14 GENERAL THEOREMS, CHIEFLY PORISMS, 



Par. L M x (M + N) 



AG : q p', consequently ACD = ^-r multi- 



M (q p) 



plied by ( -f- - + p } and diminished by - 



\ m + 2n ) M 



q . A G . Par. L M x (M + N) 



X A N x 5 therefore, transposing - X 



q p M X (q p) 



Y. , M + N 



+ p I is equal to A c D -4 X A N x 



m + 2w 1 M 



q-p 



; and par. L M will be equal to 

 / M + N o . A G\ M 



ACD H X AN X = X 



\ M q-p J q - 



^3~P 



\m + 2n 

 M 



M+N 



X (q P) X ACD + AN X AG 



Now it was before demonstrated, that the parameter of LM 



q . AG 



is equal to AP x (MP + O + ' ;. ). This is 



\ m + 2n J 



M + N 



therefore equal to ~~m~+n 



M . N 



X (qp) XACD + (7.ANXAG 



x (q- 



( vfl \ 77 i \( \ (1 - 7) t 7W" 



multiplying both by ~k + P-> we ^ ave " 



r J m + 2n M + N 



X (q p) X ACD + g-.AN x AG = APX(MPX (p + 



. AQ\ 



M + 



m + 2n 

 From these equals take q . AG x AN, and there remains 



- X (q p) X ACD equal to AP x P M X ( - 



