. He deemed
it the more salutary discipline--proofs of which opinion he would often
bring forward out of Aristotle--that it was better adapted for the
acquisition of power and riches; and that it would help me more
efficiently in restoring the fortunes of our house. He perceived moreover
that the office of teaching in the schools of the city, together with its
accompanying salary of a hundred crowns which he had enjoyed for so many
years, would not be handed on to me, as he had hoped, and he saw that a
stranger would succeed to the same. Nor was that commentary of his
destined ever to see the light or to be illustrated by my notes. Earlier
in life he had nourished a hope that his name might become illustrious as
the emendator of the 'Commentaries of John, Archbishop of Canterbury on
Optics and Perspective.'[26] Indeed the following verses were printed
thereanent:

    'Hoc Cardana viro gaudet domus: omnia novit
    Unus: habent nullum saecula nostra parem.'

"These words may be taken as a sort of augury referring rather to certain
other men about to set forth to do their work in the world, than to my
father, who, except in the department of jurisprudence (of which indeed
rumour says that he was a master), never let his mind take in aught that
was new. The rudiments of mathematics were all that he possessed, and he
gathered no fresh knowledge from the store-houses of Greek learning. This
disposition in him was probably produced by the vast multitude of subjects
to be mastered, and by his infirmity of purpose, rather than by any lack
of natural parts, or by idleness or by defect of judgment; vices to which
he was in no way addicted. But I, being firmly set upon the object of my
wishes, for the reasons given above, and because I perceived that my
father had achieved only moderate success--though he had encountered but
few hindrances--remained unconvinced by any of his exhortations."[27]

FOOTNOTES:

[1] Bayle is unwilling to admit Cardan's illegitimate birth. In _De
Consolatione_, Opera, tom. i. p. 619 (Lyons, 1663), Cardan writes in
reference to the action of the Milanese College of Physicians: "Medicorum
collegium, suspitione obortâ, quòd (tam malè à patre tractatus) spurius
essem, repellebat." Bayle apparently had not read the _De Consolatione_,
as he quotes the sentence as the work of a modern writer, and affirms that
the word "suspitio" would not have been used had the fact been notorious.
But in the _Dialogus de Morte_, Opera, tom. i. p. 676, Cardan declares
that his father openly spoke of him as a bastard.

[2] _De Utilitate ex adversis Capienda_ (Franeker, 1648), p. 357.

[3] Matteo Visconti was born in 1250, and died in 1322. He was lord of
Novara Vercello Como and Monferrato, and was made Vicar Imperial by
Adolphus of Nassau. Though he was worsted in his conflict with John XXII.
he did much to lay the foundations of his family.

[4] _De Vita Propria_ (Amsterdam, 1654), ch. i. p. 4.

[5] Cardan makes a statement in _De Consolatione_, Opera, tom. i. p. 605,
which indicates that her disposition was not a happy one. "Matrem meam
Claram Micheriam, juvenem vidi, cum admodum puer essem, meminique hanc
dicere solitam, Utinam si Deo placuisset, extincta forem in infantia."

[6] _De Vita Propria_, ch. i. p. 4.

[7] _Geniturarum Exempla_ (Basil, 1554), p. 436.

[8] _De Rerum Varietate_ (Basil, 1557), p. 655.

[9] _De Utilitate_, p. 347. There is a passage in _Geniturarum Exempla_,
p. 435, dealing with Fazio's horoscope, which may be taken to mean that
these children were his. "Alios habuisse filios qui obierint ipsa genitura
dem[o=]strat, me solo diu post eti[a=] illius mort[e=] superstite."

[10] With regard to the union of his parents he writes: "Uxorem vix duxit
ob Lunam afflictam et eam in senectute."--_Geniturarum Exempla_, p. 435.

[11] "Igitur ut ab initio exordiar, in pestilentia conceptus, matrem,
nondum natus (ut puto) mearum calamitatum participem, profugam
habui."--_Opera_, tom. i. p. 618.

"Mater ut abortiret medicamentum abortivum dum in utero essem, alieno
mandato bibit."--_De Utilitate_, p. 347.

[12] _De Vita Propria_, ch. ii. p. 6.

[13] In one passage, _De Utilitate_, p. 348, he sums up his physical
misfortunes: "Hydrope, febribus, aliisque morbis conflictatus sum, donec
sub fine octavi anni ex dysenteria ac febre usque ad mortis limina
perveni, pulsavi ostium sed non aperuere qui intro erant."

[14] "Inde lac praegnantis hausi per varias nutrices lactatus ac
jactatus."--_De Utilitate_, p. 348.

[15] The _De Vita Propria_, the chief authority for these remarks, was
written by Cardan in Rome shortly before his death.

[16] The illness would have occurred about October 1508, and the victory
of the Adda was on May 14, 1509. This fact fixes his birth in 1501, and
shows that his illness must have lasted six or seven months.

[17] _De Vita Propria_, ch. iv. p. ii.

[18] _Opera_, tom. i. p. 676.

[19] "Quod munus profitendi institutiones in urbe ipsa cum honorario
centum coronatorum, quo jam tot annis gaudebat, non in me (ut speraverat)
transiturum intelligebat."--_De Vita Propria_, ch. x. p. 35.

[20] "Pater jam antè concesserat ut Geometriæ et Dialecticæ operam darem,
in quo (quanquam præter paucas admonitiones, librosque, ac licentiam,
nullum aliud auxilium præbuerit) eas tamen ego (succicivis temporibus
studens) interim feliciter sum assecutus."--_De Consolatione_, Opera, tom.
i. p. 619.

[21] "Facius Cardanus dæmonem ætherium, ut ipse dicebat, diu familiarem
habuit; qui quamdiu conjuratione usus est, vera illi dabat responsa, cùm
autem illam exussisset, veniebat quidem, sed responsa falsa dabat. Tenuit
igitur annis, ni fallor, vinginti octo cum conjuratione, solutum autem
circiter quinque."--_De Varietate_, p. 629.

In the _Dialogus Tetim_ (_Opera_, tom. i. p. 672), Cardan writes: "Pater
honeste obiit et ex senio, sed multo antea eum Genius ille reliquerat."

[22] There is a discrepancy between this date and the one given in _De
Vita Propria_, ch. iv. p. 11. "Anno exacto XIX contuli me in Ticinensem
Academiam."

[23] "Inde (desiderium augente absentiâ) mortuus est, sæviente peste, cùm
primum me diligere coepisset."--_De Consolatione_, Opera, tom. i. p. 619.

[24] _De Utilitate_, p. 348.

[25] "Nimis satis fuit defuisse tot, memoriam, linguam Latinam per
adolescentiam."--_De Vita Propria_, ch. li. p. 218.

[26] John Peckham was a Franciscan friar, and was nominated to the see of
Canterbury by Nicholas III. in 1279. He had spent much time in the convent
of his Order at Oxford, and there is a legend connecting him with a
Johannes Juvenis or John of London, a youth who had attracted the
attention and benevolence of Roger Bacon. This Johannes became one of the
first mathematicians and opticians of the age, and was sent to Rome by
Bacon, who entrusted to him the works which he was sending to Pope Clement
IV. There is no reason for this view beyond the fact that both were called
John, and distinguished in the same branches of learning. The _Perspectiva
Communis_ was his principal work; it does not deal with perspective as now
understood, but with elementary propositions of optics. It was first
printed in Milan in or about 1482.

[27] _De Vita Propria_, ch. x. p. 34. A remark in _De Sapientia_, Opera,
tom. i. p. 578, suggests that Fazio began life as a physician: "Pater meus
Facius Cardanus Medicus primò, inde Jurisconsultus factus est."




CHAPTER II


THE University of Pavia to which Jerome now betook himself was by
tradition one of the learned foundations of Charlemagne.[28] It had
certainly enjoyed a high reputation all through the Middle Ages, and had
recently had the honour of numbering Laurentius Valla amongst its
professors. In 1362, Galeazzo Visconti had obtained a charter for it from
the Emperor Charles IV., and that it had become a place of consequence in
1400 is proved by the fact that, besides maintaining several professors in
the Canon Law, it supported thirteen in Civil Law, five in Medicine, three
in Philosophy, and one each in Astrology, Greek, and Eloquence. Like all
the other Universities of Northern Italy, it suffered occasional eclipse
or even extinction on account of the constant war and desolation which
vexed these parts almost without intermission during the years following
the formation of the League of Cambrai. Indeed, as recently as 1500, the
famous library collected by Petrarch, and presented by Gian Galeazzo
Visconti to the University, was carried off by the French.[29]

To judge from the pictures which the Pavian student, writing in after
years, gives of his physical self, it may be inferred that he was
ill-endowed by the Graces. "I am of middle height. My chest is somewhat
narrow and my arms exceedingly thin: my right hand is the more grossly
fashioned of the two, so that a chiromantist might have set me down as
rude or doltish: indeed, should such an one examine my hand, he would be
ashamed to say what he thought. In it the line of life is short, and that
named after Saturn long and well marked. My left hand, however, is seemly,
with fingers long, tapering, and well-set, and shining nails. My neck is
longer and thinner than the rule, my chin is divided, my lower lip thick
and pendulous, my eyes are very small, and it is my wont to keep them
half-closed, peradventure lest I should discern things over clearly. My
forehead is wide and bare of hair where it meets the temples. My hair and
beard are both of them yellow in tint, and both as a rule kept close cut.
My chin, which as I have said already is marked by a division, is covered
in its lower part with a thick growth of long hair. My habit is to speak
in a highly-pitched voice, so that my friends sometimes rebuke me
thereanent; but, harsh and loud as is my voice, it cannot be heard at any
great distance while I am lecturing. I am wont to talk too much, and in
none too urbane a tone. The look of my eyes is fixed, like that of one in
deep thought. My front teeth are large, and my complexion red and white:
the form of my countenance being somewhat elongated, and my head is
finished off in narrow wise at the back, like to a small sphere. Indeed,
it was no rare thing for the painters, who came from distant countries to
paint my portrait, to affirm that they could find no special
characteristic which they could use for the rendering of my likeness, so
that I might be known by the same."[30]

After giving this account of his person, Cardan writes down a catalogue of
the various diseases which vexed him from time to time, a chapter of
autobiography which looks like a transcript from a dictionary of Nosology.
More interesting is the sketch which he makes of his mental state during
these early years. Boys brought up in company of their elders often show a
tendency to introspection, and fall into a dreamy whimsical mood, and his
case is a striking example. "By the command of my father I used to lie
abed until nine o'clock,[31] and, if perchance I lay awake any time before
the wonted hour of rising, it was my habit to spend the same by conjuring
up to sight all sorts of pleasant visions, nor can I remember that I ever
summoned these in vain. I used to behold figures of divers kinds like airy
bodies. Meseemed they were made up of tiny rings, like those in coats of
chain-armour, though at this time I had seen nought of the kind. They
would rise at the bottom of the bed, from the right-hand corner; and,
moving in a semi-circle, would pass slowly on and disappear in the left.
Moreover I beheld the shapes of castles and houses, of horses and riders,
of plants, trees, musical instruments, theatres, dresses of men of all
sorts, and flute-players who seemed to be playing upon their instruments,
but neither voice nor sound was heard therefrom. And besides these things
I beheld soldiers, and crowds of men, and fields, and certain bodily
forms, which seem hateful to me even now: groves and forests, and divers
other things which I now forget. In all this I took no small delight, and
with straining eyes I would gaze upon these marvels; wherefore my Aunt
Margaret asked me more than once whether I saw anything. I, though I was
then only a child, deliberated over this question of hers before I
replied, saying to myself: 'If I tell her the facts she will be wroth at
the thing--whatever it may be--which is the cause of these phantasms, and
will deprive me of this delight.' And then I seemed to see flowers of all
kinds, and four-footed beasts, and birds; but all these, though they were
fashioned most beautifully, were lacking in colour, for they were things
of air. Therefore I, who neither as a boy nor as an old man ever learned
to lie, stood silent for some time. Then my aunt said--'Boy, what makes
you stare thus and stand silent?' I know not what answer I made, but I
think I said nothing at all. In my dreams I frequently saw what seemed to
be a cock, which I feared might speak to me in a human voice. This in
sooth came to pass later on, and the words it spake were threatening ones,
but I cannot now recall what I may have heard on these occasions."[32]

With a brain capable of such remarkable exercises as the above-written
vision, living his life in an atmosphere of books, and with all games and
relaxations dear to boys of his age denied to him, it was no marvel that
Jerome should make an early literary essay on his own account. The death
of a young kinsman, Niccolo Cardano,[33] suggested to him a theme which he
elaborated in a tract called _De immortalitate paranda_, a work which
perished unlamented by its author, and a little later he wrote a treatise
on the calculation of the distances between the various heavenly
bodies.[34] But he put his mathematical skill to other and more sinister
uses than this; for, having gained practical experience at the
gaming-tables, he combined this experience with his knowledge of the
properties of numbers, and wrote a tract on games of chance. Afterwards he
amplified this into his book, _Liber de Ludo Aleæ_.

With this equipment and discipline Jerome went to Pavia in 1520. He found
lodging in the house of Giovanni Ambrogio Targio, and until the end of his
twenty-first year he spent all his time between Pavia and Milan. By this
date he had made sufficiently good use of his time to let the world see of
what metal he was formed, for in the year following he had advanced far
enough in learning to dispute in public, to teach Euclid in the Gymnasium,
and to take occasional classes in Dialectics and Elementary Philosophy. At
the end of his twenty-second year the country was convulsed by the wars
between the Spaniards and the French under Lautrec, which ended in the
expulsion of the last-named and the establishment of the Imperial power in
Milan. Another result of the war, more germane to this history, was the
closing of the University of Pavia through lack of funds. In consequence
of this calamity Jerome remained some time in Milan, and during these
months he worked hard at mathematics; but he was not destined to return to
Pavia as a student. The schools there remained some long time in
confusion, so in 1524 he went with his father's consent to Padua. In the
autumn of that same year he was summoned back to Milan to find Fazio in
the grip of his dying illness. "Whereupon he, careful of my weal rather
than his own, bade me return to Padua at once, being well pleased to hear
that I had taken at the Venetian College the Baccalaureat of Arts.[35]
After my return to Padua, letters were brought to me which told me that he
had died on the ninth day after he had refused nourishment. He died on the
twenty-eighth of August, having last eaten on Sunday the twentieth of the
month. Towards the close of my twenty-fourth year I was chosen Rector of
the Academy at Padua,[36] and at the end of the next was made Doctor of
Medicine. For the first-named office I came out the victor by one vote,
the suffrages having to be cast a second time; and for the Doctorate of
Medicine my name had already twice come forth from the ballot with
forty-seven votes cast against me (a circumstance which forbade another
voting after the third), when, at the third trial, I came out the winner,
with only nine votes against me (previously only this same number had been
cast for me), and with forty-eight in my favour.

"Though I know well enough that affairs like these must needs be of small
account, I have set them down in the order in which they came to pass for
no other reason than that I give pleasure to myself who write these words
by so doing: and I do not write for the gratification of others. At the
same time those people who read what I write--if indeed any one should
ever be so minded--may learn hereby that the beginnings and the outcomes
of great events may well be found difficult to trace, because in sooth it
is the way of such things to come to the notice of anybody rather than of
those who would rightly observe them."[37]

Padua cannot claim for its University an antiquity as high as that which
may be conceded to Pavia, but in spite of its more recent origin, there is
no little obscurity surrounding its rise. The one fact which may be put
down as certain is that it sprang originally from the University of
Bologna. Early in the thirteenth century violent discords arose between
the citizens of Bologna and the students, and there is a tradition that
the general school of teaching was transferred to Padua in 1222. What
happened was probably a large migration of students, part of whom remained
behind when peace between town and gown in Bologna was restored. The
orthodox origin of the University is a charter granted by Frederic II. in
1238. Frederic at this time was certainly trying to injure Bologna,
actuated by a desire to help on his own University at Naples, and to crush
Bologna as a member of the Lombard League.[38] Padua, however, was also a
member of this league, so his benevolent action towards it is difficult to
understand. In 1228 the students had quarrelled with the Paduan citizens,
and there was a movement to migrate to Vercelli; but, whether this really
took place or not, the Paduan school did not suffer: its ruin and
extinction was deferred till the despotism of the Ezzelini. In 1260 it
was again revived by a second migration from Bologna, and this movement
was increased on account of the interdict laid by the Pope upon Bologna in
1306 after the expulsion of the Papal Legate by the citizens.

In the early days Medicine and Arts were entirely subordinate to the
schools of canon and civil law; but by the end of the fourteenth century
these first-named Faculties had obtained a certain degree of independence,
and were allowed an equal share in appointing the Rector.[39] The first
College was founded in 1363, and after 1500 the number rapidly increased.
The dominion of the Dukes of Carrara after 1322 was favourable to the
growth of the University, which, however, did not attain its highest point
till it came under Venetian rule in 1404. The Venetian government raised
the stipends of the professors, and allowed four Paduan citizens to act as
_Tutores Studii_; the election of the professors being vested in the
students, which custom obtained until the end of the sixteenth
century.[40] The Rector was allowed to wear a robe of purple and gold;
and, when he retired, the degree of Doctor was granted to him, together
with the right to wear the golden collar of the order of Saint Mark.

Padua like Athens humanized its conquerors. It became the University town
of Venice, as Pavia was of Milan, and it was for a long time protected
from the assaults of the Catholic reaction by its rulers, who possibly
were instigated rather by political jealousy of the Papacy as a temporal
power, than by any enthusiasm for the humanist and scientific studies of
which Padua was the most illustrious home south of the Alps; studies which
the powers of the Church began already to recognize as their most
dangerous foes.

