D E L L' ACCADEMIA. 147 



rr i f^j:=zoy ac fiet dy^^iidf, atque ob datam rationcm ele- 

 menti cujuslibet &. arcus>& Amiordinata;, punica arcus omnia 

 jacebunt in una> eadcmque linea re61a . Si quanritas prcpollta 

 elFet dumtaxat Sa-' df-, & differentia ^A-eflet conftans » folus coef- 

 ficiens te' clementi arcus df fpedandus eilet , atque ex eadem 



formula eruerctur</r_-2-^j = </ ( -^j = o : & lì etiam propo- 



netur quantJtas a"' àj^t juxra Cordi. II. Probi. IH.» prò cafu 

 maximi aut minimi valoris debcret cd'c tn.d{X'ds''~* <(y) = o. 



Po(ìtoautcm^r^^-] =0 , iìeret x- dy — a'df-, atque ob 



/ a" d X \ 



df—\/{dx'^ -V- dy"^ )eiret curvx quefitae a^quatio j/ =S/ 7.-a,_^- s j ; 

 ac polito « =: — 3) prodiret eadem cycloidis se^uatio y == 



C O ROLLARIUM IV. 



Si quantiras S^-^'^y efle debeat maxima, vel minima, com- 

 paratis formulae gcneralis terniinis fiet Y = atJ/", eritque A'j/coef- 

 llciens elementi arcus df-, adeoque prò eodem maximi , aut mi- 

 nimi valoris cafu iìctA'^^/^^|*^j=:o. Efl: axitem— <// ~7r') — 

 _xdy-__ydxdy_xydjj,_^xjdy'djf ^^ ^^ ^^ ',,,^^^,J^ 



df df df df^ ; ^ ^ df* 



■=:-LJ ^ . Oliare erit Problemaris a:quatio xdf — — -Z_ — 



dfi ^~ , ^ "^ <//* 



•^^-^l^=:^^^j-,eaquedu£i:a inj recidet in aequationem aliam 



xdx-ydx-^^^^, quam Eulerus in cxemplo VI. Probi. IH- 



inveoerat 



Problema V. 



Si fit dZziLyidx^ ì^dy -*- P^^-y ^ 9-JJ^Scc. invenire gai- 



bus in cafìbus quantitas SZ. dx cfle poffir maxima vel minima. 



Si ira comparata lit funótio Zut fumpris dilferentialibns ter- 



minusM^A- prodeat, hahita dumtaxat abfcina .vpro variabili , & 



•erminusNV^ prodeat, habita prò variabili dumtaxat femiordina- 



T 2 ta^, 



