Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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202FED. COMMANDINI
ABSCINDATVR à portione conoidis rectanguli
a b c alia portio e b f, plano baſi æquidiſtante:
& eadem
portio ſecetur alio plano per axem;
ut ſuperficiei ſectio ſit
parabole a b c:
planorũ portiones abſcindentium rectæ
lineæ a c, e f:
axis autem portionis, & ſectionis diameter
b d;
quam linea e fin puncto g ſecet. Dico portionem co-
noidis a b c ad portionem e b f duplam proportionem ha-
bere eius, quæ eſt baſis a c ad baſim e f;
uel axis d b ad b g
axem.
Intelligantur enim duo coni, ſeu coni portiones
a b c, e b f, eãdem baſim, quam portiones conoidis, &
æqua
lem habentes altitudinem.
& quoniam a b c portio conoi
dis ſeſquialtera eſt coni, ſeu portionis coni a b c;
& portio
e b f coniſeu portionis coni e b feſt ſeſquialtera, quod de-
149[Figure 149] monſtrauit Archimedes in propoſitionibus 23, &
24 libri
de conoidibus, &
ſphæroidibus: erit conoidis portio ad
conoidis portionem, ut conus ad conum, uel ut coni por-
tio ad coni portionem.
Sed conus, uel coni portio a b c ad
conum, uel coni portionem e b f compoſitam proportio-
nem habet ex proportione baſis a c ad baſim e f, &
ex pro-
portione altitudinis coni, uel coni portionis a b c ad alti-
tudinem ipſius e b f, ut nos demonſtrauimus in com men-
tariis in undecimam propoſitionem eiuſdem libri A rchi-
medis:
altitudo autem ad altitudinem eſt, ut axis ad axem.
quod quidem in conis rectis perſpicuum eſt, in ſcalenis

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