Such was the University of Padua at the height of its glory, and it will
be apparent at once that Padua must have fallen considerably in its
fortunes when it installed as its Rector an obscure student, only
twenty-four years of age, and of illegitimate birth, and conferred upon
him the right to go clad in purple and gold, and to claim, as his
retiring gift, the degree of Doctor and the cross of Saint Mark. In 1508
the League of Cambrai had been formed, and Venice, not yet recovered
from the effects of its disastrous wars with Bajazet II., was forced to
meet the combined assault of the Pope, the Emperor, and the King of
France. Padua was besieged by the Imperial forces, a motley horde of
Germans, Swiss, and Spaniards, and the surrounding country was pillaged
and devastated by these savages with a cruelty which recalled the days
of Attila. It is not wonderful that the University closed its doors in
such a time. When the confederates began to fight amongst themselves the
class-rooms were reopened, intermittently at first, but after 1515 the
teaching seems to have been continuous. Still the prevalent turmoil and
poverty rendered it necessary to curtail all the mere honorary and
ornamental adjuncts of the schools, and for several years no Rector was
appointed, for the good and sufficient reason that no man of due
position and wealth and character could be found to undertake the
rectorial duties, with the Academy just emerging from complete
disorganization. These duties were many and important, albeit the Rector
could, if he willed, appoint a deputy, and the calls upon the purse of
the holder must have been very heavy. It would be hard to imagine any
one less fitted to fill such a post than Cardan, and assuredly no office
could befit him less than this pseudo-rectorship.[41] It must ever
remain a mystery why he was preferred, why he was elected, and why he
consented to serve: though, as to the last-named matter, he hints in a
passage lately cited from _De Utilitate_, that it was through the
persuasions of his mother that he took upon himself this disastrous
honour. Many pasages in his writings suggest that Chiara was an
indulgent parent. She let Fazio have no peace till he consented to allow
the boy to go to college; she paid secretly for music-lessons, so that
Jerome was enabled to enjoy the relaxation he loved better than anything
else in the world--except gambling; she paid all his charges during his
student life at Padua; and now, quite naturally, she would have shed her
heart's blood rather than let this son of hers--ugly duckling as he
was--miss what she deemed to be the crowning honour of the rectorship;
but after all the sacrifices Chiara made, after all the misfortunes
which attended Jerome's ill-directed ambition, there is a doubt as to
whether he ever was Rector in the full sense of the term. Many times and
in divers works he affirms that once upon a time he was Rector, and over
and beyond this he sets down in black and white the fact, more than
once, that he never told a lie; so it is only polite to accept this
legend for what it is worth. But it must likewise be noted that in the
extant records of the University there is no mention of his name in the
lists of Rectors.[42]

Jerome has left very few details as to his life at Padua. Of those which
he notices the following are the most interesting: "In 1525, the year in
which I became Rector, I narrowly escaped drowning in the Lago di Garda. I
went on board the boat, unwillingly enough, which carried likewise some
hired horses; and, as we sailed on, the mast and the rudder, and one of
the two oars we had with us, were broken by the wind. The sails, even
those on the smaller mast, were split, and the night came on. We landed at
last safe and sound at Sirmio, but not before all my companions had given
up hope, and I myself was beginning to despair. Indeed, had we been a
minute later we must have perished, for the tempest was so violent that
the iron hinges of the inn windows were bent thereby. I, though I had been
sore afraid ever since the wind began to blow, fell to supper with a good
heart when the host set upon the board a mighty pike, but none of the
others had any stomach for food, except the one passenger who had advised
us to make trial of this perilous adventure, and who had proved to be an
able and courageous helper in our hour of distress.

"Again, once when I was in Venice on the birthday of the Virgin, I lost
some money at dicing, and on the day following all that was left me went
the same way. This happened in the house of the man with whom I was
gambling, and in the course of play I noticed that the cards were marked,
whereupon I struck him in the face with my dagger, wounding him slightly.
Two of his servants were present at the time; some spears hung all ready
from the beams of the roof, and besides this the house door was fastened.
But when I had taken from him all the money he had about him--his own as
well as that which he had won from me by cheating, and my cloak and the
rings which I had lost to him the day before--I was satisfied that I had
got back all my possessions. The chattels I sent home by my servant at
once, but a portion of the money I tossed back to the fellow when I saw
that I had drawn blood of him. Then I attacked the servants who were
standing by; and, as they knew not how to use their weapons and besought
my mercy, I granted this on the condition that they should unlock the
door. Their master, taking account of the uproar and confusion, and
mistrusting his safety in case the affair should not be settled forthwith
(I suspect he was alarmed about the marked cards), commanded the servants
to open the door, whereupon I went my way.

"That very same evening, while I was doing my best to escape the notice of
the officers of justice on account of the wound I had given to this
Senator, I lost my footing and fell into a canal, having arms under my
cloak the while. In my fall I did not lose my nerve, but flinging out my
right arm, I grasped the thwart of a passing boat and was rescued by those
on board. When I had been hauled into the boat I discovered--wonderful to
relate--that the man with whom I had lately played cards was likewise on
board, with his face bandaged by reason of the wounds I had given him.
Now of his own accord he brought out a suit of clothes, fitted for
seafaring, and, having clad myself in them, I journeyed with him as far as
Padua."[43]

Cardan's life from rise to set cannot be estimated otherwise than an
unhappy one, and its least fortunate years were probably those lying
between his twenty-first and his thirty-first year of age. During this
period he was guilty of that crowning folly, the acceptance of the
Rectorship of the Gymnasium at Padua, he felt the sharpest stings of
poverty, and his life was overshadowed by dire physical misfortune. He
gives a rapid sketch of the year following his father's death. "Then, my
father having breathed his last and my term of office come to an end, I
went, at the beginning of my twenty-sixth year, to reside at Sacco, a town
distant ten miles from Padua and twenty-five from Venice. I fixed on this
place by the advice of Francesco Buonafidei, a physician of Padua, who,
albeit I brought no profit to him--not even being one of those who
attended his public teaching--helped me and took a liking for me, being
moved to this benevolence by his exceeding goodness of heart. In this
place I lived while our State was being vexed by every sort of calamity.
In 1524 by a raging pestilence and by a two-fold change of ruler. In 1526
and 1527 by a destructive scarcity of the fruits of the earth. It was hard
to get corn in exchange for money of any kind, and over and beyond this
was the intolerable weight of taxation. In 1528 the land was visited by
divers diseases and by the plague as well, but these afflictions seemed
the easier to bear because all other parts were likewise suffering from
the same. In 1529 I ventured to return to Milan--these ill-starred
troubles being in some degree abated--but I was refused membership by the
College of Physicians there, I was unable to settle my lawsuit with the
Barbiani, and I found my mother in a very ill humour, so I went back to my
village home, having suffered greatly in health during my absence. For
what with cruel vexations, and struggles, and cares which I saw impending,
and a troublesome cough and pleurisy aggravated by a copious discharge of
humour, I was brought into a condition such as few men exchange for aught
else besides a coffin."[44]

The closing words of his eulogy on his father tell how the son, on the
father's death, found that one small house was all he could call his own.
The explanation of this seems to be that the old man, being of a careless
disposition and litigious to boot, had left his affairs in piteous
disorder. In consequence of this neglect Jerome was involved in lawsuits
for many years, and the one afore-mentioned with the Barbiani was one of
them. This case was subsequently settled in Jerome's favour.

FOOTNOTES:

[28] Pavia, like certain modern universities, did not spend all its time
over study. "Aggressus sum Mediolani vacationibus quadragenariæ, seu
Bacchanalium potius, anni MDLXI. Ita enim non obscurum est, nostra ætate
celebrari ante quadragenariam vacationes, in quibus ludunt, convivantur,
personati ac larvati incedunt, denique nullum luxus ac lascivæ genus
omittunt: Sybaritæ et Lydi Persæque vincuntur." _Opera_, tom. i. p. 118.

[29] These books were taken to Blois. They were subsequently removed by
Francis I. to Fontainebleau, and with the other collections formed the
nucleus of the Bibliothèque Nationale.

[30] _De Vita Propria_, ch. v. p. 18.

[31] The time covered by this experience was from his fourth to his
seventh year.

[32] _De Vita Propria_, ch. xxxvii. p. 114; _De Rerum Subtilitate_ (Basil,
1554), p. 524.

[33] _Opera_, tom. i. p. 61.

[34] "Erat liber exiguus, rem tamen probe absolvebat: nam tunc forte in
manus meas inciderat, Gebri Hispani liber, cujus auxilio non parum adjutus
sum."--_Opera_, tom. i. p. 56.

[35] "Initio multi quidem paupertate aliave causa quum se nolunt subjicere
rigoroso examini Cl. Collegii in artibus Medicinae vel in Jure,
Baccalaureatus, vel Doctoratus gradum a Comitibus Palatinis aut
Lateranensibus sumebant. Postea vero, sublata hac consuetudine, Gymnasii
Rector, sive substitutus, convocatis duobus professoribus, bina puncta
dabantur, iisque recitatis et diligentis [_sic_] excussis, illis gradus
Baccalaureatus conferebatur."--_Gymnasium Patavinum_ (1654), p. 200.

[36] He constantly bewails this step as the chief folly of his life:
"Stulte vero id egi, quod Rector Gymnasii Patavini effectus sum, tum, cum,
inops essem, et in patria maxime bella vigerent, et tributa intolerabilia.
Matris tamen solicitudine effectum est, ut pondus impensarum, quamvis
aegre, sustinuerim."--_De Utilitate_, p. 350.

[37] _De Vita Propria_, ch. iv. p. 11.

[38] Muratori, _Chron. di Bologna_, xviii. 254.

[39] The stipends paid to teachers of jurisprudence were much more liberal
than those paid to humanists. In the Diary of Sanudo it is recorded that a
jurist professor at Padua received a thousand ducats per annum. Lauro
Quirino, a professor of rhetoric, meantime received only forty ducats, and
Laurentius Valla at Pavia received fifty sequins.--Muratori, xxii. 990.

[40] Tomasinus, _Gymnasium Patavinam_ (1654), p. 136.

[41] Tomasinus writes that the Rector should be "Virum illustrem,
providum, eloquentem ac divitem, quique eo pollet rerum usu ut Gymnasi
decora ipsius gubernatione et splendore augeantur."--_Gymnasium
Patavinum_, p. 54. He likewise gives a portrait of the Rector in his robes
of office, and devotes several chapters to an account of his duties.

[42] "Ab anno 1509 usque ad annum 1515 ob bellum Cameracense Gymn.
interrmissum fuit."--_Elenchus nominum Patavii_ (1706), p. 28. The first
names given after this interregnum are Dom. Jo. Maria de Zaffaris, Rector
in Arts, and Dom. Marinus de Ongaris, Rector in Jurisprudence in 1527.

Papadapoli (_Historia Gymn. Patav._) gives the name of Ascanius Serra as
pro-Rector in 1526: no Rector being mentioned at all.

[43] _De Vita Propria_, ch. xxx. p. 79.

[44] _De Vita Propria_, ch. iv. p. 13.




CHAPTER III


DURING his life at Padua it would appear that Cardan, over and above the
allowance made to him by his mother, had no other source of income than
the gaming-table.[45] However futile and disastrous his sojourn at this
University may have been, he at least took away with him one possession of
value, to wit his doctorate of medicine, on the strength of which he began
to practise as a country physician at Sacco. The record of his life during
these years gives the impression that he must have been one of the most
wretched of living mortals. The country was vexed by every sort of
misfortune, by prolonged warfare, by raging pestilence, by famine, and by
intolerable taxation;[46] but while he paints this picture of misery and
desolation in one place, he goes on to declare in another that the time
which he spent at Sacco was the happiest he ever knew.[47] No greater
instance of inconsistency is to be found in his pages. He writes: "I
gambled, I occupied myself with music, I walked abroad, I feasted, giving
scant attention the while to my studies. I feared no hurt, I paid my
respects to the Venetian gentlemen living in the town, and frequented
their houses. I, too, was in the very flower of my age, and no time could
have been more delightful than this which lasted for five years and a
half."[48]

But for almost the whole of this period Cardan was labouring under a
physical misfortune concerning which he writes in another place in terms
of almost savage bitterness. During ten years of his life, from his
twenty-first to his thirty-first year, he suffered from the loss of virile
power, a calamity which he laments in the following words: "And I maintain
that this misfortune was to me the worst of evils. Compared with it
neither the harsh servitude under my father, nor unkindness, nor the
troubles of litigation, nor the wrongs done me by my fellow-townsmen, nor
the scorn of my fellow-physicians, nor the ill things falsely spoken
against me, nor all the measureless mass of possible evil, could have
brought me to such despair, and hatred of life, and distaste of all
pleasure, and lasting sorrow. I bitterly wept this misery, that I must
needs be a laughing-stock, that marriage must be denied me, and that I
must ever live in solitude. You ask for the cause of this misfortune, a
matter which I am quite unable to explain. Because of the reasons just
mentioned, and because I dreaded that men should know how grave was the
ill afflicting me, I shunned the society of women; and, on account of this
habit, the same miserable public scandal which I desired so earnestly to
avoid, arose concerning me, and brought upon me the suspicion of still
more nefarious practices: in sooth it seemed that there was no further
calamity left for me to endure."[49] After reading these words, it is hard
to believe that a man, afflicted with a misfortune which he characterizes
in these terms, could have been even moderately happy; much less in that
state of bliss which he sits down to describe forty years afterwards.

But the end of his life at Sacco was fated to be happier than the
beginning, and it is possible that memories of the last months he spent
there may have helped to colour with rosy tint the picture of happiness
recently referred to. In the first place he was suddenly freed from his
physical infirmity, and shortly after his restoration he met and married
the woman who, as long as she lived with him, did all that was possible to
make him happy. Every momentous event of Cardan's life--and many a
trifling one as well--was heralded by some manifestation of the powers
lying beyond man's cognition. In writing about the signs and tokens which
served as premonitions of his courtship and marriage, he glides easily
into a description of the events themselves in terms which are worth
producing. "In times past I had my home in Sacco, and there I led a joyful
life, as if I were a man unvexed by misfortune (I recall this circumstance
somewhat out of season, but the dream I am about to tell of seems only too
appropriate to the occasion), or a mortal made free of the habitations of
the blest, or rather of some region of delight. Then, on a certain night,
I seemed to find myself in a pleasant garden, beautiful exceedingly,
decked with flowers and filled with fruits of divers sorts, and a soft air
breathed around. So lovely was it all that no painter nor our poet Pulci,
nor any imagination of man could have figured the like. I was standing in
the forecourt of this garden, the door whereof was open, and there was
another door on the opposite side, when lo! I beheld before me a damsel
clad in white. I embraced and kissed her; but before I could kiss her
again, the gardener closed the door. I straightway begged him earnestly
that he would open it again, but I begged in vain; wherefore, plunged in
grief and clinging to the damsel, I seemed to be shut out of the garden.

"A little time after this there was a rumour in the town of a house on
fire, and I was roused from sleep to hurry to the spot. Then I learned
that the house belonged to one Altobello Bandarini,[50] a captain of the
Venetian levies in the district of Padua. I had no acquaintance with him,
in sooth I scarcely knew him by sight. Now it chanced that after the fire
he hired a house next door to my own, a step which displeased me somewhat,
for such a neighbour was not to my taste; but what was I to do? After the
lapse of a few days, when I was in the street, I perceived a young girl
who, as to her face and her raiment, was the exact image of her whom I had
beheld in my dream. But I said to myself, 'What is this girl to me? If I,
poor wretch that I am, take to wife a girl dowered with naught, except a
crowd of brothers and sisters, it will be all over with me; forasmuch as I
can hardly keep myself as it is. If I should attempt to carry her off, or
to have my will of her by stealth, there will of a surety be some
tale-bearers about; and her father, being a fellow-townsman and a soldier
to boot, would not sit down lightly under such an injury. In this case, or
in that, it is hard to say what course I should follow, for if this
affair should come to the issue I most desire, I must needs fly the
place.' From that same hour these thoughts and others akin to them
possessed my brain, which was only too ready to harbour them, and I felt
it would be better to die than to live on in such perplexity. Thenceforth
I was as one love-possessed, or even burnt up with passion, and I
understood what meaning I might gather from the reading of my dream.
Moreover I was by this time freed from the chain which had held me back
from marriage. Thus I, a willing bridegroom, took a willing bride, her
kinsfolk questioning us how this thing had been brought about, and
offering us any help which might be of service; which help indeed proved
of very substantial benefit.

"But the interpretation of my dreams did not work itself out entirely in
the after life of my wife; it made itself felt likewise in the lives of my
children. My wife lived with me fifteen years, and alas! this ill-advised
marriage was the cause of all the misfortunes which subsequently happened
to me. These must have come about either by the working of the divine
will, or as the recompense due for some ill deeds wrought by myself or by
my forefathers."[51]

The dream aforesaid was not the only portent having reference to his
marriage. After describing shakings and tremblings of his bed, for which
indeed a natural cause was not far to seek, he tells how in 1531 a certain
dog, of gentle temper as a rule, and quiet, kept up a persistent howling
for a long time; how some ravens perched on the house-top and began
croaking in an unusual manner; and how, when his servant was breaking up a
faggot, some sparks of fire flew out of the same; whereupon, "by an
unlooked-for step I married a wife, and from that time divers misfortunes
have attended me."[52] Lucia, the wife of his choice, was the eldest
daughter of Altobello Bandarini, who had, besides her, three daughters and
four sons. Jerome, as it has been already noted, was possessed with a fear
lest he should be burdened by his brothers- and sisters-in-law after his
marriage; but, considering that he was a young unknown physician, without
either money or patients, and that Bandarini was a man of position and
repute, with some wealth and more shrewdness, the chances were that the
burden would lie on the other side. Cardan seems to have inherited Fazio's
contempt for wealth, or at least to have made a profession thereof; for,
in chronicling the event of his marriage, he sets down, with a certain
degree of pomposity, that he took a wife without a dower on account of a
certain vow he had sworn.[53] If the bride was penniless the father-in-law
was wealthy, and the last-named fact might well have proved a powerful
argument to induce Cardan to remain at Sacco, albeit he had little scope
for his calling. That he soon determined to quit the place, is an evidence
of his independence of spirit, and of his disinclination to sponge upon
his well-to-do connections. Bandarini, when this scheme was proposed to
him, vetoed it at once. He was unwilling to part with his daughter, and
possibly he may have taken a fancy to his son-in-law, for Cardan has left
it on record that Bandarini was greatly pleased with the match; he ended,
however, by consenting to the migration, which was not made without the
intervention of a warning portent. A short time before the young couple
departed, it happened that a tile got mixed with the embers in Bandarini's
bed-chamber; and, in the course of the night, exploded with a loud
report, and the fragments thereof were scattered around. This event
Bandarini regarded as an augury of evil, and indeed evil followed swiftly
after. Before a year had passed he was dead, some holding that his death
had been hastened by the ill conduct of his eldest son, and others
whispering suspicions of poison.

