Page:Annales de mathématiques pures et appliquées, 1826-1827, Tome 17.djvu/379

${\begin{array}{ll}S-A+B-\ldots -N+P-Q&=R',\\A-B+C-\ldots -P+Q-R&=S'\,;\end{array}}$

on aura de même

${\begin{array}{clr}A'+B'+C'+\ldots +Q'+R'+S'&=0,\qquad &(5)\\AA'+BB'+CC'+\ldots +QQ'+RR'+SS'&=0.\qquad &(6)\end{array}}$

$\left.{\begin{array}{ll}A-A'&=S+S',\\B-B'&=A+A',\\C-C'&=B+B',\\\ldots \ldots &\ldots \ldots \\Q-Q'&=P+P',\\R-R'&=Q+Q',\\S-S'&=R+R',\end{array}}\right\}\quad$(7)

$(A+A')+(B+B')+\ldots +(R+R')+(S+S')$

$-(A-A')-(B-B')-\ldots -(R-R')-(S-S')=0.\quad$(8)

Des équations (7) on conclura encore,

${\begin{array}{ll}\operatorname {Cos} .(A-A')=\operatorname {Cos} .(S+S'),&\qquad \operatorname {Sin} .(A-A')=\operatorname {Sin} .(S+S'),\\\operatorname {Cos} .(B-B')=\operatorname {Cos} .(A+A'),&\qquad \operatorname {Sin} .(B-B')=\operatorname {Sin} .(A+A'),\\\operatorname {Cos} .(C-C')=\operatorname {Cos} .(B+B'),&\qquad \operatorname {Sin} .(C-C')=\operatorname {Sin} .(B+B'),\\\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots &\qquad \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \end{array}}$