( 8o8 ; 
mASoyi de M> Roherval, quatnque De la Hirt confiderat ^ 
ut Comhoidm Bafis Circularis, in Adlis Academism Pa- 
rifienfis Anni 1708. Perpendicularcs omnesLN, In 
concurrunt in pundo B, adeoque BNr=o: unde B P= 
tB L : Hinc Cutva tota B P S=^ B S, ac Ion- 
I — m ^ 
g\t\xdo Epcycloidis femperdupla eft chords arcus in cir- . 
culo correfpondentis. ‘Ex Eftqcloide defcribacuc 
Curva BnS, eadem ratione qua Epicjcloidm ex Cir- 
culo defcripfimus : In hoccafu>?=r» & 
4-f* 
_ • • * f 
z=z\, ac proinde squatio Curvs BnS eric s : y :: a^:r^ 
BL-fLP 
Longitude Curvs eric — rBL-|-LP=^BL-|-LG, 
& proinde Bn eft fefquiplus fumms Arcus circularis ejuf- 
que Sinus redi. Quod ft fumatur C D^B D, & radio 
S D centre S deferibatur Circulus occurrens reds S P in 
H, & ftt H K perpendicularis in B S; quoniam D H= 
jBL, eric B n=D H-j-H K. Hinc arcus Bn neque 
lunt redis neque arcubus circularibus commenfurabi- 
les, differentia tamen arcuum Bn & DH eft reda 
H K. In pundo S evanelcit LG, adeoque Bn S=tB L S, 
unde tota Curva eft fefcupla femicirculi. Nulla vero 
pars hujus Curvs alBgnabilis commenfurari poceft toti, 
nee Integra Curva in data quavis ratione fccabilis eft, 
ita ut portiones rationem affignabilem habeant ad fe mu- 
tuo aut ad totam. Si hsc curva in data aliqua ratione 
Geomecfice fecari poffec, conftarec Quadratura Circuli, 
nam fi e.gr. eflet B n ad B n S ut i ad w, & BL ad B L S 
ut I ad », eflet Bn=--=— = = HT+lg „ 
unde eflet H & B L S=:^. L G j"' Ex BnS 
ft — M 
conftruatuj: explicata. methodo Curva B R, & quoniam 
