riwayat niccolo fontana

7/25/2019 RIWAYAT Niccolo Fontana

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Niccolo Fontana,known as Tartaglia,was born in Brescia in 1499 or 1500, the son of an

honest mail rider Michele Fontana who was known as 'Micheletto the Rider'. Micheletto

would ride his horse between Brescia and other towns in the district makin deli!eries.

"lthouh he was #oor, Micheletto did his best for his wife, dauhter and two sons, and

$iccolo attended school from the ae of about four %ears. &ife miht ha!e been !er% different

for $iccolo had traed% not come when he was si %ears old, for at that time his father wasmurdered while out makin deli!eries. From bein a child in a #oor famil%, he was suddenl%

#luned into total #o!ert%.

$iccolo was nearl% killed as a teenaer when, in 151(, the French ca#tured his home town

and #ut it to the sword. )he French arm% was commanded b% *aston de Foi and the% had

suffered humiliation at the hands of some determined Brescia militia. )he% decided to teach

the local inhabitants a lesson and retook Brescia durin se!en da%s of fihtin in which time

4+,000 residents of the cit% were killed in an act of re!ene. "midst the eneral slauhter, the

twel!e %ear old $iccolo took refue in the cathedral with his mother and %ouner sister, but

was dealt horrific facial sabre wounds b% a French soldier that cut his aw and #alate. -e was

left for dead and e!en when his mother disco!ered that he was still ali!e she could not affordto #a% for an% medical hel#. -owe!er, his mother's tender care ensured that the %ounster did

sur!i!e, but in later life $iccolo alwa%s wore a beard to camouflae his disfiurin scars and

he could onl% s#eak with difficult%, hence his nickname )artalia, or stammerer.

)artalia was self tauht in mathematics but, ha!in an etraordinar% abilit%, his mother was

able to find him a #atron. &udo!ico Balbisonio took him to adua to stud% there, but when he

returned with his #atron to Brescia he made himself un#o#ular b% ha!in an inflated o#inion

of himself. -e left Brescia to earn his li!in teachin mathematics at /erona which he did

between 151+ and 151. &ater, still in /erona, he tauht at a school in the alao Mianti

but it is recorded that at that time he was married with a famil%, %et was !er% #oor. -e mo!ed

to /enice in 1524. "s a lowl% mathematics teacher in /enice, )artalia raduall% ac3uired a

re#utation as a #romisin mathematician b% #artici#atin successfull% in a lare number of

debates.

)he first #erson known to ha!e sol!ed cubic e3uationsalebraicall% was del Ferro but he told

nobod% of his achie!ement. n his deathbed, howe!er, del Ferro #assed on the secret to his

rather #oor6 student Fior. For mathematicians of this time there was more than one t%#e of

cubic e3uation and Fior had onl% been shown b% del Ferro how to sol!e one t%#e, namel%

'unknowns and cubes e3ual to numbers' or in modern notation6x27 ax8 b. "s neati!e

numbers were not used this led to a number of other cases, e!en for e3uations without a

s3uare term. Fior bean to boast that he was able to sol!e cubics and a challene between himand )artalia was arraned in 1525. n fact )artalia had also disco!ered how to sol!e one

t%#e of cubic e3uation since his friend :uanne da ;oi had set two #roblems which had led

)artalia to a eneral solution of a different t%#e from that which Fior could sol!e, namel%

's3uares and cubes e3ual to numbers' or in modern notation6x27 ax(8 b. For the contest

between )artalia and Fior, each man was to submit thirt% 3uestions for the other to sol!e.

Fior was su#remel% confident that his abilit% to sol!e cubics would be enouh to defeat

)artalia but )artalia submitted a !ariet% of different 3uestions, e#osin Fior as an, at best,

mediocre mathematician. Fior, on the other hand, offered )artalia thirt% o##ortunities to

sol!e the 'unknowns and cubes' #roblem since he belie!ed that he would be unable to sol!e

this t%#e, as in fact had been the case when the contest was set u#. -owe!er, in the earl%

hours of 12 Februar% 1525, ins#iration came to )artalia and he disco!ered the method tosol!e 's3uares and cubes e3ual to numbers'. )artalia was then able to sol!e all thirt% of Fior's


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#roblems in less than two hours. "s Fior had made little headwa% with )artalia's 3uestions,

it was ob!ious to all who was the winner. )artalia didn't take his #rie for winnin from

Fior, howe!er, the honour of winnin was enouh.

