tefima k mctoAx or^ines ir^ctam mfi tertiam ptopQf- 
tionalcm pofl CK, Cb, & ducas per puncti^m m tangen- 
tem tractori* t^^l concurrentem in / cum norfnali hl: puti- 
ftum / erit in nolifa curva infinite proKirnum punsfto D , 
Concurrat autem ti cum DE in f ; ajo elTe differen- 
tiam duarum iinearum /^, DT. Inrclljgatur dudus D^ ar, 
cus fyntraClorix , cujus maxima ordinata ^quat DF; tum 
ex centro h defcribantur arcus miriimi D/, tf» Q^uoniani 
curva KD/ tranfit per punc^a , qux m&-%ims elevantur in 
fyntractoriis , linea tanget arcum Dd: Ergo iniercepta 
eO: infinirerima fecundi ordinis , & incomparabilis cum 
di infinitefima primi ordinis ; sgitur dizzziq; fed ^/rs 
}Ar^ — Tf; Ergo qi^Tf; fed differentia duarum //, DT 
eft // -4- T/ :=z l i i q ^ l q » Ergo prsdicta differentia 
gquat /f . Q. E. D» 
/ Corollarinm fecundum , Producta D, donee concurrat 
cum hl in /2, ajo a cj divifam effe bifariam in D. Quum 
enim TD fit certia proportionaiis pcfi CK, CF, fi voce- 
turTDrrj-, erittf^=rzz', & fomptis differentiis =: 2z^s . 
Ergo ti s : 1 d z : : z : a , five ex demonftratis in corol, fupe- 
yiore /f : 2 . D : : R. T : M T , five DT:TR; fed etiam 
: /jrtf::DT:TR. Ergo /^; 2 . aD : : i tj : q a » Igitur 
2 ,aD — q a ; atque adeo q a bifariam divifa erit in D • 
CL E. D. 
Corollarium tertium , Nullo negotio ex fuperiore inve- 
Jiies xquationem analyticam curvx maximanim elevationum . 
Voca CF=zz, "BD — u \ igitur — aD ~ dz^ & a q 
r=:idz, al^du ; fed eii l a : a q i : DK : KT l l PvM : MT, 
(ive analytice du:7dz:: R : at 
Ergo adu ~ iRdz ; fed Rrr:v/z.z, — ^^: Igitur adu— idz ^ 
y/zz, — a a ; quac formula pertinet ad hyperbol^ quadratu^ 
ram , eaque pofita nullo negotio defcribitur , 
CoroUarium quartum , Si dividas RT bifariam in O, & 
ducas DO, habebis tangentem curvac maximarum elevano- 
num in pundo D ; quod proclive ad.moduro demonfiratu 
eft . Sed didum fit fatis de curva hac, in qoa fpatium 
KCFD =y-]^> & cujus reflificatio pendet ab hyperbolae 
quadratura . Ad fyntradorias redeamus. 
'i - ii/, Q.qq P^c^- 
