CJtCVLl VAKIATIONVMV 7,^, 



CoroUarium. 



49. Sic ergo variatio definitur qiiantitatis O per 

 acquationem difForentialeni </<I) n^ Z ^.r datae , in qua Z 

 non (olum praeter litteras a', 7, p, ^, r ete. ipfam O, 

 fed infuper formubm integralem J^^dx—Yi vtcunque 

 inuoluitvdummodo 3 P^^ ^^^^* litteras a,^, p, ^, r etCc 

 dcterminetur: 



Problema 8. 



5^0; Si in formula intcgrali OzrfZdx quanti-- 

 tas Z praettr litteras x^y, p, q, r etc. formulam in- 

 tegralem U.—f^dx inuoluat , hic autem quantitas 3' 

 praeter litteras x, j, p, ^, r etc. ipfim formulam in- 

 tegralem Ti—j^^dx contineaf, definire variationemi 

 formulae propofitae. O—fZdx. 



So I u t i o. 



Cum Z fit fundlio quantitatum x^y.p, q^r etc,- 

 er ipfius ll—j^^dx y eius difFcrentiale erit liuiusmodi ;: 

 ^Z = L ^n -h M df j + N ^ H- P «'p -5- Q.^^ + R </r + etc. . 

 hinc eiilis variatio erif 



a:Z=L^n + N5j+P^^ + Q.l^'^+R?|-^ + etc. 

 ex; quo ob ^(^'zizJ^Zdx habebitur : 



80-VLdxBU+Jdx{^^v-\-?^-\-(^4^-\- etc. )• 

 At quia ^ ^'^ fundio ipfarum A, /, p^ q^ r etc. et 

 U—J^^dx , fit eius difFerentiale : 



^^- £^n-f- ^DJ^A- -^^dy^ ^dp +OJq + etc 

 eritque 



Ponatur 



