314 GREEK SCIENCE. 



lonius, describes it as kind and unassuming, and particularly disposed 

 to encourage mathematical merit in others. He is said to have been 

 attracted to Alexandria by the patronage offered to learned men under 

 the first Ptolemy; and to that monarch, when he had expressed 

 some dissatisfaction at the prolixity of the reasonings, through which 

 the study required him to proceed, Euclid is reported to have repre- 

 sented, that " there was no royal road to geometry." Besides the 

 celebrated * Elements,' he was the author of mathematical works upon 

 almost every branch of the science which we have mentioned. He 

 wrote four books 'On Conies ;' a treatise 'On Loci at Surfaces ;' and one 

 ' On Porisms,' a species of geometrical proposition, which, after being long 

 involved in obscurity, was elucidated by Robert Simson, and after him 

 by Professor Playfair. We have his data, and a ' Treatise on Divisions,' 

 that is, on dividing a figure in a given ratio by lines drawn under 

 certain conditions. Another work which Pappus praises much, was 

 an arrangement and analysis of mathematical paralogisms. We have 

 already referred to his Optics, of which science, mathematically con- 

 sidered, it is by no means improbable, from the nature of the treatise, 

 that he was the inventor. We possess also a work on Music attri- 

 buted to him, but which, Montucla thinks, consists of two parts, 

 the first written by an Aristoxenian, and the second by a Pythagorean. 

 In the latter capacity, Euclid is said to have been the person who 

 first demonstrated that the Aristoxenian method of proceeding by 

 tones and half tones, would necessarily give the octaves out of tune. 

 We have already mentioned the fragment, referring to mechanics, 

 which is ascribed to Euclid ; and arithmetic may be considered as the 

 subject of the 7th, 8th, 9th, and 10th books of the 'Elements.' In 

 astronomy we have a work of his upon the doctrine of the sphere, 

 entitled ' Phenomena.' This last science was one of those which 



Astronomy at occupied most, and most successfully, the Alexandrian mathematicians. 

 Above all, the importance of observation began to be better under- 



Aristiiius stood. ARISTILLUS and TIMOCHARIS for a long course of years made 



Timocharis. observations on the stars, many of which are preserved by Ptolemy. 



Aratus. The poem of ARATUS, so popular among the ancients, and which was 

 translated by men of no less name than Cicero and Germanicus, was 

 about this time written at the court of Antigonus Gonatas. And 



Ar tarchus. ARISTARCHUS of Sam os, besides his method of determining the 

 distance of the sun by the dichotomy of the moon, mentioned in the 

 4 History of Astronomy,' l made an observation of the solstice 281 

 B. C., and is remarkable as having attempted to revive the true doctrine 

 of the universe which places the sun in the centre. This we learn 



Archimedes, from ARCHIMEDES, of whose life we shall now collect what is known, 

 and examine the improvements of which he was the author in the 

 different branches of science. 



This extraordinary man is said by Plutarch to have been a relation, 

 as well as friend, to Hiero, king of Syracuse, and flourished under the 

 1 Page 335 of this volume. 