"t this #oint ;ardan enters the stor%. "s #ublic lecturer of mathematics at the iatti

Foundation in Milan, he was aware of the #roblem of sol!in cubic e3uations, but, until thecontest, he had taken acioli at his word and assumed that, as acioli stated in the Suma

#ublished in 1494, solutions were im#ossible. ;ardan was reatl% intriued when :uanne da

;oi told him about the contest and he immediatel% set to work tr%in to disco!er )artalia's

method for himself, but was unsuccessful. " few %ears later, in 1529, he contacted )artalia,

throuh an intermediar%, re3uestin that the method could be included in a book he was

#ublishin that %ear. )artalia declined this o##ortunit%, statin his intention to #ublish his

formula in a book of his own that he was oin to write at a later date. ;ardan , acce#tin

this, then asked to be shown the method, #romisin to kee# it secret. )artalia, howe!er,

refused.

"n incensed ;ardan now wrote to )artalia directl%, e#ressin his bitterness, challeninhim to a debate but, at the same time, hintin that he had been discussin )artalia's brilliance

with the o!ernor of Milan, "lfonso d'"!alos, the Marchese del /asto, who was one of

;ardan 's #owerful #atrons. n recei#t of this letter, )artalia radicall% re!ised his attitude,

realisin that ac3uaintance with the influential Milanese o!ernor could be !er% rewardin

and could #ro!ide a wa% out of the modest teacher's ob he then held, and into a lucrati!e ob

at the Milanese court. -e wrote back to ;ardan in friendl% terms, anlin for an introduction

to the


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;ardan and Ferrari tra!elled to Bolona in 1542 and learnt from della $a!e that it had been

del Ferro , not )artalia, who had been the first to sol!e the cubic e3uation. ;ardan felt that

althouh he had sworn not to re!eal )artalia's method surel% nothin #re!ented him from

#ublishin del Ferro 's formula. n 1545 ;ardan #ublishedArtis magnae sive de regulis

algebraicis liber unus,orArs magnaas it is more commonl% known, which contained

solutions to both the cubic and 3uartic e3uationsand all of the additional work he hadcom#leted on )artalia's formula. =el Ferro and )artalia are credited with their disco!eries,

as is Ferrari , and the stor% written down in the tet.

)artalia was furious when he disco!ered that ;ardan had disrearded his oath and his

intense dislike of ;ardan turned into a #atholoical hatred. )he followin %ear )artalia

#ublished a book,New Problems and Inventionswhich clearl% stated his side of the stor% and

his belief that ;ardan had acted in etreme bad faith. For ood measure, he added a few

malicious #ersonal insults directed aainst ;ardan .

Ars Magnahad clearl% established ;ardan as the world's leadin mathematician and he was

not much damaed b% )artalia's !enomous attacks. Ferrari , howe!er, wrote to )artalia,beratin him mercilessl% and challened him to a #ublic debate. )artalia was etremel%

reluctant to dis#ute with Ferrari , still a relati!el% unknown mathematician, aainst whom

e!en a !ictor% would do little material ood. " debate with ;ardan , on the other hand, held

reat a##eal for )artalia. $ot onl% did he hate him but ;ardan was a leadin fiure in the

mathematical, medical and literar% worlds, and e!en to enter a debate with him would reatl%

enhance )artalia's standin. For all the brilliance of his disco!er% of the solution to the cubic

e3uation #roblem, )artalia was still a relati!el% #oor mathematics teacher in /enice.


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first firin tables. -e also wrote a #o#ular arithmetic tet and was the first talian translator

and #ublisher of ?uclid 'sElementsin 1542. n 154+ he #ublished Quesiti et Inventioni

diverse de Nicolo Tartaleareferred to abo!e.

>e i!e man% 3uotes from this work b% )artalia in the article )artalia ! ;ardan

where the e!ents described abo!e are recounted in the mathematicians own words.

)artalia also #ublished &atin editions of "rchimedes 's works. -e died in #o!ert% in his

house in the ;alle del

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