Jerome and his young wife betook themselves to Milan, but this visit seems
to have been fully as unprofitable as the one he had paid in 1529. In that
year he had to face his first rejection by the College of Physicians, when
he made application for admission; and there is indirect evidence that he
now made a second application with no better result.[54] In any case his
affairs were in a very bad way. If he had money in his pocket he would not
keep long away from the gaming-table; and, with the weight of trouble ever
bearing him down more and more heavily, it is almost certain that his
spirits must have suffered, and that poor Lucia must have passed many an
unhappy hour on account of his nervous irritability. Then the gates of his
profession remained closed to him by the action of the College. The
pretext the authorities gave for their refusal to admit him was his
illegitimate birth; but it is not unlikely that they may have mistrusted
as a colleague the son of Fazio Cardano, and that stories of the
profligate life and the intractable temper of the candidate may have been
brought to them.[55] His health suffered from the bad air of the city
almost as severely as before, and Lucia, who was at this time pregnant,
miscarried at four months, and shortly afterwards had a second misfortune
of the same kind. His mother's temper was not of the sweetest, and it is
quite possible that between her and her daughter-in-law there may have
been strained relations. Cardan at any rate found that he must once more
beat a retreat from Milan, wherefore, at the end of April 1533, he made up
his mind to remove to Gallarate.

This town has already been mentioned as chief place of the district, from
which the Cardan family took its origin. Before going thither Jerome had
evidently weighed the matter well, and he has set down at some length the
reasons which led him to make this choice. "Thus, acting under the reasons
aforesaid (the family associations), I resolved to go to Gallarate, in
order that I might have the enjoyment of four separate advantages which it
offered. Firstly, that in the most healthy air of the place I might shake
off entirely the distemper which I had contracted in Milan. Secondly, that
I might earn something by my profession, seeing that then I should be free
to practise. Thirdly, that there would be no need for me to pine away
while I beheld those physicians, by whom I reckoned I had been despoiled,
flourishing in wealth and in the high estimation of all men. Lastly, that
by following a more frugal way of life, I might make what I possessed last
the longer. For all things are cheaper in the country, since they have to
be carried from the country into the town, and many necessaries may be had
for the asking. Persuaded by these arguments, I went to this place, and I
was not altogether deceived, seeing that I recovered my health, and the
son--who was to be reft from me later on by the Senate--was born to
me."[56]

Employment at Gallarate was, however, almost as scarce as it had been at
Sacco, wherefore Jerome found leisure in plenty for literary work. He
began a treatise on Fate; but, even had this been completed, it would
scarcely have filled the empty larder by the proceeds of its sale. More
profitable was some chance employment which was given to him by Filippo
Archinto,[57] a generous and accomplished young nobleman of Milan, who was
ambitious to figure as a writer on Astronomy, and, it may be remarked,
Archinto's benefactions were not confined to the payment for the hack work
which Jerome did for him at this period. Had it not been for his
subsequent patronage and support, it is quite possible that Cardan would
have gone under in the sea of adversity.

In spite of the cheapness of provisions at Gallarate, and of occasional
meals taken gratis from the fields, complete destitution seemed to be only
a matter of days, and just at this crisis, to add to his
embarrassments--though he longed earnestly for the event--Lucia was
brought to bed with her first-born living child on May 14, 1534. The
child's birth was accompanied by divers omens, one of which the father
describes, finding therein some premonition of future disaster. "I had
great fear of his life until the fifteenth day of June, on which day,
being a Sunday, he was baptized. The sun shone brightly into the
bed-chamber: it was between the hours of eleven and twelve in the
forenoon; and, according to custom, we were all gathered round the
mother's bed except a young servant, the curtain was drawn away from the
window and fastened to the wall, when suddenly a large wasp flew into the
room, and circled round the infant. We were all greatly afeard for the
child, but the wasp did him no hurt. The next moment it came against the
curtain, making so great a noise that you would have said that a drum was
being beaten, and all ran towards the place, but found no trace of the
wasp. It could not have flown out of the room, because all eyes had been
fixed upon it. Then all of us who were then present felt some foreboding
of what subsequently came to pass, but did not deem that the end would be
so bitter as it proved to be."[58]

The impulse which drives men in desperate straits to seek shelter in the
streets of a city was as strong in Cardan's time as it is to-day. At
Gallarate the last coin was now spent, and there was an extra mouth to
feed. There seemed to be no other course open but another retreat to
Milan. Archinto was rich in literary ambitions, which might perchance
stimulate him to find farther work for the starving scholar: and there was
Chiara also who would scarcely let her grandchild die of want. The
revelation which Cardan makes of himself and of his way of life at this
time is not one to enlist sympathy for him entirely; but it is not wanting
in a note of pathetic sincerity. "For a long time the College at Milan
refused to admit me, and during these days I was assuredly a spendthrift
and heedless. In body I was weakly, and in estate plundered by thieves on
all sides, yet I never grudged money for the buying of books. My residence
at Gallarate brought me no profit, for in the whole nineteen months I
lived there, I did not receive more than twenty-five crowns towards the
rent of the house I hired. I had such ill luck with the dice that I was
forced to pawn all my wife's jewels, and our very bed. If it is a wonder
that I found myself thus bereft of all my substance, it is still more
wonderful that I did not take to begging on account of my poverty, and a
wonder greater still that I harboured in my mind no unworthy thoughts
against my forefathers, or against right living, or against those honours
which I had won--honours which afterwards stood me in good stead--but bore
my misfortunes with mind undisturbed."[59]

Cardan's worldly fortunes were now at their lowest ebb. Burdened with a
wife and child, he had found it necessary to return, after a second futile
attempt to gain a living by his calling in a country town, to Milan, his
"stony-hearted step-mother." If he had reckoned on his mother's bounty he
was doomed to disappointment, for Chiara was an irritable woman, and as
her son's temper was none of the sweetest, it is almost certain that they
must have quarrelled occasionally. It is hard to believe that they could
have been on good terms at this juncture, otherwise she would scarcely
have allowed him to take his wife and child to what was then the public
workhouse of the city;[60] but this place was his only refuge, and in
October 1534 he was glad to shelter himself beneath its roof.

There was in Cardan's nature a strong vein of melancholy, and up to the
date now under consideration he had been the victim of a fortune
calculated to deepen rather than disperse his morbid tendencies. A proof
of his high courage and dauntless perseverance may be deduced from the
fact that neither poverty, nor the sense of repeated failure, nor the
flouts of the Milanese doctors, prevailed at any time to quench in his
heart the love of fame,[61] or to disabuse him of the conviction that he,
poverty-stricken wretch as he was, would before long bind Fortune to his
chariot-wheels, and would force the adverse world to acknowledge him as
one of its master minds. The dawn was now not far distant, but the last
hours of his night of misfortune were very dark. The worst of the
struggle, as far as the world was concerned, was over, and the sharpest
sorrows and the heaviest disgrace reserved for Cardan in the future were
to be those nourished in his own household.

Writing of his way of life and of the vices and defects of his character,
he says: "If a man shall fail in his carriage before the world as he fails
in other things, who shall correct him? Thus I myself will do duty for
that one leper who alone out of the ten who were healed came back to our
Lord. By reasoning of this sort, Physicians and Astrologers trace back the
origin of our natural habits to our primal qualities, to the training of
our will, and to our occupations and conversation. In every man all these
are found in proper ratio to the time of life of each individual;
nevertheless it will be easy to discern marked variations in cases
otherwise similar. Therefore it behoves us to hold fast to some guiding
principle chosen out of these, and I on my part am inclined, as far as it
may be allowed, to say with respect to all of them, [Greek: gnôthi
seauton].

"My own nature in sooth was never a mystery to myself. I was ever
hot-tempered, single-minded, and given to women. From these cardinal
tendencies there proceeded truculence of temper, wrangling, obstinacy,
rudeness of carriage, anger, and an inordinate desire, or rather a
headstrong passion, for revenge in respect to any wrong done to me; so
that this inclination, which is censured by many, became to me a delight.
To put it briefly, I held _At vindicta bonum vita jucundius ipsa_. As a
general rule I went astray but seldom, though it is a common saying,
'_Natura nostra prona est ad malum_.' I am moreover truthful, mindful of
benefits wrought to me, a lover of justice and of my own people, a
despiser of money, a worshipper of that fame which defies death, prone to
thrust aside what is commonplace, and still more disposed to treat mere
trifles in the same way. Still, knowing well how great may be the power of
little things at any moment during the course of an undertaking, I never
make light of aught which may be useful. By nature I am prone to every
vice and ill-doing except ambition, and I, if no one else does, know my
own imperfections. But because of my veneration for God, and because I
recognize the vanity and emptiness of all things of this sort, it often
happens that, of my own free will, I forego certain opportunities for
taking revenge which may be offered to me. I am timid, with a cold heart
and a hot brain, given to reflection and the consideration of things many
and mighty, and even of things which can never come to pass. I can even
let my thoughts concern themselves with two distinct subjects at the same
time. Those who throw out charges of garrulity and extravagance by way of
contradicting any praise accorded to me, charge me with the faults of
others rather than my own. I attack no man, I only defend myself.

"And what reason is there why I should spend myself in this cause since I
have so often borne witness of the emptiness of this life of ours? My
excuse must be that certain men have praised me, wherefore they cannot
deem me altogether wicked. I have always trained myself to let my face
contradict my thoughts. Thus while I can simulate what is not, I cannot
dissimulate what is. To accomplish this is no difficult task if a man
cultivates likewise the habit of hoping for nothing. By striving for
fifteen years to compass this end and by spending much trouble over the
same I at last succeeded. Urged on by this humour I sometimes go forth in
rags, sometimes finely dressed, sometimes silent, sometimes talkative,
sometimes joyful, sometimes sad; and on this account my two-fold mood
shows everything double. In my youth I rarely spent any care in keeping my
hair in order, because of my inclination for other pursuits more to my
taste. My gait is irregular. I move now quickly, now slowly. When I am at
home I go with my legs naked as far as the ankles. I am slack in duty and
reckless in speech, and specially prone to show irritation over anything
which may disgust or irk me."

The above-written self-description does not display a personality
particularly attractive. Jerome Cardan was one of those men who experience
a morbid gratification in cataloguing all their sinister points of
character, and exaggerating them at the same time; and in this picture, as
in many others scattered about the _De Vita Propria_, the shadows may have
been put in too strongly.

In the foregoing pages reference was made to certain acts of benevolence
done to Cardan by the family of Archinto. It is not impossible that the
promises and persuasions of his young patron Filippo may have had some
weight in inducing Jerome to shift his home once more. Whatever befell he
could hardly make his case worse; but whether Filippo had promised help or
not, he showed himself now a true and valuable friend. There was in Milan
a public lectureship in geometry and astronomy supported by a small
endowment left by a certain Tommaso Plat, and to this post, which happened
opportunely to be vacant, Cardan was appointed by the good offices of
Filippo Archinto. Yet even when he was literally a pauper he seems to have
felt some scruples about accepting this office, but fortunately in this
instance his poverty overcame his pride. The salary was indeed a very
small one,[62] and the lecturer was not suffered to handle the whole of
it, but it was at least liberal enough to banish the dread of starvation,
and his duties, which consisted solely in the preparation and delivery of
his lectures, did not debar him from literary work on his own account.
Wherefore in his leisure time he worked hard at his desk.

Any differences which may have existed between him and his mother were now
removed, for he took her to live with him, the household being made up of
himself, his wife, his mother, a friend (a woman), a nurse, the little
boy, a man- and maidservant, and a mule.[63] Possibly Chiara brought her
own income with her, and thus allowed the establishment to be conducted on
a more liberal scale. The Plat lectureship would scarcely have maintained
three servants, and Jerome's gains from other sources must have been as
yet very slender. His life at this time was a busy one, but he always
contrived to portion out his days in such wise that certain hours were
left for recreation. At such times as he was called upon to teach, the
class-room, of course, had the first claims. After the lecture he would
walk in the shade outside the city walls, then return to his dinner, then
divert himself with music, and afterwards go fishing in the pools and
streams hard by the town. In the course of time he obtained other
employment, being appointed physician to the Augustinian friars. The Prior
of this Order, Francesco Gaddi, was indeed his first patient of note. He
tells how he cured this man of a biennial leprosy after treating him for
six months;[64] adding that his labour was in vain, inasmuch as Gaddi died
a violent death afterwards. The refusal of the College of Milan to admit
him to membership did not forbid him to prescribe for whatever patients
might like to consult him by virtue of his Paduan degree. He read
voraciously everything which came in his way, and it must have been during
these years that he stored his memory with that vast collection of facts
out of which he subsequently compounded the row of tomes which form his
legacy to posterity. Filippo Archinto was unfailing in his kindness, and
Jerome at this time was fortunate enough to attract the attention of
certain other Milanese citizens of repute who afterwards proved to be
valuable friends; Ludovico Madio, Girolamo Guerrini a jeweller, Francesco
Belloti, and Francesco della Croce. The last-named was a skilled
jurisconsult, whose help proved of great service in a subsequent
litigation between Jerome and the College of Physicians.

All his life long Cardan was a dreamer of dreams, and he gives an account
of one of his visions in this year, 1534, which, whether regarded as an
allegory or as a portent, is somewhat remarkable. "In the year 1534, when
I was as it were groping in the dark, when I had settled naught as to my
future life, and when my case seemed to grow more desperate day by day, I
beheld in a dream the figure of myself running towards the base of a
mountain which stood upon my right hand, in company with a vast crowd of
people of every station and age and sex--women, men, old men, boys,
infants, poor men and rich men, clad in raiment of every sort. I inquired
whither we were all running, whereupon one of the multitude answered that
we were all hastening on to death. I was greatly terrified at these words,
when I perceived a mountain on my left hand. Then, having turned myself
round so that it stood on my right side, I grasped the vines (which, here
in the midst of the mountains and as far as the place wherein I stood,
were covered with dry leaves, and bare of grapes, as we commonly see them
in autumn) and began to ascend. At first I found this difficult, for the
reason that the mountain was very steep round the base, but having
surmounted this I made my way upward easily. When I had come to the summit
it seemed that I was like to pass beyond the dictates of my own will.
Steep naked rocks appeared on every side, and I narrowly escaped falling
down from a great height into a gloomy chasm. So dreadful is all this that
now, what though forty years have rolled away, the memory thereof still
saddens and terrifies me. Then, having turned towards the right where I
could see naught but a plain covered with heath, I took that path out of
fear, and, as I wended thither in reckless mood, I found that I had come
to the entrance of a rude hut, thatched with straw and reeds and rushes,
and that I held by my right hand a boy about twelve years of age and clad
in a grey garment. Then at this very moment I was aroused from sleep, and
my dream vanished.

"In this vision was clearly displayed the deathless name which was to be
mine, my life of heavy and ceaseless work, my imprisonment, my seasons of
grievous terror and sadness, and my abiding-place foreshadowed as
inhospitable, by the sharp stones I beheld: barren, by the want of trees
and of all serviceable plants; but destined to be, nevertheless, in the
end happy, and righteous, and easy. This dream told also of my lasting
fame in the future, seeing that the vine yields a harvest every year. As
to the boy, if he were indeed my good spirit, the omen was lucky, for I
held him very close. If he were meant to foreshadow my grandson it would
be less fortunate. That cottage in the desert was my hope of rest. That
overwhelming horror and the sense of falling headlong may have had
reference to the ruin of my son.[65]

"My second dream occurred a short time after. It seemed to me that my soul
was in the heaven of the moon, freed from the body and all alone, and when
I was bewailing my fate I heard the voice of my father, saying: 'God has
appointed me as a guardian to you. All this region is full of spirits, but
these you cannot see, and you must not speak either to me or to them. In
this part of heaven you will remain for seven thousand years, and for the
same time in certain other stars, until you come to the eighth. After
this you shall enter the kingdom of God.' I read this dream as follows. My
father's soul is my tutelary spirit. What could be dearer or more
delightful? The Moon signifies Grammar; Mercury Geometry and Arithmetic;
Venus Music, the Art of Divination, and Poetry; the Sun the Moral, and
Jupiter the Natural, World; Mars Medicine; Saturn Agriculture, the
knowledge of plants, and other minor arts. The eighth star stands for a
gleaning of all mundane things, natural science, and various other
studies. After dealing with these I shall at last find my rest with the
Prince of Heaven."[66]

FOOTNOTES:

[45] "Nec ullum mihi erat relictum auxilium nisi latrunculorum
Ludus."--_Opera_, tom. i. p. 619.

[46] From the formation of the League of Cambrai in 1508 to the
establishment of the Imperial supremacy in Italy in 1530, the whole
country was desolated by the marching and counter-marching of the
contending forces. Milan, lying directly in the path of the French armies,
suffered most of all.

[47] Compare _De Vita Propria_, chaps. iv. and xxxi. pp. 13 and 92.

[48] _De Vita Propria_, ch. xxxi. p. 92. In taking the other view he
writes: "Vitam ducebam in Saccensi oppido, ut mihi videbar,
infelicissime."--_Opera_, tom. i. p. 97.

[49] _De Utilitate_, p. 235.

[50] He gives a long and interesting sketch of his father-in-law in _De
Utilitate_, p. 370.

[51] _De Vita Propria_, ch. xxvi. p. 68; _Opera_, tom. i. p. 97.

[52] _De Vita Propria_, ch. xli. p. 149.

[53] _De Utilitate_, p. 350.

[54] _De Utilitate_, p. 357: "Nam in urbe nec collegium recipere volebat
nec cum aliquo ex illis artem exercere licebat et sine illis difficillimum
erat." He writes thus while describing this particular visit to Milan.

[55] Ill fortune seems to have pursued the whole family in their relations
with learned societies. "Nam et pater meus ut ab eo accepi, diu in
ingressu Collegii Jurisconsultorum laboravit, et ego, ut alias testatus
sum, bis a medicorum Patavino, toties filius meus natu major, a Ticinensi,
uterque a Mediolanensi rejecti sumus."--_Opera_, tom. i. p. 94.

[56] _De Utilitate_, p. 358.

[57] He became a priest, and died Archbishop of Milan in 1552. Cardan
dedicated to him his first published book, _De Malo Medendi_.

[58] _De Vita Propria_, ch. xxxvii. p. 119.

[59] _De Vita Propria_, ch. xxv. p. 67.

