324 GREEK SCIENCE. 



each other, to be erroneously reported to us. Besides his astronomical 

 merits, he was an eminent geometer. He turned his attention to 

 conic sections ; and we have his description of a mesdabium, or 

 instrument for finding any number of mean proportionals, which is 

 ingenious, though it is said to have been ridiculed by Nicomedes ; 

 who, probably soon after, invented the conchoid for a similar object. 

 He is said to have written ' De locis ad medietates,' the subject 

 of which treatise can only be a matter of conjecture; and he is 

 also known for what is called his * Sieve,' which is a method 

 of finding prime numbers. We possess likewise his ' Catasterism,' 

 which is a description of the constellations. After living to the 

 age of eighty-three, he found his sight fail and his health decay, 

 and came to the resolution that life was not worth preserving under 

 such circumstances. He died by voluntarily abstaining from food, 

 B. c. 194. 



The principal remaining name which offers itself to our notice in 

 us the Alexandrian school, is the illustrious one of APOLLONIUS, whom 

 ?c!28i-204. antiquity distinguished by the name of " The Great Geometer," and 

 who has been considered with corresponding admiration by some of 

 the most profound of modern mathematicians. He was born at Parga 

 hi Pamphylia, in the time of Ptolemy Euergetes : was instructed in 

 mathematics by those who had been the disciples of Euclid: and 

 flourished at the museum under Philopater (221 to 204 B. c.). We 

 learn from Pappus that he employed himself in what has been a 

 favourite, but not very profitable, speculation of the most acute 

 mathematicians, an attempt to prove the elementary axioms on 

 which geometry is founded. The works of his which remain are a 

 treatise on conic sections. The four first books of this, which were 

 all that were known in Europe till 1658, contain the properties 

 observed previously to his time ; but the three following ones, which 

 were brought from the East and translated from the Arabic, give his 

 own discoveries. They are principally on the greatest and least lines 

 which can be drawn from any point to the curve of a conic section. 

 They show wonderful powers in the management of the ancient 

 geometry, and though it might be imagined that the instrument was 

 scarcely capable of such results, they lead to the borders of the 

 modern theories of evolute curves and centres of osculation. 1 Besides 



1 The history of the recovery of these books is remarkable. Upon the syllabus 

 given by Pappus of the lost books of Apollonius's conies, several persons had 

 attempted to form a conjectural restoration, or divination, as it was called. In 

 particular, Viviani had been for some time silently and laboriously engaged in this 

 investigation, when it was discovered by Borelli (in 1658) that the fifth, sixth, and 

 seventh books existed in Arabic in the Medicean library. Viviani saw himself on ; 

 the point of losing the credit due to several years of research by this unexpected ; 

 discovery. He, however, obtained from the Grand Duke an attestation of the state \ 

 of forwardness in which his own MSS. then were, signed by his hand ; and an 

 injunction to Borelli to keep secret his translation tiU Viviani's book had been , 

 published. The Divinatio in V. Apollonii Conicorum appeared in 1 659, and the j 



V - 



