30 DISSERTATION SECOND. [parti 



mathematical sciences. This was the application of the alge- 

 braick analysis, to define the nature, and investigate the 

 properties, of curve lines, and, consequently, to represent 

 the notion of variable quantity. It is often said, that Des- 

 cartes was the first who applied algebra to geometry ; but 

 ibis is inaccurate ; for such applications had been made 

 before, particularly by Vieta, in his treatise on angular sec- 

 lions. The invention just mentioned is the undisputed 

 property of Descarles, and opened vast fields of disco* 

 very for those who were to come after him. 



The work in which this was contained is a tract of no 

 more than 106 quarto pages; and there is probably no 

 book of the same size which has conferred so much and so 

 just celebrity on its author. It was first published in 

 1637. 



In the first of the three books into which the tract just 

 mentioned is divided, the author begins with the considera- 

 tion of such geometrical problems as may be resolved by 

 circles and straight lines ; and explains the method of con- 

 structing algebraic k formulas, or of translating a truth from 

 the language of algebra into that of geometry. He then 

 proceeds to the consideration of the problem, known among 

 the ancients by the name of the locus ad quatuor rectas, 

 and treated of by Apollonius and Pappus. The algebraick 

 analysis afforded a method of resolving this problem in its 

 full extent ; and the consideration of it is again resumed in 

 the second book. The thing required is, to find the locus 

 of a point, from which, if perpendiculars be drawn to four 

 lines given in position, a given function of these perpendicu- 

 lars in which the variable quantities are only of two dimen- 

 sions, shall be always of the same magnitude. 1 Descartes 



1 It will easily be perceived, that the word function is not con- 

 tained in the original enunciation of the problem. It is a term 

 but lately introduced into mathematical language, and affords 



