10 G. H. KNIBBS. 



physics, it may be mentioned, contain suggestive hints of the 

 principle of 'virtual velocities,' the foundation afterwards of the 

 imperishable ' Mecanique analytique ' of Lagrange. 



About 300 B.C. the study of geometry was revived in Egypt 

 by the establishment of the first Alexandrian school, with Euclid 

 as it master. About fifty years later flourished the greatest 

 mathematician of antiquity, Archimedes [287 — 212 B.C.], who 

 shewed that the ratio of the circumference to the diameter of a 

 circle lies between 3i and 3f£. The mean of these 3*1418, is 

 sufficiently exact for most purposes. A contemporary, Eratosthenes, 

 [276 - 196 B.C.], was the first to attempt to ascertain, on correct 

 principles, the size of our earth. Forty years later again, the 

 'great geometer' Apollonius of Perga [b. 250 ? B.C.], second only to 

 Archimedes, enriched the world with his talents : to him we owe 

 the further development of the conic sections and developments 

 in astronomical theory. About 150 B.C., Hipparchus of Nicsea 

 in Bithynia, the greatest astronomer of antiquity, is said to have 

 invented trigonometry ; it is worthy of mention that spherical, 

 and not plane trigonometry, was first developed. For this branch 

 of mathematics we are also no less indebted to Claudius Ptolemseus 

 of the second Alexandrian School [about 130 A.D.], celebrated as 

 the founder of the system of astronomy which bears his name. 

 'The theorems of Hipparchus and Ptolemseus,' said Delambre, 

 ' will forever constitute the basis of trigonometry.' 



The second Alexandrian School closes with Diophantus [246 - 

 330], about 300 A.D., so distinguished as an algebraist, that it 

 has been said, that but for him algebra among the Greeks would,, 

 comparatively, have been an unknown science. 



Splendid as was the Greek mind in respect of its love of pure 

 science, it did not rise in mathematics, to generality of method. 

 The brilliant talents of Euclid, Archimedes and Apollonius had 

 indeed brought geometry to a high state of perfection ; the crystal- 

 line clearness of its concepts, and the logical rigour of its con- 

 clusions, were ideal : but its inherent limitation lay in the fact 

 that it was essentially special in character. Further advance 



