MATHEMATICS. 323 



maticians from that time were made almost entirely in pure geometry, 

 and even these are very limited, if we except what was done by 

 Apollonius ; and of his propositions it is said that he owed some to 

 Archimedes, whose results were left unedited and fell into his hands. 



In practical mechanics the ancients appear to have gone somewhat 

 further than we have yet mentioned. Hero seems to have been well 

 acquainted with the effects, if not with the theory, of the elasticity of 

 the air ; and we have a treatise of his called ' Pneumatica ' or 

 * Spiritalia,' describing divers machines depending upon that property, 

 and most of them containing the principle of the syphon. We have 

 also a treatise by him ' On Automatons ;' his automatons, which are 

 principally toys moved by very simple machinery. And besides 

 several mechanicians who are remarked for their inventions of warlike 

 machines, CTESIBIUS, the master of Hero, who lived apparently about ctesibius. 

 150 B. c. invented a pump which is yet considered of a very efficient 

 construction. 



In order to finish what relates to the great age of Greek geometry, 

 we shall notice some of the eminent characters who flourished with, or 

 immediately after, Archimedes. These all seemed to have belonged 

 to the college of Alexandria. ERATOSTHENES was a cotemporary of Eratosthenes, 

 the Sicilian mathematicians, and was a remarkable instance of great B - c< 277 ~ 194 - 

 acquirements in very different branches of knowledge. He is generally 

 called by the ancients " Eratosthenes the grammarian " or philologer ; 

 and though he comes under our notice as a great geometer and 

 astronomer, he was also a poet and an antiquary. It is seldom that 

 one person attempts to master so many subjects, without incurring 

 the charge, and perhaps the danger, of being superficial. His enemies 

 gave him the name of Beta, as occupying only the second place in his 

 pursuits : his admirers called him the Pentathlete, thus comparing 

 him to a person who at the public games had been victorious in all 

 the subjects of emulation. He was appointed superintendent of the 

 library of Alexandria, under the third Ptolemy (Euergetes 246-221 

 B. c.) : and he had the merit of inducing that monarch to place in the 

 vestibule of the museum the arrmllce, or combinations of graduated 

 circles which were the principal instruments of observation among 

 the ancients. These instruments were about 20 inches diameter, and 

 the observations made with them are quoted in the ' Almagest.' The 

 mode of observing was by placing a pin on one limb of the circle, so 

 that its shadow might fall upon another at the opposite extremity of 

 the diameter, and thus indicate the position of the sun. By this 

 means Eratosthenes is said to have found, that the interval between 

 the tropics was -j^ of the circumference, which makes the obliquity 

 of the ecliptic 23 J 51' 19*5". His measurement of the earth is 

 remarkable and celebrated, and has been described in the ' History 

 of Astronomy.' 1 He also gave determinations of the magnitude and 

 distance of the sun, which appear, from their discordance with 

 1 Page 336 of this volume. 



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