MATHEMATICAL SCIENCES SEVENTEENTH CENT. 145 



official appointment in Paris, and yet found time to cultivate mathe- 

 matics so as to become the great ornament of the French science of 

 his time. He introduced the use of letters of the alphabet to stand for 

 the knoivn quantities, and though this may seem a small matter, all 

 those who are practically acquainted with the science will understand 

 how much this contributed to the progress of algebra, which then for 

 the first time became capable of expressing general truths. Vieta also 

 advanced the theory of equation, and introduced some considerable 

 improvements into trigonometry. His mathematical works were pub- 

 lished about 1590, and he died in Paris in 1603. THOMAS HARRIOT, 

 an Englishman, made the discovery that all the higher equations are 

 composed of so many simple equations multiplied together as are equal 

 in number to the highest index of the unknown quantity. Hence, the 

 number of roots in an equation is expressed by the index of its highest 

 power : thus, a cubic equation has three roots ; an equation of the 

 fourth degree four roots ; and so on. 



One of the inventions or improvements, which we must consider 

 of the first importance, from its general utility and the conspicuous 

 part it plays in the higher mathematics, was due to JOHN NAPIER, 

 Merchiston, near Edinburgh. Napier was born of a noble family in 

 1550, and had the advantage of the best education that could be 

 obtained in his time. He appears to have, at an early age, been 

 attracted to arithmetical and astronomical studies, and experiencing 

 the wearisomeness of making the laborious calculations which astro- 

 nomical investigations required, he bent his mind towards the discovery 

 of some method of facilitating trigonometrical computations. Here 

 we have an example of one of the ways in which the advancement of 

 one branch of science reacts upon others. In all preceding ages 

 mathematics stood apart from every other learning ; and this very ab- 

 straction was the boast of its cultivators. But when in the hands of 

 Kepler, Galileo, and others, astronomical, mechanical, and other physical 

 phenomena were reduced to strict quantitative estimation, the pro- 

 blems which presented themselves for investigation found .the resources 

 of mathematicians inadequate for their solution ; hence mathematical 

 genius was stimulated to supply the deficiencies by the invention of 

 more powerful methods. The mere labour of calculation by such 

 methods as were in use at the beginning of the seventeenth century 

 would have greatly impeded the progress of physical science but for 

 Napier's timely discovery. One of his first devices was for facilitating 

 multiplication by means of certain scales or rules, which were afterwards 

 known as Napier's Bones, from the material of which they were made. 

 But he soon discovered a higher mathematical principle, which he at 

 once reduced to a practical form as simple as it was powerful. And 

 these combinations of simplicity with power will always command the 

 admiration of those who understand the principle and the use of 

 Napier's invention. It is remarkable, also, that the invention came 



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