524. 
wal*. No fooner was the cycloid known 
than it excited difputes among geometri- 
cians. The firtt idea of that remarkable 
curve feemed to have occurred to Galileo}. 
bers may be performed by the ufe of the 
eyes and hands alone. Shortly afterwards 
his experiments decided the opinions of phi- 
lofophers refpe&ting the weight of the air. He 
invented the Arithmetical Triangle, and the 
Elements. of the Arithmetic of Probabilities. 
All thefe labours ruined the health of Paf- 
cal. Bodily weaknefs forced him to fufpend 
all mental exertions, and to enter ona courfe 
of a moderate exercife. One day, in the 
month of October 1654, as he was going to 
the bridge of Neuilly, in a chariot and four, 
the two foremoft horfes ran away clofe to a 
precipice, where there was no parapet, down 
which they rufhéed into the Seine. Fortu- 
mately they. broke the traces by their firit 
effort, and left the chariot ftanding’on the 
very brink of the precipice, This accident 
fo much difturbed the brain of Pafcal, that 
ever after he imagined there was an abyfs on 
his left hand. He wholly renounced the 
world, and retired to the Abbey of Port 
Royal. The regular life which he led in 
that retreat, procured him very long inter- 
_ wals of health, during which he wrote the 
Provincial Letters, one of the moft perfect 
works which exiftin the French language. 
For many years Pafcal relinquifhed all purely 
human fciences. Having been tormented by 
a moft fevere tooth-ach, which almoft wholly 
deprived him of reft, he fought in intenfe 
application the means of mitigating his pain 3 
and the difcoveries which he then made in 
the cycloid are, even at the prefent day, 
reckoned among the greateft efforts of the 
human mind. Pafcal died at Paris on the 
roth of Auguft, 1662, inthe 39th year of 
his age. 
* Gilles Perfonne de Roberval was born 
in 1602, at Roberval, a village in the diocefe 
of Beauvais. He had fome fharp difputes 
with Defcartes, whofe enemy he always was. 
Although Roberval was an able geometrician, 
he did not poffefs the art of clearly exprefling 
his ideas. Hedied in November, 1675. 
+ Galileo was bornat Pifa, in 1564. His 
father, Vincent Galilei, a noble Florentine, 
gave fin an extraordinary education, defign- 
ing him for the ftudy of medicine ; but the 
impulfe of nature made him a mathematician, 
and he occupied, for 18 years, a proteflor’s 
chair at Padua, from which the Grand Duke 
of Tufcany removed him, in order to fettle 
him in his territories. Galileo rendered great 
fervices to aftronomy and mechanics, and: his 
difcoveries confirmed the fyftem of -Coperni- 
cus. Every one knows what a deteftable per- 
fecution Galileo endured on that occafion, 
from the odious tribunal of the Inquifition. 
Sketch of the Eiftory of Pure Mathematics. 
[July 1, 
It is alfo faid, that father Merfexnus* 
tagk onisetotne Sat 1615. Roberval 
found its area, about the fame time that 
Fermat and Defcartes determined its tan- 
gents. Death prevented Galileo from 
folving thefe problems, in which Caval- 
leri failed ; but cf which Torricelli+ and 
Vivianit furmounted the difficulties. The 
former found the area, and the latter the 
tangents, of the cycloid. 
65. Pafcal, who had attentively confi- 
dered that curve, wifhed to make a trial 
of the abilities of his cotemporary geo- 
metricians. With this view he propofed 
to them fome new problems on the cycloid, 
promifing 40 piftoles to the firft perfon, 
and 20 to the fecond, who. fhould folve 
thefe problems. The only candidates, 
who returned anfwers to all the problems, 
and claimed the prizes, were Wallis§ and 
Father Lallouere, otherwife called Lalou- 
demned to abjure his opinions. Not content- 
_ed with demanding this humiliating recantae 
tion, they enjoined him not to depart from 
the territory of Florence, in which he died 
in 1642, at his country-houfe of Arcetri. 
* Marinus Merfennus, a Minime friar, 
born in the Maine, in 1588, ftudied at La 
Fleche, along with Defcartes, a circumftance 
which united them for life in an intimate 
friendfhip. He rendered himfelf, as it were, 
the centre of the learned, by the mutual 
correfpondence which he kept up among 
them. He died at Paris in 1648. 
+ Torricelli, who became fo celebrated 
for his difcovery of the preffure of the at. 
mofphere, was born at Faenza in 1608, and ~ 
died in 1647. ‘This pupil of Galileo difco- 
vered the folidity ofthe hyperbolic conoid, 
infinite in length, formed by the revolution 
of the afymptotic {pace about the wfymp- 
tote as an axis. 
~ Viviani was born at Florence in 1622, 
and died in 1703. _ That mathematician was 
for three years, namely, from his 17th to his 
2oth year, under the tuition of Galileo, and 
he conceived fuch an attachment to his maf- 
ter, that he never put his name to the title 
of any of his works, without accompanying it 
with the diftin@tive appellation of ¢* the laft 
Scholar of the Great Galileo.” 
§ Dr. John Wallis, who was born in 
Kent in 1616, and died at Oxford in 1703, 
merited the reputation which he held asa 
mathematician, 
Note by the Tranflator—Dr. Wallis was’ a 
remarkable rep a to Pope’s general tule 
that 
—In the foul, while memory prevails, 
The folid power of underftanding fails. 
aie great man, at the age 70, was cone, That difinguifhed mathematician tells usy 
2 that 
