DESCARTES 



mathematical. Posterity has not ratified his judg- 

 ment in this respect. It is upon the latter that his 

 fame now rests. To him is due the present system 

 of notation by which the degree of involution of a 

 number is represented by a smaller numeral placed 

 above and to the right of the said number, thus 

 making the former the exponent thereof, and dis- 

 placing the various and cumbersome methods of ex- 

 pression then in use. The method of expressing in 

 Algebraic terms the properties of a curve is his 

 discovery, by which its nature is defined by the 

 relation existing between two variable lines the 

 ordinates and the abscissa. From the equation thus 

 obtained all the other geometric relations of the curve 

 can be deduced. The inverse proceeding, by which, 

 when having the algebraic formula he could regard 

 the abscissa as the roots of an equation, enabled him 

 readily to solve problems in Geometry that had 

 arrested all antiquity. Among his other discoveries 

 was the rule he has given by which to recognize the 

 number of real roots which an equation may only 

 have, from the alternatives of the signs that have 

 among them the terms which compose it. These 

 treatises on Geometry assure to Descartes an immortal 

 renown. Having rendered him this just homage, 

 we may venture to speak with equal truth in regard 

 to his other writings. The knowledge of the laws of 

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