GREEK SCIENCE IN ALEXANDRIA 107 



ment of the dimensions of lines and curved surfaces and which require 

 the consideration of the infinite. Mach. 



The genius of Archimedes created the theory of the composition 

 of parallel forces, of centres of gravity, and of equilibrium of float- 

 ing bodies. But antiquity went no farther ; not only were the first 

 principles of dynamics unsuspected, but the statistical composition of 

 concurrent forces was unknown, and the explanation of machines 

 was confined to extension of the principles of the lever, which is the 

 starting-point of the works of Archimedes, but may nevertheless 

 have been recognized before him. Tannery. 



ALEXANDRIAN GEOGRAPHY : EARTH MEASUREMENT. The far 

 reaching conquests of Alexander and the resulting migrations and 

 colonizations naturally gave a powerful stimulus to geography 

 as a branch of descriptive knowledge. Chaldean records became 

 accessible to the Alexandrian Greeks and a more accurate system 

 of time-measurement was introduced. Until about this period 

 it had been customary to make appointments at the time when 

 a person's shadow should have a certain length. 



ERATOSTHENES, -- 275-194 B.C., librarian of the great library at 

 Alexandria, making a systematic quantitative study of the data 

 thus collected, laid the foundations of mathematical geography 

 a transformation quite analogous to that taking place in as- 

 tronomy. After a historical review he gives numerical data about 

 the inhabited earth, which he estimates to have a length of 78,000 

 stadia and a breadth of 38,000. In connection with this he gives 

 also a remarkably successful determination of the circumference 

 of the earth. This was based on his observation that a gnomon at 

 Syene (Assouan) threw no shadow at noon of the summer solstice, 

 while at Alexandria the zenith distance of the sun at noon was 

 sir of the circumference of the heavens. Assuming the two places 

 to lie on the same meridian and taking their distance apart as 

 5000 stadia, he infers that the whole circumference must be 250,000 

 stadia. He or some successor afterwards substituted 252,000, 

 perhaps in order to obtain a round number, 700 stadia, for the 

 length of one degree. 



This result, subject to some uncertainty as to the length of 



