‘108 
a meafure of angles, and difcovered that 
every infcribed angle, fubtended by the 
diameter of a circle, is a right angle. 
15. The fcholars and the fucceffors of 
Thales carefully cultivated Geometry. 
Anaximander*™ wrote an elementary trea- 
—tife on that {cience; and \4zaxagoras fF at- 
tempted to fquare the ‘circle. 
16. While the philofophers of the Io- 
nian feé flourifhed in Greece, thofe of the 
Italian fchool purfued the fame refearches 
with great faccefs. Pythagoras had dif- 
covered that fine property of a right-an- 
gled triangle, that the fquare of the hy- 
pothenufe is equal to the fum of. the 
f{quares of the two other fides.{ The Py- 
‘thagoreans added feveral new theories to 
Geometry, fuch as that of the incom- 
men(urability of the diagonal of a {quare 
to its fide, and that of the five regular bo- 
dies. i 
17. Democritus || did not negle& geo- 
metry, and it appears that he made fome 
progrefs in that {cience. 
18. Hippocrates of Chie§ rendered him- 
felf famous by the quadrature of the 
* Anaximander, alfo a native of Miletus, 
was the fcholar of Thales, and fucceeded his 
mafter in the fonian fchool, and Azaximenes, 
his countryman, fucceeded him. 
+ Anaxagoras, the pupil of Anaximenes, 
was the fourth chief of the Ionian fe&t, and 
lived 430 years before Chrift. He was ac- 
cufed of impiety, for having fhewn that the 
ftars were. material. He was imprifoned, 
and, but for Pericles, would have been con: 
demned to die. Whilein prifon, Anaxagoras 
laboured to effect the quadrature of the circle. 
t It is faid that Pythagoras was fo tranf- 
ported with joy, on making this difcovery, 
that he facrificet¢ a hecatomb, or 100 oxen, 
in gratitude to the Mufes for having fo hap- 
pily infpired him. But this ftory cannot be 
reconciled with the fortune, and ftill lefs 
with the doG@rines, of Pythagoras 5 a circum- 
ftance which has induced a certain author to 
alledge, that the oxen were made of wax or 
pafie. 
{| Democritus, a native of Abdera, died at 
a very advanced age, 362 years before Chrift. 
Having been a profound mathematician, aa 
ingenious natural philofopher, and an enlight- 
ened moralift, he had every title to be ranked 
among men of the greateft merit in the fci- 
ences. 
§ Hippocrates of Chio was a merchant, 
and extremely unfkilful in his bufinefs. The 
farmers of the revenue at Byzantium (now 
Conftantinople), taking advantage of his fim- 
plicity, cheated him in a ftrange manner, 
Being half ruined, and obliged to fufpend his 
commerce, Hippocrates went to Athens to 
retrieve his affairs, and there he firft became 
acquainted with geometry. Curiofity, or a 
,diftinguifhed geometrician, 
'.philefophy, 
A Sketch of the Hiptory of Pure Mathematics.’ [March 1, 
lune, which bears his name. But Plato*®- ~ 
and his fcholars gave a new vigour and 
appearance to Geometry. ‘That philofo- 
pher is regarded as the inventor of the 
geometrical analyfis, and as having been 
the firft obferver of the formation of the 
Conic Seétions. It is at leaft certain that. 
the properties of thofe curves were invef- 
tigated in the Lyceum, and that feveral of 
them were known.to Arifieus, Menechmus,+ 
Dinofiratus, and other Platonic geometri- 
cians, ‘There was foon occafion to ap- 
ply that knowledge to the duplication of — 
the cube, a problem famous in antiquity, 
of the origin’ of which’ we have the fol- 
lowing account from an ancient author., 
19. While the plague ravaged Attica, 
deputies were fent to Delos, to confult the 
oracle on the means of appeafing the 
wrath of Heaven. ‘The-anfwer returned 
by the god was, that, to make the plague 
ceafe, they muft double the altar of Apol- 
lo. Thataltar was of gold, and in a cu- 
bical form. ‘The thing appeared eafy to 
thofe who ignorantly undertook to folve 
with to occupy his time, having led him one 
day to vifit one of the fchools of philofophy, 
he fo much relifhed the letures on geometry, 
which he there heard, that he abandoned 
commerce, in order to devote himfelf to the 
ftudy of that fcience. He foon became a 
The quadratute 
of the lune, which he difcovered, embolden- 
ed him to inveftigate that of the circle. He 
alfo compofed Elements of Geometry, which 
have not reached our times. 
* Plato, the founder of the Academic 
feé&t, born at Athens, about the 429th year 
before Chrift, was, from his infancy, diftin- 
guifhed for a brilliant and lively imagination. 
At the age of twenty, he attached himfelf 
to Socrates 5 and, after his mafter’s death, he | 
travelled into Egypt, to converfe with the 
priefts ; and into Italy, to confult the famous 
Pythagoreans, Philolaus and Archytas. On 
his return home, he founded that celebrated 
fchool which has given fo many difciples-to 
He looked upon the ftudy of 
geometry as fo néceffary, that he put an in- 
{cription upon the door of his fchool, im- 
porting, that no perfon ignorant of geometry 
fhould enter it. He fuffered not a day to 
‘pats, without fhewing his pupils fome new | 
truth in that fcience. That great man, to 
wham pofterity hath given the name of Di- 
vine, on account of the excellence of his 
morality, dicd on the. anniverfary of his 
birth, in the 81ft year-of his age, and the 
348th year before the Chriftian era. Vy 
+ Menechmus fo much amplified the the- 
ory of the conic feétions, that fome, have 
given him the honour of having difcoyered 
them. His brother, Dinoftratus, invented 
the quadratrix, 
the 
