VIII. New Series for the Quadrature of the Conic Sec- 

 tions, and the Computation of Logarithms. 

 By William Wallace, one of the Professors of Ma- 

 thematics in the Royal Military College at Great Mar- 

 low, and F. R. S. Ed in. 



[Read 27th June 1808.] 



i. r TPHE Quadrature of the Conic Sections, and the Compu- 

 X tation of Logarithms, are problems of confiderable 

 importance, not only in the elements of Mathematics, but alfo 

 in the higher branches of that fcience. On this account, every 

 fuccefsful attempt to Amplify their refolution, as well as any 

 new formulae which may be found applicable to that purpofe, 

 muft always be interefling, and muft in fome meafure contri- 

 bute to the improvement of mathematical knowledge. 



2. The object of this Paper, is to give folutions of thefe 

 problems, which fhall be at once fimple and elementary, with- 

 out employing the fluxional or other equivalent calculus ; and 

 it is prefumed, that thofe which follow, will be found to par- 

 take fo much of both thefe properties, that they may even ad- 

 mit of being incorporated with the elements of Geometry and 

 Analyfis. Befides, the formulas which refult from the invefti- 

 gations, are, as far as I know, entirely new, while each is appli- 



Ll 2 cable 



