MAXlMQRm ET MINIMORFM. 117 



Efl; vero, fumto difFerentiali dx conftaate , 



1.. S d y d S y 



^ S dp d^ ddS y 



°? — dx — dx — d*» 



't- S dq dS q ^^^_y 



°^ — dx — dx dz« 



^ S dr d S r d*Sy ^ 



S ■ <i 35 -^ _- J^ 'y 



vnde obtinebimus : 



lam pro integratione formulae /(J^Z^/at, pcr partes ia' 

 ftituenda, vidimus eflc 



jVdBy—?Sy-J§yd? 



JQ}^ = Qg -'dd(l-^fddd(l 



/R 'i^ = R^^^^-g^R + ^ddR -J%d'K 



J^^dx^ __5 d^, — j^, ab + a;gt(iab—j^td i>-Jdfsd S 



etc. 

 Ex his ergo colligitur variatio differentialis quacfita : 



H-Jj,(P-j-J+^_|y + ecc.) 



•^-dxiQ.-d-x -i- di^ - etc.) 



-+- 'd^ (R-d3i -4- etc) 



-H d*» (S - etc.) 



vbi pars prima intcgralis a termino ;»;— o vsque ad 

 x — a extendi debet , quae ergo omnes variationes in- 

 termedias complecflitur : in reliquis autem partibus ab* 

 folutis ftatim ponere licet x—a^ et ^j denotabit in« 



r 3 cremen- 



