Page:Annales de mathématiques pures et appliquées, 1822-1823, Tome 13.djvu/50

46

INTÉGRALES

${\begin{alignedat}{3}{\frac {\operatorname {d} z}{\operatorname {d} x}}=&l,&{\frac {\operatorname {d} ^{2}z}{\operatorname {d} x^{2}}}=&n,&{\frac {\operatorname {d} ^{3}z}{\operatorname {d} x^{3}}}=&q,\ldots \\\\{\frac {\operatorname {d} z}{\operatorname {d} y}}=&m,\qquad &{\frac {\operatorname {d} ^{2}z}{\operatorname {d} x\operatorname {d} y}}=&0,\qquad &{\frac {\operatorname {d} ^{3}z}{\operatorname {d} x^{2}\operatorname {d} y}}=&r,\ldots \\\\&&{\frac {\operatorname {d} ^{2}z}{\operatorname {d} y^{2}}}=&p,&{\frac {\operatorname {d} ^{3}z}{\operatorname {d} x\operatorname {d} y^{2}}}=&s,\ldots \\\\&&&&{\frac {\operatorname {d} ^{3}z}{\operatorname {d} y^{3}}}=&t,\ldots &\\\\\end{alignedat}}$

$\ldots \ldots \ldots$^[1]

Quant aux différentielles partielles, nous poserons

${\begin{alignedat}{4}\left({\frac {\operatorname {d} V}{\operatorname {d} x}}\right)=&K,\quad &\left({\frac {\operatorname {d} V}{\operatorname {d} l}}\right)=&L,\quad &\left({\frac {\operatorname {d} V}{\operatorname {d} n}}\right)=&N,\quad &\left({\frac {\operatorname {d} V}{\operatorname {d} q}}\right)=&Q,\ldots ,\\\\&&\left({\frac {\operatorname {d} V}{\operatorname {d} m}}\right)=&M,&\left({\frac {\operatorname {d} V}{\operatorname {d} o}}\right)=&O,&\left({\frac {\operatorname {d} V}{\operatorname {d} r}}\right)=&R,\ldots ,\\\\&&&&\left({\frac {\operatorname {d} V}{\operatorname {d} p}}\right)=&P,&\left({\frac {\operatorname {d} V}{\operatorname {d} s}}\right)=&S,\ldots ,\\\\&&&&&&\left({\frac {\operatorname {d} V}{\operatorname {d} t}}\right)=&T,\ldots ,\\\\&&&&&&&\ \ \ldots \,;\end{alignedat}}$

1. Nous aurions bien désiré de pouvoir employer les notations ordinaires ; c’est-à-dire, de faire ${\frac {\operatorname {d} z}{\operatorname {d} x}}=p,\ {\frac {\operatorname {d} z}{\operatorname {d} y}}=q,$ et ainsi du reste ; mais, dans le dessein où nous étions de pousser les développemens un peu plus loin qu’on ne le fait communément, cela devenait impossible.