290 A SHORT HISTORY OF SCIENCE 



which they first found out those Propositions, which they thus demon- 

 strate by other ways. . . . Nonius ' O how well it had been if those 

 Authors, who have written in Mathematics, had delivered to us their 

 Inventions, in the same way, and with the same Discourse, as they 

 were found out ! And not as Aristotle says of Artificers in Mechanics 

 who show us the Engines they have made, but conceal the Artifice, 

 to make them the more admired ! ' 



His Analytical Conic Sections (1665) made Descartes's geometri- 

 cal ideas much more intelligible, and his Algebra (1686) marks an 

 important step forward in its systematic use of formulas. He 

 also wrote A Summary Account ... of the General Laws of Mo- 

 tion, enunciating the formulas for velocity after impact of masses 

 mi and ra 2 with velocities vi and v% : 



mi + ra 2 



Barrow, after varied adventures, became first Lucasian professor 

 at the University of Cambridge, but resigned his chair six years 

 later to his pupil Newton. His work on optics and geometry 

 contains a notable discussion of the tangent problem and of what 

 he calls the differential triangle, so important in modern elementary 

 differential calculus. His general point of view is illustrated by 

 the following passage : 



Now as to what pertains to these Surd numbers (which, as it 

 were by way of reproach and calumny, having no merit of their own 

 are also styled Irrational, Irregular, and Inexplicable) they are by many 

 denied to be numbers properly speaking, and are wont to be banished 

 from arithmetic to another Science (which yet is no science), viz. 

 algebra. 



ISAAC NEWTON, was born within a year after Galileo's death, 

 a century after that of Copernicus December 25, 1642 (O.S.). 

 Destined at first to become a farmer, he was fortunately sent at 

 17 to the university, where he quickly and eagerly mastered the 

 mathematical work of Euclid, Descartes and Wallis, and Kepler's 

 Dioptrics. His discovery of the general binomial theorem dates 

 from this time, and he even ventured to attack the great problem 



