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A SYNTHETICAL DEMONSTRATION of the RULE 

 for the Q^UADRATURE o;^SIMPLE CURVES, 



in the Analyfis per Equationes terminorum niimero infnitas. 

 By the Rev. M. YOUNG, D. D. 



13 OCT OR Wallis, about the year 1651, having met with Read March 

 the mathematical writings of TorriceUi, in which, amongft 

 other things, he explains Cavalerius's attempt to render the 

 ancient method of Exhauftions more concife by his Geometry 

 of indivifibles, conceived that an Arithmetic of infinites might 

 be applied to the contemplation of curve lines with fuccefs ; 

 and that perhaps the quadrature of the circle, were it at all pof- 

 fible, might finally be attained in this manner. What led him 

 to thefe expedations, as he tells us in his dedication to Ough- 

 tred, was this : the ratio of the infinite circles of a cone to 

 as many of a cylinder on the fame bafe and of the fame 



altitude. 



