135 ATTI 



qua abfciffie, & conftantium quanrifarum , fìet femper^ nax^ Scc. 

 denotante ^rx^ quemcumque i'criei termiiium, iti quo occurrat 

 quantitas comtans, & ablciila at ad poteliatem quamlibet ff?eve- 

 fta i fumptis i' irar \\\ unoq'joque feriei termino differentialibus 

 ^xixdy — amx"—'- dv ^y dJyz=:am r?t^T~t . x"—^ ix'^ &j.,atque 

 ita porro rt'J^)' = ^»'- /^^ • OT^- x^—^dx^ &c. Jam vero li 

 in priori jeq^iatione loco x fubllitaamus abrciifas ordine fubfe- 

 quentes x-*-dx , x-hidxScc , aut uni/erfiin x-^ndx^ fìet ( x-^iidx j" 



^x'-'^j/mx--' dx-hn . m / "" ~ ' \ x"-""- dx^-i-n^ m 

 \~~^ ì \ J^"~ "•^'J&c.ltaque ^^ó'^zx-^ dx refpondebit 



lemiordinata'v-»- dy-^ ■ 1 — H ^- h &c. » atqne uni- 



-'- - 1.2- 1.2.3 1-2-34 ~ ^ 



verdtn abfciirae x -i- ndx refpondebit femiordinata y -t- ndy-^ 



— H 1- H ^ -H g^g 



1- 2 — 1.2.3, 1.2.3.4 - * 



e O R O L L A R I U M L 



Ira igifur ex generali squatione coUigitur breviffime theo- 

 rema a Tayloro oilm tradituni in Propof vii. de Metbodo In- 

 crcmentorum, atque a M.i e- Laurino in Propof. xx. Lib. i.> & 

 §. 751. Lib. 1 1. deFluxionibus. Si acquati-) {izy-^ax-^b >. & cur- 

 va in lineam rectain degcnerst, polita tì^x conftante evanefcent 

 difterentias inferiorisordinis,Sc tiet femiord'nataqaielibetj/ jH ìtdy. 

 Hoc autem pofito, ducla tangente ìLYk ad puncìum F, eric 

 dy difFerentia oinais GK ». qate ad tangentem ufque protendetur 

 & dy : dx esprimer rationeni lemiordinatte ai fubtangentem , & 

 & lubnormalis ad femiordinatani: atque inde colligecur fubtan- 



gentis expreflioS— , & fubnormalis =^-^. 



C O R O L L A R 1 U M li.. 



lifdem etiam podtis denominatfonibns erit intcrcepta tan- 

 genrem inter, & curvam GK=:— ^'^''j' — ii^j»» ^ gk'='—~'i'^y 

 "*" é'iy' ^c fi curva vcrfus axem in concava, & iì curva co^ve- 

 xa lir er;t prior interc.'^pra4^*y -<-|'i^ v&C&intereeptaalia |i*^ 

 — \^y 3tc : atq'ie ira. facile cognofcetur (i curva axeni verfus 

 fu conca^-a, ve! coavexa ex quo fecunJa fcmiordinarns diff.rea- 

 tia .ie^atwum, vel poùtivurn valorem habeac . Et cum interce- 



pta. 