[60] The Xenodochium, which was originally a stranger's lodging-house. By
this time places of this sort had become little else than _succursales_ of
some religious house. The Governors of the Milanese Xenodochium were the
patrons of the Plat endowment which Cardan afterwards enjoyed.

[61] "Hoc unum sat scio, ab ineunte ætate me inextinguibili nominis
immortalis cupiditate flagrasse."--_Opera_, tom. i. p. 61.

[62] "Minimo tamen honorario, et illud etiam minimum suasu cujusdam amici
egregii praefecti Xenodochii imminuerunt; ita cum hujus recordor in mentem
venit fabellæ illius Apuleii de annonæ Praefecto."--_Opera_, tom. i. p.
64.

[63] _De Utilitate_, p. 351.

[64] The following gives a hint as to the treatment followed: "Referant
leprosos balneo ejus aquae in qua cadaver ablutum sit, sanari."--_De
Varietate_, p. 334.

[65] _De Vita Propria_, ch. xxxvii. p. 121. This dream is also told in _De
Libris Propriis_, Opera, tom. i. p. 64.

[66] _De Vita Propria_, ch. xxxvii. p. 121.




CHAPTER IV


JEROME CARDAN is now standing on the brink of authorship. The very title
of his first book, _De Malo Recentiorum Medicorum Medendi Usu_, gives
plain indication of the humour which possessed him, when he formulated his
subject and put it in writing. With his temper vexed by the persistent
neglect and insult cast upon him by the Milanese doctors he would
naturally sit down _con amore_ to compile a list of the errors perpetrated
by the ignorance and bungling of the men who affected to despise him, and
if his object was to sting the hides of these pundits and arouse them to
hostility yet more vehement, he succeeded marvellously well. He was
enabled to launch his book rather by the strength of private friendship
than by the hope of any commercial success. Whilst at Pavia he had become
intimate with Ottaviano Scoto, a fellow-student who came from Venice, and
in after times he found Ottaviano's purse very useful to his needs. Since
their college days Ottaviano's father had died and had left his son to
carry on his calling of printing. In 1536 Jerome bethought him of his
friend, and sent him the MS. of the treatise which was to let the world
learn with what little wisdom it was being doctored.[67]

Ottaviano seems to have expected no profit from this venture, which was
manifestly undertaken out of a genuine desire to help his friend, and he
generously bore all the costs. Cardan deemed that, whatever the result of
the issue of the book might be, it would surely be to his benefit; he
hazarded nothing, and the very publication of his work would give him at
least notoriety. It would moreover give him the intense pleasure of
knowing that he was repaying in some measure the debt of vengeance owing
to his professional foes. The outcome was exactly the opposite of what
printer and author had feared and hoped. The success of the book was rapid
and great.

Ottaviano must soon have recouped all the cost of publication; and, while
he was counting his money, the doctors everywhere were reading Jerome's
brochure, and preparing a ruthless attack upon the daring censor, who,
with the impetuosity of youth, had laid himself open to attack by the
careless fashion in which he had compiled his work. He took fifteen days
to write it, and he confesses in his preface to the revised edition that
he found therein over three hundred mistakes of one sort or another. The
attack was naturally led by the Milanese doctors. They demanded to be told
why this man, who was not good enough to practise by their sanction, was
good enough to lay down the laws for the residue of the medical world.
They heaped blunder upon blunder, and held him up to ridicule with all the
wealth of invective characteristic of the learned controversy of the age.
Cardan was deeply humbled and annoyed. "For my opponents, seizing the
opportunity, took occasion to assail me through the reasoning of this
book, and cried out: 'Who can doubt that this man is mad? and that he
would teach a method and a practice of medicine differing from our own,
since he has so many hard things to say of our procedure.' And, as Galen
said, I must in truth have appeared crazy in my efforts to contradict this
multitude raging against me. For, as it was absolutely certain that either
I or they must be in the wrong, how could I hope to win? Who would take my
word against the word of this band of doctors of approved standing,
wealthy, for the most part full of years, well instructed, richly clad and
cultivated in their bearing, well versed in speaking, supported by crowds
of friends and kinsfolk, raised by popular approval to high position, and,
what was more powerful than all else, skilled in every art of cunning and
deceit?"

Cardan had indeed prepared a bitter pill for his foes, but the draught
they compelled him to swallow was hardly more palatable. The publication
of the book naturally increased the difficulties of his position, and in
this respect tended to make his final triumph all the more noteworthy.

It was in 1536 that Cardan made his first essay as an author.[68] The next
three years of his life at Milan were remarkable as years of preparation
and accumulation, rather than as years of achievement. He had struck his
first blow as a reformer, and, as is often the lot of reformers, his sword
had broken in his hand, and there now rested upon him the sense of failure
as a superadded torment. Yet now and again a gleam of consolation would
disperse the gloom, and advise him that the world was beginning to
recognize his existence, and in a way his merits. In this same year he
received an offer from Pavia of the Professorship of Medicine, but this he
refused because he did not see any prospect of being paid for his
services. His friend Filippo Archinto was loyal still, and zealous in
working for his success, and as he had been recently promoted to high
office in the Imperial service, his good word might be very valuable
indeed. He summoned his _protégé_ to join him at Piacenza, whither he had
gone to meet Paul III., hoping to advance Cardan's interests with the
Pope; but though Marshal Brissac, the French king's representative,[69]
joined Archinto in advocating his cause, nothing was done, and Jerome
returned disappointed to Milan.

In these months Cardan, disgusted by the failure of his late attack upon
the fortress of medical authority, turned his back, for a time, upon the
study of medicine, and gave his attention almost entirely to mathematics,
in which his reputation was high enough to attract pupils, and he always
had one or more of them in his house, the most noteworthy of whom was
Ludovico Ferrari of Bologna, who became afterwards a mathematician of
repute, and a teacher both at Milan and Bologna. While he was working at
the _De Malo Medendi_, he began a treatise upon Arithmetic, which he
dedicated to his friend Prior Gaddi; but this work was not published till
1539. In 1536 he first heard a report of a fresh and important discovery
in algebra, made by one Scipio Ferreo of Bologna; the prologue to one of
the most dramatic incidents in his career, an incident which it will be
necessary to treat at some length later on.

Cardan was well aware that his excursions into astrology worked to his
prejudice in public esteem, but in spite of this he could not refrain
therefrom. It was during the plentiful leisure of this period that he
cast the horoscope of Jesus Christ, a feat which subsequently brought upon
him grave misfortune; a few patients came to him, moved no doubt by the
spirit which still prompts people suffering from obscure diseases to
consult professors of healing who are either in revolt or unqualified in
preference to going to the orthodox physician. In connection with this
irregular practice of his he gives a curious story about a certain Count
Borromeo. "In 1536, while I was attending professionally in the house of
the Borromei, it chanced that just about dawn I had a dream in which I
beheld a serpent of enormous bulk, and I was seized with fear lest I
should meet my death therefrom. Shortly afterwards there came a messenger
to summon me to see the son of Count Carlo Borromeo. I went to the boy,
who was about seven years old, and found him suffering from a slight
distemper, but on feeling his pulse I perceived that it failed at every
fourth beat. His mother, the Countess Corona, asked me how he fared, and I
answered that there was not much fever about him; but that, because his
pulse failed at every fourth beat, I was in fear of something, but what it
might be I knew not rightly (but I had not then by me Galen's books on the
indications of the pulse). Therefore, as the patient's state changed not,
I determined on the third day to give him in small doses the drug called
_Diarob: cum Turbit_: I had already written my prescription, and the
messenger was just starting with it to the pharmacy, when I remembered my
dream. 'How do I know,' said I to myself, 'that this boy may not be about
to die as prefigured by the portent above written? and in that case these
other physicians who hate me so bitterly, will maintain he died through
taking this drug.' I called to the messenger, and said there was wanting
in the prescription something which I desired to add. Then I privately
tore up what I had written, and wrote out another made of pearls, of the
horn of unicorn,[70] and certain gems. The powder was given, and was
followed by vomiting. The bystanders perceived that the boy was indeed
sick, whereupon they called in three of the chief physicians, one of whom
was in a way friendly to me. They saw the description of the medicine, and
demanded what I would do now. Now although two of these men hated me, it
was not God's will that I should be farther attacked, and they not only
praised the medicine, but ordered that it should be repeated. This was the
saving of me. When I went again in the evening I understood the case
completely. The following morning I was summoned at daybreak, and found
the boy battling with death, and his father lying in tears. 'Behold him,'
he cried, 'the boy whom you declared to ail nothing' (as if indeed I could
have said such a thing); 'at least you will remain with him as long as he
lives.' I promised that I would, and a little later the boy tried to rise,
crying out the while. They held him down, and cast all the blame upon me.
What more is there to say? If there had been found any trace of that drug
_Diarob: cum Turbit_: (which in sooth was not safe) it would have been all
over with me, since Borromeo all his life would either have launched
against me complaints grave enough to make all men shun me, or another
Canidia, more fatal than African serpents, would have breathed poison upon
me."[71]

In this same year, 1536, Lucia brought forth another child, a daughter,
and it was about this time that Cardan first attracted the attention of
Alfonso d'Avalos, the Governor of Milan, and an intimacy began which,
albeit fruitless at first, was destined to be of no slight service to
Jerome at the crisis of his fortunes.[72] In the following year, in 1537,
he made a beginning of two of his books, which were subsequently found
worthy of being finished, and which may still be read with a certain
interest: the treatises _De Sapientia_ and _De Consolatione_. Of the
last-named, he remarks that it pleased no one, forasmuch as it appealed
not to those who were happy, and the wretched rejected it as entirely
inadequate to give them solace in their evil case. In this year he made
another attempt to gain admission to the College at Milan, and was again
rejected; the issue of the _De Malo Medendi_ was too recent, and it needed
other and more potent influences than those exercised by mere merit, to
appease the fury of his rivals and to procure him due status. But it would
appear that, in 1536 or 1537, he negotiated with the College to obtain a
quasi-recognition on conditions which he afterwards describes as
disgraceful to himself, and that this was granted to him.[73]

Whatever his qualifications may have been, Cardan had no scruples in
treating the few patients who came to him. The first case he notes is that
of Donato Lanza,[74] a druggist, who had suffered for many years with
blood-spitting, which ailment he treated successfully. Success of this
sort was naturally helpful, but far more important than Lanza's cure was
the introduction given by the grateful patient to the physician,
commending him to Francesco Sfondrato, a noble Milanese, a senator, and a
member of the Emperor's privy council. The eldest son of this gentleman
had suffered many months from convulsions, and Cardan worked a cure in his
case without difficulty. Shortly afterwards another child, only ten months
old, was attacked by the same complaint, and was treated by Luca della
Croce, the procurator of the College of Physicians, of which Sfondrato was
a patron. As the attack threatened to be a serious one, Della Croce
recommended that another physician, Ambrogio Cavenago, should be called
in, but the father, remembering Cardan's cure of Lanza, wished for him as
well. The description of the meeting of the doctors round the sick child's
bed, of their quotations from Hippocrates, of the uncertainty and
helplessness of the orthodox practitioners, and of the ready resource of
the free-lance--who happens also to be the teller of the story--is a
richly typical one.[75] "We, the physicians and the father of the child,
met about seven in the morning, and Della Croce made a few general
observations on death, for he knew that Sfondrato was a sensible man, and
he himself was both honoured and learned. Cavenago kept silence at this
stage, because the last word had been granted to him. Then I said, 'Do you
not see that the child is suffering from Opisthotonos?' whereupon the
first physician stood as one dazed, as if I were trying to trouble his
wits by my hard words. But Della Croce at once swept aside all uncertainty
by saying, 'He means the backward contraction of the muscles.' I confirmed
his words, and added, 'I will show you what I mean.' Whereupon I raised
the boy's head, which the doctors and all the rest believed was hanging
down through weakness, and by its own weight, and bade them put it into
its former position. Then Sfondrato turned to me, and said, 'As you have
discovered what the disease is, tell us likewise what is the remedy
therefor.' Since no one else spoke, I turned towards him and--careful lest
I should do hurt to the credit I had gained already,--I said, 'You know
what Hippocrates lays down in a case like this--_febrem convulsioni_'--and
I recited the aphorism. Then I ordered a fomentation, and an application
of lint moistened with linseed-oil and oil of lilies, and gave directions
that the child should be gently handled until such time as the neck
should be restored; that the nurse should eat no meat, and that the child
should be nourished entirely by the milk of her breast, and not too much
of that; that it should be kept in its cradle in a warm place, and rocked
gently till it should fall asleep. After the other physicians had gone, I
remember that the father of the child said to me, 'I give you this child
for your own,' and that I answered, 'You are doing him an ill turn, in
that you are supplanting his rich father by a poor one.' He answered, 'I
am sure that you would care for him as if he were your own, fearing naught
that you might thereby give offence to these others' (meaning the
physicians). I said, 'It would please me well to work with them in
everything, and to win their support.' I thus blended my words, so that he
might understand I neither despaired of the child's cure, nor was quite
confident thereanent. The cure came to a favourable end; for, after the
fourteenth day of the fever--the weather being very warm--the child got
well in four days' time. Now as I review the circumstances, I am of
opinion that it was not because I perceived what the disease really was,
for I might have done so much by reason of my special practice; nor
because I healed the child, for that might have been attributed to chance;
but because the child got well in four days, whereas his brother lay ill
for six months, and was then left half dead, that his father was so much
amazed at my skill, and afterwards preferred me to all others. That he
thought well of me is certain, because Della Croce himself, during the
time of his procuratorship, was full of spite and jealousy against me, and
declared in the presence of Cavenago and of Sfondrato, that he would not,
under compulsion, say a word in favour of a man like me, one whom the
College regarded with disfavour. Whereupon Sfondrato saw that the envy
and jealousy of the other physicians was what kept me out of the College,
and not the circumstances of my birth. He told the whole story to the
Senate, and brought such influence to bear upon the Governor of the
Province and other men of worship, that at last the entrance to the
College was opened to me."

Up to the time of his admission to the College, Jerome had never felt that
he could depend entirely upon medicine for his livelihood. He now
determined to publish his _Practica Arithmeticæ_, the book which he had
prepared _pari passu_ with the ill-starred _De Malo Medendi_. It seems to
have been thoroughly revised and corrected, and was finally published in
1539, in Milan; Cardan only received ten crowns for his work, but the
sudden fame he achieved as a mathematician ought to have set him on firm
ground. His friends were still working to secure for him benefits yet more
substantial. Alfonso d'Avalos, Francesco della Croce, the jurisconsult
whose name has already been mentioned, and the senator Sfondrato, were
doing their best to bring the physicians of the city into a more
reasonable temper, and they finally succeeded in 1539; when, after having
been denied admission for twelve years, Jerome Cardan became a member of
the College, and a sharer in all the privileges appertaining thereto.

Though Cardan was now a fully qualified physician, he spent his time for
the next year or two rather with letters than with medicine. He worked
hard at Greek, and as the result of his studies published somewhat
prematurely a treatise, _De Immortalitate Animorum_, a collection of
extracts from Greek writers which Julius Cæsar Scaliger with justice
calls a confused farrago of other men's learning.[76] He published also
about this period the treatise on Judicial Astrology, and the Essay _De
Consolatione_, the only one of his books which has been found worthy of an
English translation.[77] In 1541 he became Rector of the College of
Physicians, but there is no record of any increase in the number of his
patients by reason of this superadded dignity. A passage in the _De Vita
Propria_, written with even more than his usual brutal candour, gives a
graphic view of his manner of life at this period. "It was in the summer
of the year 1543, a time when it was my custom to go every day to the
house of Antonio Vicomercato, a gentleman of the city, and to play chess
with him from morning till night. As we were wont to play for one real, or
even three or four, on each game, I, seeing that I was generally the
winner, would as a rule carry away with me a gold piece after each day's
play, sometimes more and sometimes less. In the case of Vicomercato it was
a pleasure and nothing else to spend money in this wise; but in my own
there was an element of conflict as well; and in this manner I lost my
self-respect so completely that, for two years and more, I took no thought
of practising my art, nor considered that I was wasting all my
substance--save what I made by play--that my good name and my studies as
well would suffer shipwreck. But on a certain day towards the end of
August, a new humour seized Vicomercato (either advisedly on account of
the constant loss he suffered, or perhaps because he thought his decision
would be for my benefit), a determination from which he was to be moved
neither by arguments, nor adjurations, nor abuse. He forced me to swear
that I would never again visit his house for the sake of gaming, and I, on
my part, swore by all the gods as he wished. That day's play was our last,
and thenceforth I gave myself up entirely to my studies."[78]

But these studies unfortunately were not of a nature to keep the wolf from
the door; and Jerome, albeit now a duly qualified physician, and known to
fame as a writer on Mathematics far beyond the bounds of Italy, was
well-nigh as poor as ever. His mother had died several years before, in
1537; but what little money she may have left would soon have been wasted
in gratifying his extravagant taste for costly things,[79] and at the
gaming-table. He found funds, however, for a journey to Florence, whither
he went to see d'Avalos, who was a generous, open-handed man, and always
ready to put his purse at the service of one whom he regarded as an honour
to his city and country. There can be little doubt that he helped Cardan
liberally at this juncture. The need for a loan was assuredly urgent
enough. The recent resumption of hostilities between the French and the
Imperialists had led to intolerable taxation throughout the Milanese
provinces, and in consequence of dearth of funds in 1543, the Academy at
Pavia was forced to close its class-rooms, and leave its teachers unpaid.
The greater part of the professors migrated to Pisa; and the Faculty of
Medicine, then vacant, was, _pro formâ_, transferred to Milan. This chair
was now offered to Cardan. He was in desperate straits--a third child had
been born this year--and, though there must have been even less chance of
getting his salary paid than when he had refused it before, he accepted
the post, explaining that he took this step because there was now no need
for him to leave Milan, or danger that he would be rated as an itinerant
teacher. It is not improbable that he may have been led to accept the
office on account of the additional dignity it would give to him as a
practising physician. When, a little later on, the authorities began to
talk of returning to Pavia, he was in no mind to follow them, giving as a
reason that, were he to leave Milan, he would lose his stipend for the
Plat lectureship, and be put to great trouble in the transport of his
household, and perhaps suffer in reputation as well. The Senate was
evidently anxious to retain his services. They bade him consider the
matter, promising to send on a certain date to learn his decision; and, as
fate would have it, the question was conveniently decided for him by a
portent.

