14 G. H. KNIBBS. 



Scotland's son, John Napier of Merchiston, [1550 - 1617] in 

 1614 discovered logarithms. Henry Briggs [1556 - 1631] and 

 Napier together adapted them -to the purposes of ordinary com- 

 putation ; the latter and Adrian Vlacq of Holland calculating the 

 extensive tables with which we are familiar, and which have 

 become a necessity to the modern world. About the same time 

 the illustrious Johannes Kepler [1571 - 1630] made his great 

 discovery of the ideal laws of planetary motion. The study of 

 the conic sections by Mensechmus, Aristseus, 1 and Apollonius was a 

 matter purely of intellectual interest : those discoveries however, 

 furnished Kepler with the key, by which to unlock the real 

 character of that motion, a splendid example of the fruition of 

 abstract discovery. Into geometry Kepler introduced definitely, 

 the conception of quantities infinitely great or infinitely small, 

 another evidence that the infinitesimal calculus, yet only inchoate, 

 was nevertheless taking form in the human mind. In 1635, 

 Bonaventura Cavalieri's 2 'geometry of indivisibles' marked a still 

 further advance, and indeed this method was used as a species of 

 integral calculus for fifty years afterwards. It was improved by 

 Roberval [1602 - 1675], and by Pascal [1623 - 1662]. About the 

 same time Pierre de Fermat [1601 - 1665], for whom the credit of 

 inventing the differential calculus has been claimed by Lagrange, 

 Laplace, and Fourier, developed the modern theory of numbers ; 

 in which, for one thousand years, no substantial discovery had 

 been made. 3 Blaise Pascal, a still greater than Fermat, and a 

 contemporary, developed with him the first elements of the theory 

 of probability, afterwards enriched by the labours of Huygens, 

 Jakob Bernoulli, and Laplace. Galileo Galilei [1564 - 1642] laid 

 the foundations of dynamics ; an office, as Lagrange points out, 



1 A contemporary of Euclid. 2 [159,8 - 1647]. 



3 An interesting fact in connection with this, is that Fermat believed 

 that the expression 2 2n + 1 yielded always a prime number. Euler 

 pointed out that 2 2 * + 1 = 4294967297 = 6700417 X 611. The American 

 lightning calculator Zerah Colburn is said to have readily found the 

 factors when a boy, though he was unable to say how he made so astonish- 

 ing a mental computation. 



