(l2, ) G

differentiatione obtineo rb™dz^ddx ~ l dddx -f - nb m dz n 1 ddx r dd^

•+• mb m ~ l dhdz n ddx r 00 O, quae divisione per h m ~~ l dz ” ddx

contrahitur ad hanc rhdzdddx- -f- nbddxddz -f- mdhdzddx 00 o j haecvero terminotenüs collata cum Aquatione Problematis hdzdddx—•$ bddxddz — dhdzddx00 ©,exhibet rOO*,« 30—J, &m 00 — i" unde

ioco fictae aequationis h m dz n ddx r OO const.habetur ddxMz} ooconst«00 (ex lege homogeneorum & propter constans dy~) a itaady, aequa»tio nempe differentiatis secundi gradus j ad quam ulterius depri-mendam pono rursum aequationem adx 00 tdy,b qua debite tracta-tä fluunt sequentia , ddx 00 dtdy:a, aadx z OO ttdy 2 , 6 C ( a ddito aady 1 )aadx* aady 1 ,id est, aadz* 00 aa-\-tt,dy*, & dzOO dy 'Jaa-^-tt: a-, hivero valores loco ddx & dz in aequatione inventi ddx^jdz* 00 8 1 :aady substituti producunt aadt :aa -\-ttsjaa -f-rr 00 8 bdy: aa OOBhdxiat, seu (instituta multiplicatione per 8 O 8 aatdt:aa+tt\siw-H f 30 hdx:a 00 ( propter eandem/&x / i hdf: a 00 (per hyp,) dF ;unde factd fumatione acquiritur,partim aa: V da-\-u , partim a — aa:-saa-\-ttOO F, h, e. applicatae KR , seu huic contiguae HP a ut MN -,quam si deinceps vocare lubeat p, habebitur tum p 00 aa : V aa-\-tt,tum p 00 a— aa\\Jaa-\~tt ; unde vicitsim SctOO a^aa — pp:p , & t 00< 1 V tap — pp : 4 — p. Atque hi tandem valores in positi aequatione adx00 tdy in locum t suffecti exhibeat partim dy 00 pdx: V aa — pp, par-tim lhoo-r— p,dxxsjzap—pp , pro Aquationibus simpliciter diffe-rentialibus Curvarum , quae Maximum Minimumve spatium MV"( fpdy ) suppeditant. Quod quidem principaliter inveniendumerat,.

Utri verb harum Curvarum Maximum , 8c utri Minimumspdy conveniat , sic indagabimus: Prior Aquatio est dy OO pdx:

S Ua — pp ; unde quadrando dy* OOppdx 2 : aa—pp, & ( addendo dx *)•dy*-}-dx z sive dz* 00 aadx 2 :aa—pp ; & extrahendo radicem, dz

00 adx:\Ja: — pp: quare dy. dz::p.a\ hoc est,sumta constante dz , dy’ptoporcionatur ipsi p, Ergo si. crescentibus x. crescere supponantur