MAXIMORVM ET MINIMORFM. lol 



Tariabili x pendcret , ncqiic iiitcmm y implicarct, forc 

 ^Z~o j neqiie igitiir vaiiabilis .v, vtciinqiic c;i in for- 

 mationcm fiincftionis Z ingrediatiir , qiiicquam ad 5" Z 

 confcret , fed cius valor a (olo elemento $j, quo va- 

 riabilis y crclccrc concipitur, rcfultat. Hic alitem pront 

 Z vcl lolas qnantitates fuiitas x et ^, vcl etiam carum 

 dilFcrentialium rationem , vcl adeo formulas intcgralcs 

 inuoluit , ita diucrfi cafiis crunt cxaminandi. 



XV. 



Ponamus crgo primo, funcflioncm Z tantum ipfis 

 quantitatcs finitas .v et y inuolucrc , ita vt ncque ratio 

 diffcrcntialium , ncque vllac formulae intcgralcs, in cam 

 ingrcdiantur , atque ad cius variationem $ Z definicii- 

 dam , in fundionc Z \biquc loco j (cribi oportet 

 J-^-Sj' rcliiflo X inuariato , ficquc prodibit valor va- 

 riatus 2.-+-SZ, a qno fi principalis Z fubtrahatur, re- 

 manebit variatio $2,. Manifcfium ergo cfl, hanc va- 

 riaiionem obtincri, fi fiuKflio Z morc folito diffcrcntietur , 

 pofita lo!a y variibili , dummodo pro t^y fcribatur $y. 

 Qiiarc fi diffcrcntiationc more (blito inftituta, (iimta vtra- 

 quc quantitatc x ct y variabili , fiicrit ^ZzMr/.v-f N^, 

 erit pro translationc a fiatu principaU ad variatiim 

 $ 2.~N^y ] hacc crgo variatio rcpcritur , fi in di(ic- 

 rcntiali ordinario pro dx (cnbatur o, pro ^/ autcm <Jj/ j^ 

 hocquc mudo cadim primuni fiicillime expediuimus. 



XVI. 



Videamus aiitcm poiro, quomodo pro hoc ca(u 

 primo, quo Z cfi fundio ipfarum .v ct ^' tantnm, f()r- 

 mulae intcgralis /Z^.v valor maxiinus vcl minimus 

 inucniri qucat. Cum igitur pro quouis valorc ipfius x 

 fundtio Z ciercat cicmciito N $y , idcoquc Z c/x par- 



ticula 



