ANNIVERSARY ADDRESS. 2 



material good. Forever it will be the fate of Archimedes to be 

 esteemed by his fellow-citizens for his mechanical inventions, but 

 forever his own grateful feeling will arise, because to him it has 

 been given to penetrate the arcana of science and to reveal them 

 to mankind. This however by the way, as shewing that the pro- 

 gress of humanity depends upon the love of abstract knowledge ; 

 depends first of all upon Science, rather than upon Art. 



It is quite impossible under the limitations of our time to-night 

 to review even in the briefest manner the history of mathematical 

 progress: it is an embarras de richesse: any reference to significant 

 advances must perforce ignore others of perhaps equal moment. 

 Despite this, however, a reference to some elements of that history 

 is absolutely essential to its intelligent understanding and we 

 may therefore be pardoned for briefly scanning it. 



Introduced from Egypt by Thales of Miletus [640 - 546 B.C.] 

 about 600 B.C., raised by the genius of Pythagoras p? 582 - 504 

 B.C.] to the rank of a science less than one hundred years later, 

 geometry made rapid progress in Greece, largely through 

 Pythagoras' influence [about 550 B.C.], and still more through 

 that of the immortal Plato, about 400 B.C., ' maker,' as he has 

 been called, 'of mathematicians.' Plato [429 - 348 B.C.] himself 

 was practically the founder of solid geometry. A contemporary, 

 Archytas of Tarentum, [428 - 347 B.C.] was first in methodically 

 treating the subject of mechanics, and in applying geometry thereto. 

 To a brilliant pupil of Archytas and of Plato, Eudoxus of Cnidus 

 [408 - 355 B.C.], belongs probably the honour of inventing the 

 method of exhaustions, a method which contains the first germs of 

 the infinitesimal calculus. To Eudoxus belongs also the credit 

 of having so improved the methods of practical astronomy, as to 

 win him the appellation of 'father of scientific astronomical 

 observation.' A pupil of Eudoxus' viz., Mensechmus, was the 

 inventor of the conic sections, destined afterwards to play so 

 significant a part in dynamic and astronomical theory. About 

 350 B.C. Aristotle [384-322 B.C.] shewed that the logician may 

 assist the mathematician in the matter of difficult definitions. His 



