634 



SCIENTIFIC THOUGHT. 



Origin of 

 mathe- 

 matics. 



cal into philosophical thought ; l so much so that this 

 closing chapter on the development of mathematical 

 thought forms a fitting link with the next great depart- 

 ment of our subject the Philosophy of the Century. 



We are told that mathematics among the Greeks had 

 its origin in the Geometry invented by the ancient 

 Egyptians for practical surveying purposes. The first 

 mathematical problems arose in the practice of men- 

 suration. Modern mathematical thought received in 

 an analogous manner its greatest stimulus through the 

 Uranometry of Kepler, Newton, and Laplace : through 

 the mechanics and the survey of the heavens new 

 methods for solving astronomical problems were in- 

 vented in the seventeenth and eighteenth centuries, 

 and the nineteenth century can be said to have at- 

 tempted to perform towards . this new body of doctrine 

 the same task that Euclid, three hundred years before 

 the Christian era, performed towards the then existing 

 mathematics. As Proclus tells us, " putting together 

 the elements, arranging much from Eudoxus, furnishing 

 much from Theaetetus, he, moreover, subjected to rigorous 

 proofs what had been negligently demonstrated by his 

 predecessors." 2 What one man, so far as we know, did 

 for the Grecian science, a number of great thinkers in 



1 Thus, for instance, the recent 

 investigations and theories of the 

 " manifold," as they have been 

 set forth by Prof. Georg Cantor 

 of Halle, constitute, as it were, 

 a new chapter in mathematical 

 science, whereas they were for- 

 merly a subject merely of philoso- 

 phical interest. See a remark to 

 this effect by B. Kerry at the end 

 of his very interesting article on 



Cantor's doctrine in the 9th 

 vol. of Avenarius's ' Zeitschrift 

 fur wissenschaftliche Philosophic ' 

 (1885), p. 231, where he refers to 

 Kant's comparison of philosophy 

 to a Hecuba " tot generis natisque 

 potens." 



2 Quoted by Cantor, vol. i. p. 

 247. See also Hankel, loc. cit., 

 p. 381 sqq. 



