ANCIENT MATHEMATICIANS, 
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Antipho, and Hyppocrates of Scio ; who all applied particularly to 
the quadrupture of the circle, the duplicature qf the cube, &c. but 
the last with most success ; this last is also mentioned by Froclus, 
as the first who compiled elements of mathematics. Democritus 
excelled in mathematics as well as physics, though none of his works 
in either kind is extant, the destruction of which some authors lay at 
the door of Aristotle. 
The next in order is Plato, who not only improved geometry, but 
introduced it into physics, and so laid the foundation of a solid phi- 
losophy. Out of his school proceeded a crowd of mathematicians. 
Proclus mentions thirteen of note, among whom was Leodamus, who 
improved the analysis first invented by Plato ; Theatelus, who wrote 
elements; and Archiates, who was the first that applied mathematics 
to use in life. These were succeeded by Neocles and Theon, the last 
of whom contributed to the elements. Eudoxus excelled in arithmetic 
and geometry, and was the first Tounder of a system of astronomy. 
Menachunus invented the conic sections, and Therodius and Hennoti- 
mus improved the elements. Aristotle’s works are so stored with 
mathematics, that Blancanus compiled a whole book of them. Out 
of his school came Eudemus and Theophrastus; the first of whom 
wrote of numbers, geometry, and invisible lines ; the latter, a mathe- 
matical history. To Ari^teus, Isidorus, and Hypsicles, we ow'e the 
books of solids ; which, w ith the other books of elements, were im- 
proved, collected, and methodized by Euclid, who died in the year 
A. A. c. 284. 
A century after Euclid, came Eratosthenes and Archimedes. Con- 
temporary with the latter was Conon, a geometrician and astronomer. 
Soon after appeared Apollonius Pergseus, whose conics are still extant. 
To him are likewise ascribed the fourteenth and fifteenth books of 
Euclid, w'hich are said to have been contracted by Hypsicles. Plip- 
parclius and Menelaus wrote on the subtenses in a circle, the latter 
also on spherical triangles. Theodosius’s three books of spherics are 
still extant. All these, with the exception of Menelaus, lived before 
the Christian era. 
Ptolemy of Alexandria, the prince of ancient astronomers, and no 
mean geometrician, was born A. D. 70. He was succeeded by the 
philosopher Plutarch, of whom w e have still extant some mathematical 
problems. After him flourished Eutocius, who commented on Archi- 
medes, and occasionally mentions the inventions of Philo, Diodes, Nico- 
medes, Sporus, and Heron, on the duplicatureof thecube: to Ctesibius 
of Alexandria, we owe pumps; and Geminus, who appeared soon after, 
is preferred by Proclus to Euclid himself. Diophantus of Alexandria 
w^as a great master of numbers, and the first inventor of algebra ; 
Nicomachus is celebrated for his arithmetical, geometrical, and mu- 
sical works ; Serenus, for his books on the sections pf the cylinder ; 
Proclus, for his comments on Euclid ; and Theon has the credit, 
among some, of being the author of the books of elements ascribed to 
Euclid. The last among the ancient mathematicians, is Pappus of 
Alexandria, who flourished a. D. 400, and is celebrated for his books 
of mathematical collections, still extant. 
