1202.) 
the Great Geometrician, or the Geo- 
metrician, by way of eminence, com- 
menced his. He gave the different conic 
fe&tions the names which they ftill retain. 
The treatife, in which he collected the 
difcoveries of preceding geometricians, 
and thofe which he himfelf had made on 
‘thofe curves, is one of the moft valuable 
works of antiquity, and the moft folid 
foundation of the reputation of its au- 
thor. 
30. We there find the doctrine of the 
maxima and minima, and the determi- 
nation of evolutes; and every thing in 
the work is treated of with the greateft 
care, 
31, Among the geometricians who were 
cotemporary with the preceding, we muft 
diftinguith Eratofhenes, who gave a me- 
chanical folution to the problem of the 
duplication of the cube; Coxon of Samos, 
the friend of Archimedes ; and Nicomedes, 
the inventor of the conchoid. Hippar- 
chus* lived in the following age, and the 
numerous calculations in which he was 
engaged, gave birth to trigonometry, both | 
plain and {pherical, in the hands of that 
great aftronomer. 
32. In the interval between the time of 
Hipparchus, and the Chriftian zra, we 
find a great number of mathematicians, 
of whom Geminus of Rhodes, Theodofius, 
and fome others, are celebrated. Gemi- 
nus wrote a work, which has not reached 
us, and the lofs of which we cannot fuf- 
ficiently lament. It was an hiftorical com- 
mentary, a fort of fhilofophical explana- 
tion of geometrical difcoveries.- Theo- 
dofivs wrote a valuable and well-known 
work on {pherics. 
* 33. Several centuries of the Chriftian 
gra produced very few original writers, 
We find none, fo to fpeak, but commen. 
tators, at the head of whom we muft place 
He was born about the middle of the third 
century before the Chriftian era, and educated 
at Alexandria, under the fucceffors of Eu- 
clid. | In that fchool he acquired the ability, 
which ranks him next to Archimedes. But 
in Apollonius, the qualities of the-heart did 
not correfgond with thofe of the underftand- 
ing. He was vain, and jealous of other 
men of merit; and he took every opportu-— 
t 
nity to deprefs them. 
* Hippatchus, of Nice, in Bithynia, long 
applied himfelf to the theory and the practice 
of aftronomy, and feveral obfervations are re- 
lated, which: were made by him from the 
year 160 to 125 before Chrift. 
+ This-work, entitled Enarrationes Geome- 
trice, confifted of fix books, and is often 
cited by Proclus. . 
A Sketch of the Hiftory of Pure Mathematics. 
‘by all who knew her. 
iit 
Pappus,* who, in his Mathematical Col- 
leftions, hath given proots of great know- 
ledge in Geometry, and gemus fhines in 
different parts of that work. Theon, his 
colleague in the~fchool of Alexandria, 
has left us notes on Euclid, and Hypa- 
tia,¢ the daughter of Theon, enriched 
- Geometry with a commentary on Apollo- 
nius. 
34. About the middle of the sth cen- 
*tury, Proclus, the mater of the Platonic 
{chool eftablifhed at Athens, contributed, 
if not by his difcoveries, at leaft by his 
labours and’ his inftru&tions, to preferve 
for fome time the luftre of mathematical 
learning. The commentary which he 
has left us, on the firft book of Euclid, 
contains many obfervations, which are 
ufeful in the metaphyfics and the hiftory 
of Geometry. He was fucceeded in his 
fchool by Marinus, who wrote an intro- 
duétion to the Data of Euclid. After- 
wards appeared Ifdorus of Miletus, and 
Anthemius, both able geometricians ; Ew- 
tochius, who became celebrated for his 
commentaries on Archimedes and Apcllo- 
nius; and Diocles, the inventor of the cif- 
foid. ‘ | 
35. We have now airived at the fatal 
period of the declenfion of the mathema- 
tics. The capture of Alexandria by the 
Arabs, in the year 641, gave the mortal 
blow to the fciences, not only in that ce- 
lebrated city, but. throughout the. whole 
Greek empire. The monuments of the 
learning of antiquity were deitroyed, and. 
the ferocious Omar ordered the library of 
Alexandria to be burned; ‘* becaufe,”’ ar- 
gued he,’**the books are either agreeable 
* Pappus lived in the reign of Theodofius 
the-Great, during the 4th century. 
‘+ Hypatia was inftruéted by her father, 
and fhe furpaffed him in Geometry, which 
was her principal ftudy. Her progrefs in 
philofophy and the, mathematics was fuch 
that fhe merited the rank of profeffor of 
thofe fcienges. Being virtuous as well as 
beautiful, fhe was efteemed and refpeéted 
But fhe incurred the 
fufpicion of caufing the mifunderftanding, 
which prevailed between St. Cyrill, the pa-. 
triarch of Alexandria, and Oreftes, the go- 
vernor, who, like herfelf, was 4 Pagan. An 
implacable hatred was conceived againft her ; 
and the furious populace, conduéted by a fa- 
natic, watched the unfortunate Hyppatia as 
fhe was returning home; dragged her from 
her chariot; {tripped her, and killed her 
with blows from pothherds; after which they 
cut her body in pieces and burnt it. This. 
horrible cataftrophe was tranfatted during 
the Lent of the year 416. 
te 
