108 A SHORT HISTORY OF SCIENCE 



the stadium, was a close approximation to the real circumference, 

 but we may suppose that this degree of accuracy was to some 

 extent a matter of accident. Posidonius, a noted Stoic philosopher, 

 born in 136 B.C., stated that the bright star Canopus culminated 

 just on the horizon at Rhodes, while its meridian altitude at 

 Alexandria was " a quarter of a sign, that is, one forty-eighth part 

 of the zodiac." This would correspond with a circumference of 

 240,000 stadia, the method being quite inferior in accuracy to that 

 of Eratosthenes, on account of the impossibility of determining 

 when a star is just on the horizon. Eratosthenes is also credited 

 with measuring the obliquity of the ecliptic with an error of but 

 about seven minutes. 



A student of the Athenian Platonists and a man of extraor- 

 dinary versatility, philosopher, philologian, mathematician, ath- 

 lete, Eratosthenes wrote on many subjects. He may well have 

 been responsible for the introduction of leap-year into the Egyp- 

 tian calendar by the " Decree of Canopus " in 238 B.C., 



in order that the seasons may continually render their service accord- 

 ing to the present order and that it may not happen that some of 

 the public festivals which are celebrated in the winter come to be 

 observed sometimes in the summer. . . . 



He invented a method and a mechanical apparatus for duplicat- 

 ing the cube. 1 Such a mechanical solution is naturally obnoxious 

 to the principles of Plato and Euclid. 



His so-called "sieve" is a method for systematically separating 

 out the prime numbers by arranging all the natural numbers 

 in order, and then striking out first all multiples of 2, then of 3, 

 and so forth, thus sifting out all but the primes 1, 2, 3, 5, 7, 11, 

 13, 17, etc. 



APOLLONIUS OF PERGA, about 260-200 B.C., "the great geom- 

 eter," was the last of this famous Alexandrian group of mathema- 

 ticians, and owes his reputation to his important work on the conic 

 sections. His predecessors had in general recognized only those sec- 

 tions formed from right circular cones by planes normal to an ele- 



1 See Gow, p. 245. 