"On the night before the day upon which my answer was to be sent to the
Senate to say what course I was going to take, the whole of the house fell
down into a heap of ruins, and no single thing was left unwrecked, save
the bed in which I and my wife and my children were sleeping. Thus the
step, which I should never have taken of my own free will or without some
sign, I was compelled to take by the course of events. This thing caused
great wonder to all those who heard of it."[80]

This was in 1544. Jerome hesitated no longer, and went forthwith to Pavia
as Professor of Medicine at a salary of two hundred and forty gold crowns
per annum; but, for the first year at least, this salary was not paid;
and the new professor lectured for a time to empty benches; but, as he was
at this time engaged in the final stage of his great work on Algebra, the
leisure granted to him by the neglect of the students must have been most
acceptable. He published at this time a treatise called _Contradicentium
Medicorum_, and in 1545 his _Algebra_ or _Liber Artis Magnæ_ was issued
from the press by Petreius of Nuremberg. The issue of this book, by which
alone the name of Cardan holds a place in contemporary learning, is
connected with an episode of his life important enough to demand special
and detailed consideration in a separate place.

His practice in medicine was now a fairly lucrative one, but his
extravagant tastes and the many vices with which he charges himself would
have made short work of the largest income he could possibly have earned,
consequently poverty was never far removed from the household. Hitherto
his reputation as a man of letters and a mathematician had exceeded his
fame as a doctor; for, even after he had taken up his residence as
Professor of Medicine at Padua, many applications were made to him for his
services in other branches of learning. It was fortunate indeed that he
had let his reading take a somewhat eclectic course, for medicine at this
time seemed fated to play him false. At the end of 1544 no salary was
forthcoming at Pavia, so he abandoned his class-room, and returned to
Milan.

During his residence there, in the summer of 1546, Cardinal Moroni, acting
on behalf of Pope Paul III., made an offer for his services as a teacher
of mathematics, accompanied by terms which, as he himself admits, were not
to be despised; but, as was his wont, he found some reason for demur, and
ultimately refused the offer. In his Harpocratic vein he argued, "This
pope is an old man, a tottering wall, as it were. Why should I abandon a
certainty for an uncertainty?"[81] The certainty he here alludes to must
have been the salary for the Plat lectureship; and, as this emolument was
a very small one, it would appear that he did not rate at a high figure
any profits which might come to him in the future from his acceptance of
the Pope's offer; but, as he admits subsequently, he did not then fully
realize the benevolence of the Cardinal who approached him on the subject,
or the magnificent patronage of the Farnesi.[82] It is quite possible that
this refusal of his may have been caused by a reluctance to quit Milan,
the city which had treated him in such cruel and inhospitable fashion,
just at the time when he had become a man of mark. In the arrogance of
success it was doubtless a keen pleasure to let his fellow-townsmen see
that the man upon whom they had heaped insult after insult for so many
years was one who could afford to let Popes and Cardinals pray for his
services in vain. But whatever may have been his humour, he resolved to
remain in Milan; and, as he had no other public duty to perform except the
delivery of the Plat lectures, he had abundant leisure to spend upon the
many and important works he had on hand at this season.

Cardan had now achieved European fame, and was apparently on the high
road to fortune, but on the very threshold of his triumph a great sorrow
and misfortune befell him, the full effect of which he did not experience
all at once. In the closing days of 1546 he lost his wife. There is very
scant record of her life and character in any of her husband's
writings,[83] although he wrote at great length concerning her father; and
the few words that are to be found here and there favour the view that she
was a good wife and mother. That Jerome could have been an easy husband to
live with under any circumstances it is hard to believe. Lucia's life, had
it been prolonged, might have been more free of trouble as the wife of a
famous and wealthy physician; but it was her ill fortune to be the
companion of her husband only in those dreary, terrible days at Sacco and
Gallarate, and in the years of uncertainty which followed the final return
to Milan. In the last-named period there was at least the Plat lectureship
standing between them and starvation; but children increased the while in
the nursery, and manuscripts in the desk of the physician without
patients, and Lucia's short life was all consumed in this weary time of
waiting for fame and fortune which, albeit hovering near, seemed destined
to mock and delude the seeker to the end. Cardan was before all else a man
of books and of the study, and it is not rare to find that one of this
sort makes a harsh unsympathetic husband. The qualities which he
attributes to himself in his autobiography suggest that to live with a man
cursed with such a nature would have been difficult even in prosperity,
and intolerable in trouble and privation. But fretful and irascible as
Cardan shows himself to have been, there was a warm-hearted, affectionate
side to his nature. He was capable of steadfast devotion to all those to
whom his love had ever been given. His reverence for the memory of his
tyrannical and irascible father had been noted already, and a still more
remarkable instance of his fidelity and love will have to be considered
when the time comes to deal with the crowning tragedy of his life. If
Cardan had this tender side to his nature, if he could speak tolerant and
even laudatory words concerning such a father as Fazio Cardano, and show
evidences of a love strong as death in the fight he made for the life of
his ill-starred and unworthy son, it may be hoped--in spite of his almost
unnatural silence concerning her--that he gave Lucia some of that
tenderness and sympathy which her life of hard toil and heavy sacrifice so
richly deserved; and that even in the days when he sold her trinkets to
pay his gambling losses, she was not destined to weep the bitter tears of
a neglected wife. If her early married life had been full of care and
travail, if she died when a better day seemed to be dawning, she was at
least spared the supreme sorrow and disgrace which was destined to fall so
soon upon the household. Judging by what subsequently happened, it will
perhaps be held that fate, in cutting her thread of life, was kinder to
her than to her husband, when it gave him a longer term of years under the
sun.

FOOTNOTES:

[67] _De Libris Propriis_, Opera, tom. i. p. 102.

[68] Besides the _De Malo Medendi Usu_, he published in 1536 a tract upon
judicial astrology. This, in an enlarged form, was reprinted by Petreius
at Nuremburg in 1542.

[69] Cardan writes of Brissac: "Erat enim Brissacus Prorex singularis in
studiosis amoris et humanitatis."--_De Vita Propria_, ch. iv. p. 14.

[70] "Mirumque in modum venenis cornu ejus adversari creditur."--_De
Subtilitate_, p. 315. Sir Thomas Browne (_Vulgar Errors_, Bk. iii. 23)
deals at length with the pretended virtues of the horn, and in the
Bestiary of Philip de Thaun (_Popular Treatises on Science during the
Middle Ages_) is given an account of the many wonderful qualities of the
beast.

[71] _De Vita Propria_, ch. xxxiii. p. 105. He also alludes to this case
in _De Libris Propriis_ (Opera, tom. i. p. 65), affirming that the other
doctors concerned in the case raised a great prejudice against him on
account of his reputation as an astrologer. "Ita tot modis et insanus
paupertate, et Astrologus profitendo edendoque libros, et imperitus casu
illustris pueri, et modum alium medendi observans ex titulo libri nuper
edito, jam prope ab omnibus habebar. Atque hæc omnia in Urbe omnium
nugacissima, et quæ calumniis maximè patet."

[72] The founder of this family was Indico d'Avalos, a Spanish gentleman,
who was chosen by Alfonso of Naples as a husband for Antonella, the
daughter and heiress of the great Marchese Pescara of Aquino. This
d'Avalos Marchese dal Guasto was the grandson of Indico. He commanded the
advanced guard at the battle of Pavia, and took part in almost every
battle between the French and Imperialists, and went with the Emperor to
Tunis in 1535. Though he was a brave soldier and a skilful tactician, he
was utterly defeated by d'Enghien at Cerisoles in 1544. He has been taxed
with treachery in the case of the attack upon the messengers Rincon and
Fregoso, who were carrying letters from Francis I. to the Sultan during a
truce, but he did little more than imitate the tactics used by the French
against himself; moreover, neither of the murdered men was a French
subject, or had the status of an ambassador. D'Avalos was a liberal patron
of letters and arts, and was very popular as Governor of Milan. He was a
noted gallant and a great dandy. Brantôme writes of him--"qu'il était si
dameret qu'il parfumait jusqu'aux selles de ses chevaux."--He died in
1546.

[73] "Violentia quorundam Medicorum adactus sum anno MDXXXVI, seu XXXVII,
turpi conditione pacisci cum Collegio, sed ut dixi, postmodum dissoluta
est, anno MDXXXIX et restitutus sum integrè."--_De Vita Propria_, ch.
xxxiii. p. 105.

[74] _De Vita Propria_, ch. xl. p. 133.--He gives a long list of cases of
his successful treatment in _Opera_, tom. i. p. 82.

[75] There is a full account of this episode in _De Libris Propriis_, p.
128, and in _De Vita Propria_, ch. xl. p. 133.

[76] Exotericarum exercitationum, p. 987.

[77] _Cardanus Comforte, translated into Englishe_, 1573. It was the work
of Thomas Bedingfield, a gentleman pensioner of Queen Elizabeth.

[78] _De Vita Propria_, ch. xxxvii. p. 116.

[79] "Delectant me gladii parvi, seu styli scriptorii, in quos plus
viginti coronatis aureis impendi: multas etiam pecunias in varia pennarum
genera, audeo dicere apparatum ad scribendum ducentis coronatis non
potuisse emi."--_De Vita Propria_, ch. xviii. p. 57.

[80] _De Vita Propria_, ch. iv. p. 15.

[81] "At ego qui, ut dixi, Harpocraticus sum dicebam:--Summus Pont:
decrepitus est: murus ruinosus, certa pro incertis derelinquam?"--_De Vita
Propria_, ch. iv. p. 15. It is quite possible that Paul III. may have
desired to have Cardan about him on account of his reputation as an
astrologer, the Pope being a firm believer in the influence of the
stars.--_Vide_ Ranke, _History of the Popes_ i. 166.

[82] "Neque ego tum Moroni probitatem, nec Pharnesiorum splendorem
intelligebam."--_De Vita Propria_, ch. iv. p. 15.

[83] In writing of his own horoscope (_Geniturarum Exempla_, p. 461) he
records that she miscarried thrice, brought forth three living children,
and lived with him fifteen years. He dismisses his marriage as follows:
"Duxi uxorem inexpectato, a quo tempore multa adversa concomitata
sunt."--_De Vita Propria_, ch. xli. p. 149. But in _De Rerum Subtilitate_,
p. 375, he records his grief at her death:--"Itaque cum a luctu dolor et
vigilia invadere soleant, ut mihi anno vertente in morte uxoris Luciæ
Bandarenæ quanquam institutis philosophiæ munitus essem, repugnante tamen
natura, memorque vinculi c[o=]jugalis, suspiriis ac lachrymis et inedia
quinque dierum, a periculo me vindicavi."




CHAPTER V


AT this point it may not be inopportune to make a break in the record of
Cardan's life and work, and to treat in retrospect of that portion of his
time which he spent in the composition of his treatises on Arithmetic and
Algebra. Ever since 1535 he had been working intermittently at one or
other of these, but it would have been impossible to deal coherently and
effectively with the growth and completion of these two books--really the
most important of all he left behind him--while chronicling the goings and
comings of a life so adventurous as that of the author.

The prime object of Cardan's ambition was eminence as a physician. But,
during the long years of waiting, while the action of the Milanese doctors
kept him outside the bounds of their College, and even after this had been
opened to him without inducing ailing mortals to call for his services, he
would now and again fall into a transport of rage against his persecutors,
and of contempt for the public which refused to recognize him as a master
of his art, and cast aside his medical books for months at a time,
devoting himself diligently to Mathematics, the field of learning which,
next to Medicine, attracted him most powerfully. His father Fazio was a
geometrician of repute and a student of applied mathematics, and, though
his first desire was to make his son a jurisconsult, he gave Jerome in
early youth a fairly good grounding in arithmetic and geometry, deeming
probably that such training would not prove a bad discipline for an
intellect destined to attack those formidable tomes within which lurked
the mysteries of the Canon and Civil Law. Mathematical learning has given
to Cardan his surest title to immortality, and at the outset of his career
he found in mathematics rather than in medicine the first support in the
arduous battle he had to wage with fortune. His appointment to the Plat
lectureship at Milan has already been noted. In the discharge of his new
duties he was bound, according to the terms of the endowment of the Plat
lecturer, to teach the sciences of geometry, arithmetic, and astronomy,
and he began his course upon the lines laid down by the founder. Few
listeners came, however, and at this juncture Cardan took a step which
serves to show how real was his devotion to the cause of true learning,
and how lightly he thought of an additional burden upon his own back, if
this cause could be helped forward thereby. Keenly as he enjoyed his
mathematical work, he laid a part of it aside when he perceived that the
benches before him were empty, and, by way of making his lectures more
attractive, he occasionally substituted geography for geometry, and
architecture for arithmetic. The necessary research and the preparation of
these lectures led naturally to the accumulation of a large mass of notes,
and as these increased under his hand Jerome began to consider whether it
might not be worth his while to use them in the composition of one or more
volumes. In 1535 he delivered as Plat lecturer his address, the _Encomium
Geometriæ_, which he followed up shortly after by the publication of a
work, _Quindecim Libri Novæ Geometriæ_. But the most profitable labour of
these years was that which produced his first important book, _The
Practice of Arithmetic and Simple Mensuration_, which was published in
1539, a venture which brought to the author a reward of ten crowns.[84] It
was a well-planned and well-arranged manual, giving proof of the wide
erudition and sense of proportion possessed by the author. Besides dealing
with Arithmetic as understood by the modern school-boy, it discusses
certain astronomical operations, multiplication by memory, the mysteries
of the Roman and Ecclesiastical Calendars, and gives rules for the
solution of any problem arising from the terms of the same. It treats of
partnership in agriculture, the Mezzadria system still prevalent in
Tuscany and in other parts of Italy, of the value of money, of the strange
properties of certain numbers, and gives the first simple rules of Algebra
to serve as stepping-stones to the higher mathematics. It ends with
information as to house-rent, letters of credit and exchange, tables of
interest, games of chance, mensuration, and weights and measures. In an
appendix Cardan examines critically the work of Fra Luca Pacioli da Borgo,
an earlier writer on the subject, and points out numerous errors in the
same. The book from beginning to end shows signs of careful study and
compilation, and the fame which it brought to its author was well
deserved.

Cardan appended to the Arithmetic a printed notice which may be regarded
as an early essay in advertising. He was fully convinced that his works
were valuable and quite worth the sums of money he asked for them; the
world was blind, perhaps wilfully, to their merits, therefore he now
determined that it should no longer be able to quote ignorance of the
author as an excuse for not buying the book. This appendix was a
notification to the learned men of Europe that the writer of the _Practice
of Arithmetic_ had in his press at home thirty-four other works in MS.
which they might read with profit, and that of these only two had been
printed, to wit the _De Malo Medendi Usu_ and a tract on _Simples_. This
advertisement had something of the character of a legal document, for it
invoked the authority of the Emperor to protect the copyright of Cardan's
books within the Duchy of Milan for ten years, and to prevent the
introduction of them from abroad.

The Arithmetic proved far superior to any other treatise extant, and
everywhere won the approval of the learned. It was from Nuremberg that its
appearance brought the most valuable fruits. Andreas Osiander,[85] a
learned humanist and a convert to Lutheranism, and Johannes Petreius, an
eminent printer, were evidently impressed by the terms of Cardan's
advertisement, for they wrote to him and offered in combination to edit
and print any of the books awaiting publication in his study at Milan. The
result of this offer was the reprinting of _De Malo Medendi_, and
subsequently of the tract on Judicial Astrology, and of the treatise _De
Consolatione_; the _Book of the Great Art_, the treatises _De Sapientia_
and _De Immortalitate Animorum_ were published in the first instance by
these same patrons from the Nuremberg press.

But Cardan, while he was hard at work on his Arithmetic, had not forgotten
a certain report which had caused no slight stir in the world of
Mathematics some three years before the issue of his book on Arithmetic,
an episode which may be most fittingly told in his own words. "At this
time[86] it happened that there came to Milan a certain Brescian named
Giovanni Colla, a man of tall stature, and very thin, pale, swarthy, and
hollow-eyed. He was of gentle manners, slow in gait, sparing of his words,
full of talent, and skilled in mathematics. His business was to bring word
to me that there had been recently discovered two new rules in Algebra for
the solution of problems dealing with cubes and numbers. I asked him who
had found them out, whereupon he told me the name of the discoverer was
Scipio Ferreo of Bologna. 'And who else knows these rules?' I said. He
answered, 'Niccolo Tartaglia and Antonio Maria Fiore.' And indeed some
time later Tartaglia, when he came to Milan, explained them to me, though
unwillingly; and afterwards I myself, when working with Ludovico
Ferrari,[87] made a thorough study of the rules aforesaid. We devised
certain others, heretofore unnoticed, after we had made trial of these new
rules, and out of this material I put together my _Book of the Great
Art_."[88]

Before dealing with the events which led to the composition of the famous
work above-named, it may be permitted to take a rapid survey of the
condition of Algebra at the time when Cardan sat down to write. Up to the
beginning of the sixteenth century the knowledge of Algebra in Italy,
originally derived from Greek and Arabic sources, had made very little
progress, and the science had been developed no farther than to provide
for the solution of equations of the first or second degree.[89] In the
preface to the _Liber Artis Magnæ_ Cardan writes:--"This art takes its
origin from a certain Mahomet, the son of Moses, an Arabian, a fact to
which Leonard the Pisan bears ample testimony. He left behind him four
rules, with his demonstrations of the same, which I duly ascribe to him in
their proper place. After a long interval of time, some student, whose
identity is uncertain, deduced from the original four rules three others,
which Luca Paciolus put with the original ones into his book. Then three
more were discovered from the original rules, also by some one unknown,
but these attracted very little notice though they were far more useful
than the others, seeing that they taught how to arrive at the value of the
_cubus_ and the _numerus_ and of the _cubus quadratus_.[90] But in recent
times Scipio Ferreo of Bologna discovered the rule of the _cubus_ and the
_res_ equal to the _numerus_ (_x^3 + px=q_), truly a beautiful and
admirable discovery. For this Algebraic art outdoes all other subtlety of
man, and outshines the clearest exposition mortal wit can achieve: a
heavenly gift indeed, and a test of the powers of a man's mind. So
excellent is it in itself that whosoever shall get possession thereof,
will be assured that no problem exists too difficult for him to
disentangle. As a rival of Ferreo, Niccolo Tartaglia of Brescia, my
friend, at that time when he engaged in a contest with Antonio Maria
Fiore, the pupil of Ferreo, made out this same rule to help secure the
victory, and this rule he imparted to me after I had diligently besought
him thereanent. I, indeed, had been deceived by the words of Luca
Paciolus, who denied that there could be any general rule besides these
which he had published, so I was not moved to seek that which I despaired
of finding; but, having made myself master of Tartaglia's method of
demonstration, I understood how many other results might be attained; and,
having taken fresh courage, I worked these out, partly by myself and
partly by the aid of Ludovico Ferrari, a former pupil of mine. Now all the
discoveries made by the men aforesaid are here marked with their names.
Those unsigned were found out by me; and the demonstrations are all mine,
except three discovered by Mahomet and two by Ludovico."[91]

This is Cardan's account of the scheme and origin of his book, and the
succeeding pages will be mainly an amplification thereof. The earliest
work on Algebra used in Italy was a translation of the MS. treatise of
Mahommed ben Musa of Corasan, and next in order is a MS. written by a
certain Leonardo da Pisa in 1202. Leonardo was a trader, who had learned
the art during his voyages to Barbary, and his treatise and that of
Mahommed were the sole literature on the subject up to the year 1494, when
Fra Luca Pacioli da Borgo[92] brought out his volume treating of
Arithmetic and Algebra as well. This was the first printed work on the
subject.

