1802. ] 
For ibe Monthly Magazine. 
A skeTCu of the HISTORY of PURE MA- 
THEMAaTICS, tranflated from  Traiié 
Elementaire de Mathematiques Pures, 
par Lemoine, Profeffeur de Mathema- 
tiques et de Phyfique, &c. 
[Continued from page 329. ] 
ALGEBRA. 
63. AVALLERI*, quitting the an- 
cient indire&t method of deter- 
mining the furfaces and the folidities of bo- 
dies, opened a new path and proceeded 
more direétly to that object, by his method 
of indivifibles. In this theory, furfaces 
are regarded as being formed of the fums 
of an infinity of lines, and folids as com- 
pofed of the fums of an infinity of fur- 
faces. But thefe elementary lines and 
furfaces muft be conceived as the. laft 
terms of the decompofition of furfaces and 
folids, by dividing them continually into 
parallel fe&tions. 
64. While Cavalleri was fignalizing 
himfelf in Italy, the French geometricians 
were engaged in learned refearches, and 
were rendering themfelves illuftrious by 
great difcoveries. The logarithmic {piral 
owes its origin to our celebrated De/- 
cartest, and one of his cotemporaries, 
* Bonaventura Cavalleri was born at Mi- 
lan in 1598, and entered, at an early age, 
into the orderof the Hieronomians. Having 
been fent by his fuperiors to Pifa, to profit 
by the advantages which that univerfity then 
afforded, he ftudied the mathematics, in order 
to keep his mind free from melancholy, and 
to afford him fome amufement under the 
pain of the gout, which began toattack him, 
and which always grew worfe. He was ap- 
pointed one of the profeffors in the Univer. 
fity of Bologna, where he died, in 1647, 
after having experienced for twelve years fuch 
dreadful fits of the gout, that at laft he be- 
came incapable of holding his pen. 
+ René Defcartes, the fon of a counfellor 
of the Parliament of Britanny, was born at 
Haye, in Touraine, on the 31{t of March, 
1596. . He made a remarkable progrefs in his 
fiudies, and, from his infancy, fhewed a de- 
cided tafte for natural knowledge. Difguited 
with the jargon of a ridiculous philofophy, 
he found no where but in the mathematics. 
the certainty with which he was charmed. 
He gave himfelf up entirely to geometry, 
and from thence he derived the moit folid and 
undifputed part of his renown. This phi- 
lofopher, who taught us to think, who broke 
the yoke of antiquity, and re-eftablifhed rea- 
fon in her rights, this very Defcartes was 
_ himfeif led aftray by his imagination. Let 
“tus refpeét his errors; for never did an 
MontTuiuy Mas, No. 82; 
Sketch of the Hiftory of Pure Mathematics. 
523 
who was perhaps his equal in geome- 
try, Fermat*, ftudied the nature of {pi- 
rals and parabolas of fuperior orders. 
Thofe illuftrious rivals inveftigated the 
properties of the cycloid, which were 
alfo ftudiel by Pafcalt+ and Raber- 
ordinary man fall into the like. His edifice 
of Vortices, like the philofophy of Ariftotle, 
has been demolifhed by the efforts of his fuc- 
ceffors ; and his fyfiem concerning the nature 
of animals, in which he faw no principle fu- 
perior to mechaniim, is at. prefent reje¢ted. 
But, if we do not always find truth in the 
works of Defcartes, we are at no lofs to trace 
evident marks of genius. 
was a profound thinker, and {pent his life 
in folitude. In vain did Cardinal Riche- 
lieu, in the name of the King, offer him 
important pofis: he preferred his  retire- 
ment to the flavery of honours. Yet, yield~ 
ing to the urgent folicitations of Queen Chrif- 
tina, who wifhed to fee and converfe with 
him, he repaired to Stockholm. But the 
hours of their interviews were not regulated 
by the rules of Defcartes. That great man, 
born with a weak conftitution, which was 
rendered ftill more delicate by his cuftom’ of 
meditating in bed, then rofe every morning 
at five o’clock, notwithftanding the rigours 
of the climate, and repaired to the library of 
Chriftina. A defiuétion on the lungs termi- 
nated his days, on the rith of February, 
1650. In 1667, his corpfe was brought to 
France, and is now depofited in the Pantheon. 
* Peter Fermat was born at Thouloufe in 
1490, and died in 1665. Having beenas con- 
verfant in the ancient geometry as in the mo- 
dern analyfis, he has rendered almoft as great 
fervices to the mathematics as Defcartes, 
The accurate fciences were not the fole oc- 
cupation of Fermat, for he aifo profecutec ~ 
literature with fuccefs. He had a perfect 
knowledge of Greek, ‘and feveral modern 
languages were familiar to him, Having 
been a counfellor in the pariiament of Thou~ 
loufe, he knew how to reconcile the ftudy of 
the mathematics with that of the laxs, and 
difcharged, with equal affiduity, learning, and 
zeal, the great duties which his ftation called 
upon him to perform. 
+ Blaife Pafcal, born at Clermont, in Au- 
vergne, on the igth of June 1623, an- 
nounced almoft in his cradle the great genius 
which he afterwards exhibited. Froma fim- 
ple mathematical definition, he difcovered by 
degrees, and by the unaided force of his une 
derftanding, that the three angles of every 
triangle are together equal to two right an- 
gles, which is 32 E. a At 16 years of age 
Pafcal compofed a Tra&t on the Conic Sec- 
tions, which was looked upon as a prodigy of 
fagacity. Scarcely had he attained his nine- 
teenth year, when he invented the famous 
arithmetical machine which bears’ his namey 
and by which all forts-of operations in num-~ 
‘ef bers 
That philofopher , 
