SIR ISAAC NEWTOtf 



and such a desire to study that he was returned to 

 the school at Grantham, where he remained until 

 eighteen years old, whence, in 1660, he was admitted 

 to Cambridge. Here, under the tuition of Barrow, 

 one of the greatest mathematicians of his time, he 

 thoroughly mastered the Geometry of Descartes and 

 the "Arithmetica Infinitorum" of John Wallis. 

 From the study of the latter, when he was twenty- 

 one years old, he conceived the idea of perfecting it by 

 further developments, and worked out the details of 

 the Binomial Theorem that has since borne his name, 

 and to which he gave the necessary algebraic formula. 

 In this consisted the " method of fluxions " of which 

 Newton then laid the foundation, to be eleven years 

 later re-invented by Leibnitz and presented by him 

 under another form that of the Differential Cal- 

 culus which is in general use to-day. These pro- 

 cesses he had worked out before he was twenty-three 

 years of age. He kept them secret, not revealing 

 them even to his former teachers, Barrow and 

 Wallis. It was not until 1668, when Mercator pub- 

 lished his work entitled Logarithmo-technia, in which 

 he showed how to obtain the quadrature of an hyper- 

 bola, that Newton was forced to produce the proofs 

 of his earlier methods. He presented them to his 

 master Barrow, who was astonished at the number 

 and the value of the analytical discoveries, which far 



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