After the invention of printing the interest in Algebra grew rapidly. From
the time of Leonardo to that of Fra Luca it had remained stationary. The
important fact that the resolution of all the cases of a problem may be
comprehended in a simple formula, which may be obtained from the solution
of one of its cases merely by a change of the signs, was not known, but in
1505 the Scipio Ferreo alluded to by Cardan, a Bolognese professor,
discovered the rule for the solution of one case of a compound cubic
equation. This was the discovery that Giovanni Colla announced when he
went to Milan in 1536.

Cardan was then working hard at his Arithmetic--which dealt also with
elementary Algebra--and he was naturally anxious to collect in its pages
every item of fresh knowledge in the sphere of mathematics which might
have been discovered since the publication of the last treatise. The fact
that Algebra as a science had made such scant progress for so many years,
gave to this new process, about which Giovanni Colla was talking, an
extraordinary interest in the sight of all mathematical students;
wherefore when Cardan heard the report that Antonio Maria Fiore, Ferreo's
pupil, had been entrusted by his master with the secret of this new
process, and was about to hold a public disputation at Venice with Niccolo
Tartaglia, a mathematician of considerable repute, he fancied that
possibly there would be game about well worth the hunting.

Fiore had already challenged divers opponents of less weight in the other
towns of Italy, but now that he ventured to attack the well-known Brescian
student, mathematicians began to anticipate an encounter of more than
common interest. According to the custom of the time, a wager was laid on
the result of the contest, and it was settled as a preliminary that each
one of the competitors should ask of the other thirty questions. For
several weeks before the time fixed for the contest Tartaglia studied
hard; and such good use did he make of his time that, when the day of the
encounter came, he not only fathomed the formula upon which Fiore's hopes
were based, but, over and beyond this, elaborated two other cases of his
own which neither Fiore nor his master Ferreo had ever dreamt of.

The case which Ferreo had solved by some unknown process was the equation
_x^3 + px = q_, and the new forms of cubic equation which Tartaglia
elaborated were as follows: _x^3 + px^2 = q_: and _x^3 - px^2 = q_. Before
the date of the meeting, Tartaglia was assured that the victory would be
his, and Fiore was probably just as confident. Fiore put his questions,
all of which hinged upon the rule of Ferreo which Tartaglia had already
mastered, and these questions his opponent answered without difficulty;
but when the turn of the other side came, Tartaglia completely puzzled the
unfortunate Fiore, who managed indeed to solve one of Tartaglia's
questions, but not till after all his own had been answered. By this
triumph the fame of Tartaglia spread far and wide, and Jerome Cardan, in
consequence of the rumours of the Brescian's extraordinary skill, became
more anxious than ever to become a sharer in the wonderful secret by means
of which he had won his victory.

Cardan was still engaged in working up his lecture notes on Arithmetic
into the Treatise when this contest took place; but it was not till four
years later, in 1539, that he took any steps towards the prosecution of
his design. If he knew anything of Tartaglia's character, and it is
reasonable to suppose that he did, he would naturally hesitate to make any
personal appeal to him, and trust to chance to give him an opportunity of
gaining possession of the knowledge aforesaid, rather than seek it at the
fountain-head. Tartaglia was of very humble birth, and according to report
almost entirely self-educated. Through a physical injury which he met with
in childhood his speech was affected; and, according to the common Italian
usage, a nickname[93] which pointed to this infirmity was given to him.
The blow on the head, dealt to him by some French soldier at the sack of
Brescia in 1512, may have made him a stutterer, but it assuredly did not
muddle his wits; nevertheless, as the result of this knock, or for some
other cause, he grew up into a churlish, uncouth, and ill-mannered man,
and, if the report given of him by Papadopoli[94] at the end of his
history be worthy of credit, one not to be entirely trusted as an
autobiographer in the account he himself gives of his early days in the
preface to one of his works. Papadopoli's notice of him states that he was
in no sense the self-taught scholar he represented himself to be, but that
he was indebted for some portion at least of his training to the
beneficence of a gentleman named Balbisono,[95] who took him to Padua to
study. From the passage quoted below he seems to have failed to win the
goodwill of the Brescians, and to have found Venice a city more to his
taste. It is probable that the contest with Fiore took place after his
final withdrawal from his birthplace to Venice.

In 1537 Tartaglia published a treatise on Artillery, but he gave no sign
of making public to the world his discoveries in Algebra. Cardan waited
on, but the morose Brescian would not speak, and at last he determined to
make a request through a certain Messer Juan Antonio, a bookseller, that,
in the interests of learning, he might be made a sharer of Tartaglia's
secret. Tartaglia has given a version of this part of the transaction;
and, according to what is there set down, Cardan's request, even when
recorded in Tartaglia's own words, does not appear an unreasonable one,
for up to this time Tartaglia had never announced that he had any
intention of publishing his discoveries as part of a separate work on
Mathematics. There was indeed a good reason why he should refrain from
doing this in the fact that he could only speak and write Italian, and
that in the Brescian dialect, being entirely ignorant of Latin, the only
tongue which the writer of a mathematical work could use with any hope of
success. Tartaglia's record of his conversation with Messer Juan Antonio,
the emissary employed by Cardan, and of all the subsequent details of the
controversy, is preserved in his principal work, _Quesiti et Inventioni
Diverse de Nicolo Tartalea Brisciano_,[96] a record which furnishes
abundant and striking instance of his jealous and suspicious temper. Much
of it is given in the form of dialogue, the terms of which are perhaps a
little too precise to carry conviction of its entire sincerity and
spontaneity. It was probably written just after the final cause of quarrel
in 1545, and its main object seems to be to set the author right in the
sight of the world, and to exhibit Cardan as a meddlesome fellow not to be
trusted, and one ignorant of the very elements of the art he professed to
teach.[97]

The inquiry begins with a courteously worded request from Messer Juan
Antonio (speaking on behalf of Messer Hieronimo Cardano), that Messer
Niccolo would make known to his principal the rule by means of which he
had made such short work of Antonio Fiore's thirty questions. It had been
told to Messer Hieronimo that Fiore's thirty questions had led up to a
case of the _cosa_ and the _cubus_ equal to the _numerus_, and that
Messer Niccolo had discovered a general rule for such case. Messer
Hieronimo now especially desired to be taught this rule. If the inventor
should be willing to let this rule be published, it should be published as
his own discovery; but, if he were not disposed to let the same be made
known to the world, it should be kept a profound secret. To this request
Tartaglia replied that, if at any time he might publish his rule, he would
give it to the world in a work of his own under his own name, whereupon
Juan Antonio moderated his demand, and begged to be furnished merely with
a copy of the thirty questions preferred by Fiore, and Tartaglia's
solutions of the same; but Messer Niccolo was too wary a bird to be taken
with such a lure as this. To grant so much, he replied, would be to tell
everything, inasmuch as Cardan could easily find out the rule, if he
should be furnished with a single question and its solution. Next Juan
Antonio handed to Tartaglia eight algebraical questions which had been
confided to him by Cardan, and asked for answers to them; but Tartaglia,
having glanced at them, declared that they were not framed by Cardan at
all, but by Giovanni Colla. Colla, he declared, had sent him one of these
questions for solution some two years ago. Another, he (Tartaglia) had
given to Colla, together with a solution thereof. Juan Antonio replied by
way of contradiction--somewhat lamely--that the questions had been handed
over to him by Cardan and no one else, wishing to maintain, apparently,
that no one else could possibly have been concerned in them, whereupon
Tartaglia replied that, supposing the questions had been given by Cardan
to Juan Antonio his messenger, Cardan must have got the questions from
Colla, and have sent them on to him (Tartaglia) for solution because he
could not arrive at the meaning of them himself. He waved aside Juan
Antonio's perfectly irrelevant and fatuous protests--that Cardan would not
in any case have sent these questions if they had been framed by another
person, or if he had been unable to solve them. Tartaglia, on the other
hand, declared that Cardan certainly did not comprehend them. If he did
not know the rule by which Fiore's questions had been answered (that of
the _cosa_ and the _cubus_ equal to the _numerus_), how could he solve
these questions which he now sent, seeing that certain of them involved
operations much more complicated than that of the rule above written? If
he understood the questions which he now sent for solution, he could not
want to be taught this rule. Then Juan Antonio moderated his demand still
farther, and said he would be satisfied with a copy of the questions which
Fiore had put to Tartaglia, adding that the favour would be much greater
if Tartaglia's own questions were also given. He probably felt that it
would be mere waste of breath to beg again for Tartaglia's answers. The
end of the matter was that Tartaglia handed over to the messenger the
questions which Fiore had propounded in the Venetian contest, and
authorized Juan Antonio to get a copy of his own from the notary who had
drawn up the terms of the disputation with Fiore. The date of this
communication is January 2, 1539, and on February 12 Cardan writes a long
letter to Tartaglia, complaining in somewhat testy spirit of the reception
given to his request. He is aggrieved that Tartaglia should have sent him
nothing but the questions put to him by Fiore, thirty in number indeed,
but only one in substance, and that he should have dared to hint that
those which he (Cardan) had sent for solution were not his own, but the
property of Giovanni Colla. Cardan had found Colla to be a conceited fool,
and had dragged the conceit out of him--a process which he was now about
to repeat for the benefit of Messer Niccolo Tartaglia. The letter goes on
to contradict all Tartaglia's assertions by arguments which do not seem
entirely convincing, and the case is not made better by the abusive
passages interpolated here and there, and by the demonstration of certain
errors in Tartaglia's book on Artillery. In short a more injudicious
letter could not have been written by any man hoping to get a favour done
to him by the person addressed.

In the special matter of the problems which he sent to Tartaglia by the
bookseller Juan Antonio, Cardan made a beginning of that tricky and
crooked course which he followed too persistently all through this
particular business. In his letter he maintains with a show of indignation
that he had long known these questions, had known them in fact before
Colla knew how to count ten, implying by these words that he knew how to
solve them, while in reality all he knew about them was the fact that they
existed. Tartaglia in his answer is not to be moved from his belief, and
tells Cardan flatly that he is still convinced Giovanni Colla took the
questions to Milan, where he found no one able to solve them, not even
Messer Hieronimo Cardano, and that the mathematician last-named sent them
on by the bookseller for solution, as has been already related.

This letter of Tartaglia's bears the date of February 13, 1539, and after
reading it and digesting its contents, Cardan seems to have come to the
conclusion that he was not working in the right way to get possession of
this secret which he felt he must needs master, if he wanted his
forthcoming book to mark a new epoch in this History of Mathematics, and
that a change of tactics was necessary. Alfonso d'Avalos, Cardan's friend
and patron, was at this time the Governor of Milan. D'Avalos was a man of
science, as well as a soldier, and Cardan had already sent to him a copy
of Tartaglia's treatise on Artillery, deeming that a work of this kind
would not fail to interest him. In his first letter to Tartaglia he
mentions this fact, while picking holes in the writer's theories
concerning transmitted force and views on gravitation. This mention of the
name of D'Avalos, the master of many legions and of many cannons as well,
to a man who had written a Treatise on the management of Artillery, and
devised certain engines and instruments for the management of the same,
was indeed a clever cast, and the fly was tempting enough to attract even
so shy a fish as Niccolo Tartaglia. In his reply to Jerome's scolding
letter of February 12, 1539, Tartaglia concludes with a description of the
instruments which he was perfecting: a square to regulate the discharge of
cannon, and to level and determine every elevation; and another instrument
for the investigation of distances upon a plane surface. He ends with a
request that Cardan will accept four copies of the engines aforesaid, two
for himself and two for the Marchese d'Avalos.

The tone of this letter shows that Cardan had at least begun to tame the
bear, who now seemed disposed to dance _ad libitum_ to the pleasant music
of words suggesting introductions to the governor, and possible patronage
of these engines for the working of artillery. Cardan's reply of March 19,
1539, is friendly--too friendly indeed--and the wonder is that Tartaglia's
suspicions were not aroused by its almost sugary politeness. It begins
with an attempt to soften down the asperities of their former
correspondence, some abuse of Giovanni Colla, and an apology for the rough
words of his last epistle. Cardan then shows how their misunderstanding
arose chiefly from a blunder made by Juan Antonio in delivering the
message, and invites Tartaglia to come and visit him in his own house in
Milan, so that they might deliberate together on mathematical questions;
but the true significance of the letter appears in the closing lines. "I
told the Marchese of the instruments which you had sent him, and he showed
himself greatly pleased with all you had done. And he commanded me to
write to you forthwith in pressing terms, and to tell you that, on the
receipt of my letter, you should come to Milan without fail, for he
desires to speak with you. And I, too, exhort you to come at once without
further deliberation, seeing that this said Marchese is wonted to reward
all men of worth in such noble and magnanimous and liberal fashion that
none of them ever goes away dissatisfied."

The receipt of this letter seems to have disquieted Tartaglia somewhat;
for he has added a note to it, in which he says that Cardan has placed him
in a position of embarrassment. He had evidently wished for an
introduction to D'Avalos, but now it was offered to him it seemed a burden
rather than a benefit. He disliked the notion of going to Milan; yet, if
he did not go, the Marchese d'Avalos might take offence. But in the end he
decided to undertake the journey; and, as D'Avalos happened then to be
absent from Milan on a visit to his country villa at Vigevano, he stayed
for three days in Cardan's house. As a recorder of conversations Tartaglia
seems to have had something of Boswell's gift. He gives an abstract of an
eventful dialogue with his host on March 25, 1539, which Cardan begins by
a gentle reproach anent his guest's reticence in the matter of the rule of
the _cosa_ and the _cubus_ equal to the _numerus_. Tartaglia's reply to
this complaint seems reasonable enough (it must be borne in mind that he
is his own reporter), and certainly helps to absolve him from the charge
sometimes made against him that he was nothing more than a selfish
curmudgeon who had resolved to let his knowledge die with him, rather than
share it with other mathematicians of whom he was jealous. He told Cardan
plainly that he kept his rules a secret because, for the present, it
suited his purpose to do so. At this time he had not the leisure to
elaborate farther the several rules in question, being engaged over a
translation of Euclid into Italian; but, when this work should be
completed, he proposed to publish a treatise on Algebra in which he would
disclose to the world all the rules he already knew, as well as many
others which he hoped to discover in the course of his present work. He
concludes: "This is the cause of my seeming discourtesy towards your
excellency. I have been all the ruder, perhaps, because you write to me
that you are preparing a book similar to mine, and that you propose to
publish my inventions, and to give me credit for the same. This I confess
is not to my taste, forasmuch as I wish to set forth my discoveries in my
own works, and not in those of others." In his reply to this, Cardan
points out that he had promised, if Tartaglia so desired, that he would
not publish the rules at all; but here Messer Niccolo's patience and good
manners gave way, and he told Messer Hieronimo bluntly that he did not
believe him. Then said Cardan: "I swear to you by the Sacred Evangel, and
by myself as a gentleman, that I will not only abstain from publishing
your discoveries--if you will make them known to me--but that I will
promise and pledge my faith of a true Christian to set them down for my
own use in cypher, so that after my death no one may be able to understand
them. If you will believe this promise, believe it; if you will not, let
us have done with the matter." "If I were not disposed to believe such
oaths as these you now swear," said Tartaglia, "I might as well be set
down as a man without any faith at all. I have determined to go forthwith
to Vigevano to visit the Signor Marchese, as I have now been here for
three days and am weary of the delay, but I promise when I return that I
will show you all the rules." Cardan replied: "As you are bent on going to
Vigevano, I will give you a letter of introduction to the Marchese, so
that he may know who you are; but I would that, before you start, you show
me the rule as you have promised." "I am willing to do this," said
Tartaglia, "but I must tell you that, in order to be able to recall at any
time my system of working, I have expressed it in rhyme; because, without
this precaution, I must often have forgotten it. I care naught that my
rhymes are clumsy, it has been enough for me that they have served to
remind me of my rules. These I will write down with my own hand, so that
you may be assured that my discovery is given to you correctly." Then
follow Tartaglia's verses:

    "Quando chel cubo con le cose apresso
    Se agualia à qualche numero discreto
    Trouan dui altri differenti in esso
    Dapoi terrai questo per consueto
    Ch'el lor' produtto sempre sia eguale
    Al terzo cubo delle cose neto
    El residuo poi suo generale
    Delli lor lati cubi ben sottratti
    Varra la tua cosa principale.
    In el secondo de cotesti atti
    Quando chel cubo restasse lui solo
    Tu osseruarai quest' altri contratti
    Del numer farai due tal part 'a uolo
    Che luna in l'altra si produca schietto
    El terzo cubo delle cose in stolo
    Delle qual poi, per commun precetto
    Torrai li lati cubi insieme gionti
    Et cotal summa sara il tuo concetto
    Et terzo poi de questi nostri conti
    Se solve col recordo se ben guardi
    Che per natura son quasi congionti
    Questi trouai, et non con passi tardi
    Nel mille cinquecent' e quatro è trenta
    Con fondamenti ben sald' è gagliardi
    Nella citta del mar' intorno centa."

Having handed over to his host these rhymes, with the precious rules
enshrined therein, Tartaglia told him that, with so clear an exposition,
he could not fail to understand them, ending with a warning hint to Cardan
that, if he should publish the rules, either in the work he had in hand,
or in any future one, either under the name of Tartaglia or of Cardan, he,
the author, would put into print certain things which Messer Hieronimo
would not find very pleasant reading.

After all Tartaglia was destined to quit Milan without paying his respects
to D'Avalos. There is not a word in his notes which gives the reason of
this eccentric action on his part. He simply says that he is no longer
inclined to go to Vigevano, but has made up his mind to return to Venice
forthwith; and Cardan, probably, was not displeased at this exhibition of
petulant impatience on the part of his guest, but was rather somewhat
relieved to see Messer Niccolo ride away, now that he had extracted from
him the coveted information. From the beginning to the end of this affair
Cardan has been credited with an amount of subtle cunning which he
assuredly did not manifest at other times when his wits were pitted for
contest with those of other men. It has been advanced to his disparagement
that he walked in deceitful ways from the very beginning; that he dangled
before Tartaglia's eyes the prospect of gain and preferment simply for the
purpose of enticing him to Milan, where he deemed he might use more
efficaciously his arguments for the accomplishment of the purpose which
was really in his mind; that he had no intention of advancing Tartaglia's
fortunes when he suggested the introduction to D'Avalos, but that the
Governor of Milan was brought into the business merely that he might be
used as a potent ally in the attack upon Tartaglia's obstinate silence.
Whether this may have been his line of action or not, the issue shows that
he was fully able to fight his battle alone, and that his powers of
persuasion and hard swearing were adequate when occasion arose for their
exercise. It is quite possible that Tartaglia, when he began to reflect
over what he had done by writing out and handing over to Cardan his
mnemonic rhymes, fell into an access of suspicious anger--at Cardan for
his wheedling persistency, and at himself for yielding thereto--and packed
himself off in a rage with the determination to have done with Messer
Hieronimo and all his works. Certainly his carriage towards Cardan in the
weeks ensuing, as exhibited in his correspondence, does not picture him in
an amiable temper. On April 9 Jerome wrote to him in a very friendly
strain, expressing regret that his guest should have left Milan without
seeing D'Avalos, and fear lest he might have prejudiced his fortunes by
taking such a step. He then goes on to describe to Tartaglia the progress
he is making in his work with the Practice of Arithmetic, and to ask him
for help in solving one of the cases in Algebra, the rule for which was
indeed contained in Tartaglia's verses, but expressed somewhat obscurely,
for which reason Cardan had missed its meaning.[98] In his reply,
Tartaglia ignores Jerome's courtesies altogether, and tells him that what
he especially desires at the present moment is a sight of that volume on
the Practice of Arithmetic, "for," says he, "if I do not see it soon, I
shall begin to suspect that this work of yours will probably make manifest
some breach of faith; in other words, that it will contain as
interpolations certain of the rules I taught you." Niccolo then goes on to
explain the difficulty which had puzzled Cardan, using terms which showed
plainly that he had as poor an opinion of his correspondent's wit as of
his veracity.

Cardan was an irascible man, and it is a high tribute to his powers of
restraint that he managed to keep his temper under the uncouth insults of
such a letter as the foregoing. The more clearly Tartaglia's jealous,
suspicious nature displays itself, the greater seems the wonder that a man
of such a disposition should ever have disclosed such a secret. He did not
believe Cardan when he promised that he would not publish the rules in
question without his (the discoverer's) consent--why then did he believe
him when he swore by the Gospel? The age was one in which the binding
force of an oath was not regarded as an obligation of any particular
sanctity if circumstances should arise which made the violation of the
oath more convenient than its observance. However, the time was not yet
come for Jerome to begin to quibble with his conscience. On May 12, 1539,
he wrote another letter to Tartaglia, also in a very friendly tone,
reproaching him gently for his suspicions, and sending a copy of the
_Practice of Arithmetic_ to show him that they were groundless. He
protested that Tartaglia might search from beginning to end without
finding any trace of his jealously-guarded rules, inasmuch as, beyond
correcting a few errors, the writer had only carried Algebra to the point
where Fra Luca had left it. Tartaglia searched, and though he could not
put his finger on any spot which showed that Messer Hieronimo had broken
his oath, he found what must have been to him as a precious jewel, to wit
a mistake in reckoning, which he reported to Cardan in these words:

"In this process your excellency has made such a gross mistake that I am
amazed thereat, forasmuch as any man with half an eye must have seen
it--indeed, if you had not gone on to repeat it in divers examples, I
should have set it down to a mistake of the printer." After pointing out
to Cardan the blunders aforesaid, he concludes: "The whole of this work of
yours is ridiculous and inaccurate, a performance which makes me tremble
for your good name."[99]

Every succeeding page of Tartaglia's notes shows more and more clearly
that he was smarting under a sense of his own folly in having divulged his
secret. Night and day he brooded over his excess of confidence, and as
time went by he let his suspicions of Cardan grow into savage resentment.
His ears were open to every rumour which might pass from one class-room to
another. On July 10 a letter came to him from one Maphio of Bergamo, a
former pupil, telling how Cardan was about to publish certain new
mathematical rules in a book on Algebra, and hinting that in all
probability these rules would prove to be Tartaglia's, whereupon he at
once jumped to the conclusion that Maphio's gossip was the truth, and that
this book would make public the secret which Cardan had sworn to keep. He
left many of Cardan's letters unanswered; but at last he seems to have
found too strong the temptation to say something disagreeable; so, in
answer to a letter from Cardan containing a request for help in solving an
equation which had baffled his skill, Tartaglia wrote telling Cardan that
he had bungled in his application of the rule, and that he himself was now
very sorry he had ever confided the rule aforesaid to such a man. He ends
with further abuse of Cardan's _Practice of Arithmetic_, which he declares
to be merely a confused farrago of other men's knowledge,[100] and with a
remark which he probably intended to be a crowning insult. "I well
remember when I was at your house in Milan, that you told me you had never
tried to discover the rule of the _cosa_ and the _cubus_ equal to the
_numerus_ which was found out by me, because Fra Luca had declared it to
be impossible;[101] as if to say that, if you had set yourself to the task
you could have accomplished it, a thing which sets me off laughing when I
call to mind the fact that it is now two months since I informed you of
the blunders you made in the extraction of the cube root, which process is
one of the first to be taught to students who are beginning Algebra.
Wherefore, if after the lapse of all this time you have not been able to
find a remedy to set right this your mistake (which would have been an
easy matter enough), just consider whether in any case your powers could
have been equal to the discovery of the rule aforesaid."[102]

In this quarrel Messer Giovanni Colla had appeared as the herald of the
storm, when he carried to Milan in 1536 tidings of the discovery of the
new rule which had put Cardan on the alert, and now, as the crisis
approached, he again came upon the scene, figuring as unconscious and
indirect cause of the final catastrophe. On January 5, 1540, Cardan wrote
to Tartaglia, telling him that Colla had once more appeared in Milan, and
was boasting that he had found out certain new rules in Algebra. He went
on to suggest to his correspondent that they should unite their forces in
an attempt to fathom this asserted discovery of Colla's, but to this
letter Tartaglia vouchsafed no reply. In his diary it stands with a
superadded note, in which he remarks that he thinks as badly of Cardan as
of Colla, and that, as far as he is concerned, they may both of them go
whithersoever they will.[103]

Colla propounded divers questions to the Algebraists of Milan, and
amongst them was one involving the equation _x^4 + 6x^2 + 36 = 60x_, one
which he probably found in some Arabian treatise. Cardan tried all his
ingenuity over this combination without success, but his brilliant pupil,
Ludovico Ferrari, worked to better purpose, and succeeded at last in
solving it by adding to each side of the equation, arranged in a certain
fashion, some quadratic and simple quantities of which the square root
could be extracted.[104] Cardan seems to have been baffled by the fact
that the equation aforesaid could not be solved by the recently-discovered
rules, because it produced a bi-quadratic. This difficulty Ferrari
overcame, and, pursuing the subject, he discovered a general rule for the
solution of all bi-quadratics by means of a cubic equation. Cardan's
subsequent demonstration of this process is one of the masterpieces of the
_Book of the Great Art_. It is an example of the use of assuming a new
indeterminate quantity to introduce into an equation, thus anticipating by
a considerable space of time Descartes, who subsequently made use of a
like assumption in a like case.

How far this discovery of Ferrari's covered the rules given by Tartaglia
to Cardan, and how far it relieved Cardan of the obligation of secresy, is
a problem fitted for the consideration of the mathematician and the
casuist severally.[105] An apologist of Cardan might affirm that he cannot
be held to have acted in bad faith in publishing the result of Ferrari's
discovery. If this discovery included and even went beyond Tartaglia's, so
much the worse for Tartaglia. The lesser discovery (Tartaglia's) Cardan
never divulged before Ferrari unravelled Giovanni Colla's puzzle; but it
was inevitable that it must be made known to the world as a part of the
greater discovery (Ferrari's) which Cardan was in no way bound to keep a
secret. The case might be said to run on all fours with that where a man
confides a secret to a friend under a promise of silence, which promise
the friend keeps religiously, until one day he finds that the secret, and
even more than the secret, is common talk of the market-place. Is the
obligation of silence, with which he was bound originally, still to lie
upon the friend, even when he may have sworn to observe it by the Holy
Evangel and the honour of a gentleman; and is the fact that great renown
and profit would come to him by publishing the secret to be held as an
additional reason for keeping silence, or as a justification for speech?
In forming a judgment after a lapse of three and a half centuries as to
Cardan's action, while having regard both to the sanctity of an oath at
the time in question, and to the altered state of the case between him and
Tartaglia consequent on Ludovico Ferrari's discovery, an hypothesis not
overstrained in the direction of charity may be advanced to the effect
that Cardan might well have deemed he was justified in revealing to the
world the rules which Tartaglia had taught him, considering that these
isolated rules had been developed by his own study and Ferrari's into a
principle by which it would be possible to work a complete revolution in
the science of Algebra.

In any case, six years were allowed to elapse before Cardan, by publishing
Tartaglia's rules in the _Book of the Great Art_, did the deed which, in
the eyes of many, branded him as a liar and dishonest, and drove
Tartaglia almost wild with rage. That his offence did not meet with
universal reprobation is shown by negative testimony in the _Judicium de
Cardano_, by Gabriel Naudé.[106] In the course of his essay Naudé lets it
be seen how thoroughly he dislikes the character of the man about whom he
writes. No evil disposition attributed to Cardan by himself or by his
enemies is left unnoticed, and a lengthy catalogue of his offences is set
down, but this list does not contain the particular sin of broken faith in
the matter of Tartaglia's rules. On the contrary, after abusing and
ridiculing a large portion of his work, Naudé breaks out into almost
rhapsodical eulogy about Cardan's contributions to Mathematical science.
"Quis negabit librum de Proportionibus dignum esse, qui cum pulcherrimis
antiquorum inventis conferatur? Quis in Arithmetica non stupet, eum tot
difficultates superasse, quibus explicandis Villafrancus, Lucas de Burgo,
Stifelius, Tartalea, vix ac ne vix quidem pares esse potuissent?" It seems
hard to believe, after reading elsewhere the bitter assaults of
Naudé,[107] that he would have neglected so tempting an opportunity of
darkening the shadows, if he himself had felt the slightest offence, or if
public opinion in the learned world was in any perceptible degree
scandalized by the disclosure made by the publication of the _Book of the
Great Art_.

This book was published at Nuremberg in 1545, and in its preface and
dedication Cardan fully acknowledges his obligations to Tartaglia and
Ferrari, with respect to the rules lately discussed, and gives a catalogue
of the former students of the Art, and attributes to each his particular
contribution to the mass of knowledge which he here presents to the world.
Leonardo da Pisa,[108] Fra Luca da Borgo, and Scipio Ferreo all receive
due credit for their work, and then Cardan goes on to speak of "my friend
Niccolo Tartaglia of Brescia, who, in his contest with Antonio Maria
Fiore, the pupil of Ferreo, elaborated this rule to assure him of victory,
a rule which he made known to me in answer to my many prayers." He goes on
to acknowledge other obligations to Tartaglia:[109] how the Brescian had
first taught him that algebraical discovery could be most effectively
advanced by geometrical demonstration, and how he himself had followed
this counsel, and had been careful to give the demonstration aforesaid for
every rule he laid down.

The _Book of the Great Art_ was not published till six years after Cardan
had become the sharer of Tartaglia's secret, which had thus had ample time
to germinate and bear fruit in the fertile brain upon which it was cast.
It is almost certain that the treatise as a whole--leaving out of account
the special question of the solution of cubic equations--must have gained
enormously in completeness and lucidity from the fresh knowledge revealed
to the writer thereof by Tartaglia's reluctant disclosure, and, over and
beyond this, it must be borne in mind that Cardan had been working for
several years at Giovanni Colla's questions in conjunction with Ferrari,
an algebraist as famous as Tartaglia or himself. The opening chapters of
the book show that Cardan was well acquainted with the chief properties of
the roots of equations of all sorts. He lays it down that all square
numbers have two different kinds of root, one positive and one
negative,[110] _vera_ and _ficta_: thus the root of 9 is either 3. or -3.
He shows that when a case has all its roots, or when none are impossible,
the number of its positive roots is the same as the number of changes in
the signs of the terms when they are all brought to one side. In the case
of _x^3 + 3bx = 2c_, he demonstrates his first resolution of a cubic
equation, and gives his own version of his dealings with Tartaglia. His
chief obligation to the Brescian was the information how to solve the
three cases which follow, _i.e. x^3 + bx = c. x^3 = bx + c._ and
_x^3 + c = bx_, and this he freely acknowledges, and furthermore admits
the great service of the system of geometrical demonstration which
Tartaglia had first suggested to him, and which he always employed
hereafter. He claims originality for all processes in the book not
ascribed to others, asserting that all the demonstrations of existing
rules were his own except three which had been left by Mahommed ben Musa,
and two invented by Ludovico Ferrari.

With this vantage ground beneath his feet Cardan raised the study of
Algebra to a point it had never reached before, and climbed himself to a
height of fame to which Medicine had not yet brought him. His name as a
mathematician was known throughout Europe, and the success of his book
was remarkable. In the _De Libris Propriis_ there is a passage which
indicates that he himself was not unconscious of the renown he had won, or
disposed to underrate the value of his contribution to mathematical
science. "And even if I were to claim this art (Algebra) as my own
invention, I should perhaps be speaking only the truth, though Nicomachus,
Ptolemæus, Paciolus, Boetius, have written much thereon. For men like
these never came near to discover one-hundredth part of the things
discovered by me. But with regard to this matter--as with divers others--I
leave judgment to be given by those who shall come after me. Nevertheless
I am constrained to call this work of mine a perfect one, seeing that it
well-nigh transcends the bounds of human perception."[111]

FOOTNOTES:

[84] It was published at Milan by Bernardo Caluschio, with a
dedication--dated 1537--to Francesco Gaddi, a descendant of the famous
family of Florence. This man was Prior of the Augustinian Canons in Milan,
and a great personage, but ill fortune seems to have overtaken him in his
latter days. Cardan writes (_Opera_, tom. i. p. 107):--"qui cum mihi
amicus esset dum floreret, Rexque cognomine ob potentiam appellaretur,
conjectus in carcerem, miseré vitam ibi, ne dicam crudeliter, finivit: nam
per quindecim dies in profundissima gorgyne fuit, ut vivus sepeliretur."

[85] There is a reference to Osiander in _De Subtilitate_, p. 523. Cardan
gives a full account of his relations with Osiander and Petreius in
_Opera_, tom. i. p. 67.

[86] November 1536.

[87] Ferrari was one of Cardan's most distinguished pupils. "Ludovicus
Ferrarius Bononiensis qui Mathematicas et Mediolani et in patria sua
professus est, et singularis in illis eruditionis."--_De Vita Propria_,
ch. xxxv. p. 111. There is a short memoir of Ferrari in _Opera_, tom. ix.

[88] _Opera_, tom. i. p. 66.

[89] Fra Luca's book, _Summa de Arithmetica Geometria Proportioni é
Proportionalita_, extends as far as the solution of quadratic equations,
of which only the positive roots were used. At this time letters were
rarely used to express known quantities.

[90] The early writers on Algebra used _numerus_ for the absolute or known
term, _res_ or _cosa_ for the first power, _quadratum_ for the second, and
_cubus_ for the third. The signs + and - first appear in the work of
Stifelius, a German writer, who published a book of Arithmetic in 1544.
Robert Recorde in his _Whetstone of Wit_ seems first to have used the sign
of equality =. Vieta in France first applied letters as general symbols of
quantity, though the earlier algebraists used them occasionally, chiefly
as abbreviations. Aristotle also used them in the _Physics.--Libri. Hist.
des Sciences Mathématiques_. i. 104.

[91] _Opera_, tom. iv. p. 222.

[92] In the conclusion of the Treatise on Arithmetic, Cardan points out
certain errors in the work of Fra Luca. Fra Luca was a pupil of Piero
della Francesca, who was highly skilled in Geometry, and who, according to
Vasari, first applied perspective to the drawing of the human form.

[93] Tartaglia, _i.e._ the stutterer.

[94] Papadopoli, _Hist. Gymn. Pata._ (Ven. 1724).

[95] "Balbisonem post relatam jurisprudentiæ lauream redeuntem Brixiam
Nicolaus secutus est, cæpitque ex Mathematicis gloriam sibi ac divitias
parare, æque paupertatis impatiens, ac fortunæ melioris cupidus, quam dum
Brixiæ tuetur, homo morosæ, et inurbanæ rusticitatis prope omnium civium
odia sibi conciliavit. Quamobrem alibi vivere coactus, varias Italiæ urbes
incoluit, ac Ferrariæ, Parmæ, Mediolani, Romæ, Genuæ, arithmeticam,
geometricam, ceteraque quæ ad Mathesim pertinent, docuit; depugnavitque
scriptis accerrimis cum Cardano ac sibi ex illis quæsivit nomen et
gloriam. Tandem domicilium posuit Venetiis, ubi non a Senatoribus modo, ut
mos Venetus habet eruditorum hominum studiosissimus, maximi habitus est,
at etiam a variis Magnatum ac Principum legatis præmiis ac muneribus
auctus sortem, quam tamdiu expetierat visus sibi est conciliasse. Ergo
ratus se majorem, quam ut a civibus suis contemneretur, Brixiam rediit,
ubi spe privati stipendii Euclidis elementa explanare coepit; sed quæ
illum olim a civitate sua austeritas, rustica, acerba, morosa, depulerat,
eadem illum in eum apud omnes contemptum, et odium iterum dejicit, ut
exinde horrendus ac detestabilis omnibus fugere, atque iterum Venetias
confugere compulsus fuerit. Ibi persenex decessit."--Papadopoli, _Hist.
Gymn. Pata.,_ ii. p. 210.

[96] This work is the chief authority for the facts which follow. The
edition referred to is that of Venice, 1546. There is also a full account
of the same in Cossali, _Origine dell' Algebra_ (Parma, 1799). vol. ii. p.
96.

[97] _Quesiti et Inventioni_, p. 115.

[98] Cardan writes: "Vi supplico per l'amor che mi portati, et per
l'amicitia ch'è tra noi, che spero durara fin che viveremo, che mi mandati
sciolta questa questione. 1 cubo piu 3. cose egual à 10." Cardan had
mistaken (1/3 _b_)^3 for 1/3 _b_^3, or the cube of 1/3 of the co-efficient
for 1/3 of the cube of the co-efficient.--_Quesiti et Inventioni_ p. 124.

[99] _Quesiti et Inventioni_, p. 125.

[100] "Non ha datta fora tal opera come cose composto da sua testa ma come
cose ellette raccolte e copiate de diverse libri a penna."--_Quesiti et
Inventioni_, p. 127.

[101] Cardan repeats the remark in the first chapter of the _Liber Artis
Magnæ_ (_Opera_, tom. iv. p. 222). "Deceptus enim ego verbis Lucæ
Paccioli, qui ultra sua capitula, generale ullum aliud esse posse negat
(quanquam tot jam antea rebus a me inventis, sub manibus esset) desperabam
tamen invenire, quod quærere non audebam." Perhaps he wrote them down as
an apology or a defence against the storm which he anticipated as soon as
Tartaglia should have seen the new Algebra.

[102] Subsequently Tartaglia wrote very bitterly against Cardan, as the
latter mentions in _De Libris Propriis_. "Nam etsi Nicolaus Tartalea
libris materna lingua editis nos calumniatur, impudentiæ tamen ac
stultitiæ suæ non aliud testimonium quæras, quam ipsos illius libros, in
quibus nominatim splendidiorem unumquemque e civibus suis proscindit: adeò
ut nemo dubitet insanisse hominem aliquo infortunio."--_Opera_, tom. i. p.
80.

[103] _Quesiti et Inventioni_, p. 129.

[104] Montucla, _Histoire de Math._ i. 596, gives a full account of
Ferrari's process.

[105] In the _De Vita Propria_, Cardan dismisses the matter briefly: "Ex
hoc ad artem magnam, quam collegi, dum Jo. Colla certaret nobiscum, et
Tartalea, à quo primum acceperam capitulum, qui maluit æmulum habere, et
superiorem, quam amicum et beneficio devinctum, cum alterius fuisset
inventum."--ch. xlv. p. 175.

[106] Prefixed to the _De Vita Propria_.

[107] In a question of broken faith, Cardan laid himself open especially
to attack by reason of his constant self-glorification in the matter of
veracity.

[108] Leonardo knew that quadratic equations might have two positive
roots, and Cardan pursued this farther by the discovery that they might
also have negative roots.

[109] "Caput xxviii. De capitulo generali cubi et rerum æqualium numero,
Magistri Nicolai Tartagliæ, Brixiensis--Hoc capitulum habui à prefato viro
ante considerationem demonstrationum secundi libri super Euclidem, et
æquatio hæc cadit in [Symbol: Rx]. cu v binomii ex genere binomii secundi
et qunti [m~]. [Symbol: Rx]. cuba universali recisi ejusdem
binomii."--_Opera_, tom. iv. p. 341.

[110] Montucla, who as a historian of Mathematics has a strong bias
against Cardan, gives him credit for the discovery of the _fictæ radices_,
but on the other hand he attributes to Vieta Cardan's discovery of the
method of changing a complete cubic equation into one wanting the second
term.--Ed. 1729, p. 595.

[111] _Opera_, tom. i. p. 66.




CHAPTER VI


IT has been noted that Cardan quitted Pavia at the end of 1544 on account
of the bankruptcy of the University, and that in 1546 a generous offer was
made to him on condition of his entering the service of Pope Paul III.; an
offer which after some hesitation he determined to refuse. In the autumn
of this same year he resumed his teaching at Pavia, a fact which sanctions
the assumption that this luckless seat of learning must have been once
more in funds. In the year following, in 1547, there came to him another
offer of employment accompanied by terms still more munificent than the
Pope's, conveyed through Vesalius[112] and the ambassador of the King of
Denmark. "The emolument was to be a salary of three hundred gold crowns
per annum of the Hungarian currency, and in addition to these six hundred
more to be paid out of the tax on skins of price. This last-named money
differed in value by about an eighth from the royal coinage, and would be
somewhat slower in coming in. Also the security for its payment was not so
solid, and would in a measure be subject to risk. To this was farther
added maintenance for myself and five servants and three horses. This
offer I did not accept because the country was very cold and damp, and the
people well-nigh barbarians; moreover the rites and doctrines of religion
were quite foreign to those of the Roman Church."[113]

Cardan was now forty-six years of age, a mathematician of European fame,
and the holder of an honourable post at an ancient university, which he
might have exchanged for other employment quite as dignified and far more
lucrative. In dealing with a character as bizarre as his, it would be as a
rule unprofitable to search deeply for motives of action, but in this
instance it is no difficult matter to detect upon the surface several
causes which may have swayed him in this decision to remain at Pavia.
However firmly he may have set himself to win fame as a physician, he was
in no way disposed to put aside those mathematical studies in which he had
already made so distinguished a name, nor to abandon his astrology and
chiromancy and discursive reading of all kinds. At Pavia he would find
leisure for all these, and would in addition be able to make good any
arrears of medical and magical knowledge into which he might have fallen
during the years so largely devoted to the production of the _Book of the
Great Art_. Moreover, the time in question was one of the prime epochs in
the history of the healing art. A new light had just arisen in Vesalius,
who had recently published his book, _Corporis Humani Fabrica_, and was
lecturing in divers universities on the new method of Anatomy, the actual
dissection of the human body. He went to Pavia in the course of his
travels and left traces of his visit in the form of a revived and
re-organized school of Anatomy. This fact alone would have been a
powerful attraction to Cardan, ever greedy as he was of new knowledge, but
there was another reason which probably swayed him more strongly still, to
wit, the care of his eldest son's education and training. Gian Battista
Cardano was now in his fourteenth year, and, according to the usages of
the time, old enough to make a beginning of his training in Medicine, the
profession he was destined to follow. It is not recorded whether or not he
chose this calling for himself; but, taking into account the deep and
tender affection Jerome always manifested towards his eldest son, it is
not likely that undue compulsion was used in the matter. The youth,
according to his father's description, strongly favoured in person his
grandfather Fazio.[114] He had come into the world at a time when his
parents' fortunes were at their lowest ebb, during those terrible months
spent at Gallarate,[115] and in his adolescence he bore divers physical
evidences of the ill nurture--it would be unjust to call it neglect--which
he had received. At one time he was indeed put in charge of a good nurse,
but he had to be withdrawn from her care almost immediately through her
husband's jealousy, and he was next sent to a slattern, who fed him with
old milk, and not enough of that; or more often with chewed bread. His
body was swollen and unhealthy, he suffered greatly from an attack of
fever, which ultimately left him deaf in one ear. He gave early evidence
of a fine taste in music, an inheritance from his father, and was,
according to Cardan's showing, upright and honest in his carriage, gifted
with talents which must, under happier circumstances, have placed him in
the first rank of men of learning, and in every respect a youth of the
fairest promise. The father records that he himself, though well furnished
by experience in the art of medicine, was now and again worsted by his son
in disputation, and alludes in words of pathetic regret to divers
problems, too deep for his own powers of solution, which Gian Battista
would assuredly have mastered in the course of time. He does not forget to
notice certain of the young man's failings; for he remarks that he was
temperate of speech, except when he was angered, and then he would pour
forth such a torrent of words that he scarce seemed in his right mind.
Cardan professes to have discerned a cause for these failings, and the
calamities flowing therefrom, in the fact that Gian Battista had the third
and fourth toes of his right foot united by a membrane; he declares that,
if he had known of this in time, he would have counteracted the evil by
dividing the toes.[116] Gian Battista eventually gained the _baccalaureat_
in his twenty-second year, and two years after became a member of the
College.

The life which Cardan planned to lead at Pavia was unquestionably a full
one. He had several young men under his care as pupils besides his son,
amongst them being a kinsman of his, Gasparo Cardano, a youth of sterling
virtue and a useful coadjutor in times to come. He was at this time
engaged on his most important works in Medicine and Physical Science. He
worked hard at his profession, practising occasionally and reading
voraciously all books bearing on his studies. He wrote and published
several small works during the four years--from 1547 to 1551--of his
Professorship at Pavia; the most noteworthy of which were the Book of
Precepts for the guidance of his children, and some Treatises on the
Preservation of Health. He also wrote a book on Physiognomy, or as he
called it Metoposcopy, an abstract of which appears as a chapter in _De
Utilitate_ (lib. iii. c. 10), but the major part of his time must have
been consumed in collecting and reducing to form the huge mass of facts
out of which his two great works, _De Subtilitate_ and _De Varietate
Rerum_, were built up.

A mere abstract of the contents of these wonderful books would fill many
pages, and prove as uninteresting and unsuggestive as abstracts must
always be; and a commentary upon the same, honestly executed, would make a
heavy draft on the working life-time of an industrious student. In
reference to each book the author has left a statement of the reasons
which impelled him to undertake his task, the most cogent of which were
certain dreams.[117] Soon after he had begun to write the _De Astrorum
Judiciis_ he dreamt one night that his soul, freed from his body, was
ranging the vault of heaven near to the moon, and the soul of his father
was there likewise. But he could not see this spirit, which spake to him
saying, "Behold, I am given to you as a comrade." The spirit of the father
then went on to tell the son how, after various stages of probation, he
would attain the highest heaven, and in the terms of this discourse Cardan
professed to discern the scheme of his more important works.

The _De Subtilitate_ represents Cardan's original conception of a
treatise dealing with the Cosmos, but during the course of its preparation
a vast mass of subsidiary and contingent knowledge accumulated in his
note-books, and rendered necessary the publication of a supplementary
work, the _De Varietate_,[118] which, by the time it was finished, had
grown to a bulk exceeding that of the original treatise. The seminal ideas
which germinated and produced such a vast harvest of printed words, were
substantially the same which had possessed the brains of Paracelsus and
Agrippa. Cardan postulates in the beginning a certain sympathy between the
celestial bodies and our own, not merely general, but distributive, the
sun being in harmony with the heart, and the moon with the animal humours.
He considers that all organized bodies are animated, so that what we call
the Spirit of Nature is present everywhere. Beyond this everything is
ruled by the properties of numbers.[119] Heat and moisture are the only
real qualities in Nature, the first being the formal, and the second the
material, cause of all things; these conceptions he gleaned probably from
some criticisms of Aristotle on the archaic doctrines of Heraclitus and
Thales as to the origin of the universe.

It is no marvel that a writer, gifted with so bizarre and imaginative a
temper, so restless and greedy of knowledge, sitting down to work with
such a projection before him, should have produced the richest, and at
the same time the most chaotic, collection of the facts of Natural
Philosophy that had yet issued from the press. The erudition and the
industry displayed in the gathering together of these vast masses of
information, and in their verification by experiment, are indeed amazing;
and, in turning over his pages, it is impossible to stifle regret that
Cardan's confused method and incoherent system should have rendered his
work comparatively useless for the spread of true knowledge, and qualified
it only for a place among the _labores ineptiarum_.

Cardan begins with a definition of Subtilty. "By subtilty I mean a certain
faculty of the mind by which certain phenomena, discernible by the senses
and comprehensible by the intellect, may be understood, albeit with
difficulty." Subtilty, as he understood it, possesses a threefold
character: substance, accident, and manifestation. With regard to the
senses he admits but four to the first rank: touch, sight, smell, and
hearing; the claims of taste, he affirms, are open to contention. He then
passes on to discuss the properties of matter: fire, moisture, cold,
dryness, and vacuum. The last-named furnishes him with a text for a
discourse on a wonderful lamp which he invented by thinking out the
principle of the vacuum. This digression on the very threshold of the work
is a sample of what the reader may expect to encounter all through the
twenty-one books of the _De Subtilitate_ and the seventeen of the _De
Varietate_. Regardless of the claims of continuity, he jumps from
principle to practice without the slightest warning. Intermingled with
dissertations on abstract causes and the hidden forces of Nature are to be
found descriptions of taps and pumps and syphons, and of the water-screw
of Archimedes, the re-invention of which caused poor Galeazzo Rosso,
Fazio's blacksmith friend, to go mad for joy. There are diagrams of
furnaces, of machinery for raising sunken ships, and of the common
steelyard. Cardan finds no problem of the universe too recondite to essay,
and in like manner he sets down information as to the most trivial details
of every-day economy: how to kill mice, why dogs bay the moon, how to make
vinegar, why a donkey is stupid, why flint and steel produce fire, how to
make the hands white, how to tell good mushrooms from bad, and how to mark
household linen. He treats of the elements, Earth, Air, and Water,
excluding Fire, because it produces nothing material; of the heavens and
light: metals, stones, plants, and animals. Marvellous stories abound, and
the most whimsical theories are advanced to account for the working of
Nature. He tells how he once saw a man from Porto Maurizio, pallid, with
little hair on his face, and fat in person, who had in his breasts milk
enough to suckle a child. He was a soldier, and this strange property
caused him no slight inconvenience. Sages, he affirms, on account of their
studious lives, are little prone to sexual passion. With them the vital
power is carried from the heart to a region remote from the genitals,
_i.e._ to the brain, and for this reason such men as a rule beget children
weak and unlike themselves. Diet has a valid effect on character, as the
Germans, who subsist chiefly on the milk of wild cows, are fierce and bold
and brutal. Again, the Corsicans, who eat young dogs, wild as well as
domestic, are notably fierce, cruel, treacherous, fearless, nimble, and
strong, following thus the nature of dogs. He argues at length to show
that man is neither an animal nor a plant, but something between the two.
A man is no more an animal than an animal is a plant. The animal has the
_anima sensitiva_ which the plant lacks, and man transcends the animal
through the gift of the _anima intellectiva_, which, as Aristotle
testifies, differs from the _sensitiva_. Some maintain that man and the
animals must be alike in nature and spirit, because it is possible for man
to catch certain diseases from animals. But animals take certain
properties from plants, and no one thinks of calling an animal a plant.
Man's nature is threefold: the Divine, which neither deceives nor is
deceived; the Human, which deceives, but is not deceived; the Brutish,
which does not deceive, but is deceived. Dissertations on the various
sciences, the senses, the soul and intellect, things marvellous, demons
and angels, occupy the rest of the chapters of the _De Subtilitate_.

At the end of the last book of _De Varietate_, Cardan gives a table
showing the books of the two works arranged in parallel columns so as to
exhibit the relation they bear to each other. A comparison of the
treatment accorded to any particular branch of Natural Philosophy in the
_De Subtilitate_ with that given in the _De Varietate_, will show that in
the last-named work Cardan used his most discursive and anecdotic method.
Mechanics are chiefly dealt with in the _De Subtilitate_, and all through
this treatise he set himself to observe in a certain degree the laws of
proportion, and kept more or less to the point with which he was dealing,
a system of treatment which left him with a vast heap of materials on his
hands, even after he had built up the heavy tome of the _De Subtilitate_.
Perhaps when he began his work upon the fresh volume he found this _ingens
acervus_ too intractable and heterogeneous to be susceptible of
symmetrical arrangement, and was forced to let it remain in confusion. Few
men would sit down with a light heart to frame a well-ordered treatise out
of the _débris_ of a heap of note-books, and it would be unjust to
censure Cardan's literary performance because he failed in this task.
Probably no other man living in his day would have achieved a better
result. It is certain that he expended a vast amount of labour in
attempting to reduce his collected mass of facts even to the imperfect
form it wears in the _De Varietate Rerum_.[120]

Considering that this book covers to a great extent the same ground as its
predecessor, Cardan must be credited with considerable ingenuity of
treatment in presenting his supplementary work without an undue amount of
repetition. In the _De Varietate_ he always contrives to bring forward
some fresh fact or fancy to illustrate whatever section of the universe he
may have under treatment, even though this section may have been already
dealt with in the _De Subtilitate_. The characteristic most strongly
marked in the later book is the increased eagerness with which he plunges
into the investigation of certain forces, which he professes to appreciate
as lying beyond Nature, and incapable of scientific verification in the
modern sense, and the fabled manifestations of the same. He loses no
opportunity of trying to peer behind the curtain, and of seeking--honestly
enough--to formulate those various pseudo-sciences, politely called
occult, which have now fallen into ridicule and disrepute with all except
the charlatan and the dupe, who are always with us. Where he occupies in
the _De Subtilitate_ one page in considering those things which lie
outside Nature--demons, ghosts, incantations, succubi, incubi,
divinations, and such like--he spends ten in the _De Varietate_ over
kindred subjects. There is a wonderful story[121] told by his father of a
ghost or demon which he saw in his youth while he was a scholar in the
house of Giovanni Resta at Pavia. He searches the pages of Hector
Boethius, Nicolaus Donis, Rugerus, Petrus Toletus, Leo Africanus, and
other chroniclers of the marvellous, for tales of witchcraft, prodigies,
and monstrous men and beasts, and devotes a whole chapter to
chiromancy,[122] a subject with which he had occupied his plenteous
leisure when he was waiting for patients at Sacco. The diagram of the
human hand given by him does not differ greatly from that of the
contemporary hand-books of the "Art," and the leading lines are just the
same. The heavenly bodies are as potent here as in Horoscopy. The thumb is
given to Mars, the index finger to Jupiter, the middle finger to Saturn,
the ring finger to the Sun, and the little finger to Venus. Each
finger-joint has its name, the lowest being called the procondyle, the
middle the condyle, and the upper the metacondyle. He passes briefly over
as lines of little

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