Full text: Archimedes: Archimedis De iis qvae vehvntvr in aqva libri dvo

ARCHIMEDIS quædam recta linea g i, ſectionibus a g q l, a x d interiecta,
& ipſi b d æquidiſtans; quæ mediam coni ſectionem in pun
cto h, & rectam
lineam r y in y
ſecet. demonſtra
bitur g h dupla
h i, quemadmo-
dum demonſtra
ta eſt o g ipſius
g x dupla. duca-
tur poſtea g ω cõ
tingens a g q l ſe
ctioneming: & g c ad b d perpé
dicularis: iun-
ctaq; ai produ-
catur ad q. erit
ergo a i æqualis
i q: & a q ipſi g ω
æquidiſtans. Demonſtrandũ eſt portionẽ in humidũ demiſ
fam, inclinatamq; adeo, ut baſis ipſius non cõtingat humi-
dũ, conſiſtere inclinatã ita, ut axis cum ſuperficie humidi
angulum faciat minorem angulo φ: & baſis humidi ſuper-
ficiem nullo modo contingat. Demittatur enim in humi-
dum; & conſiſtat ita, ut baſis ipſius in uno puncto contin-
gat ſuperficiem humidi. ſecta autem portione per axem,
plano ad humidi ſuperficiem recto, ſit portionis ſectio a n
z l rectanguli coni ſectio: ſuperficiei humidi a z: axis autẽ
portionis, & ſectionis diameter b d: ſeceturq; b d in pun-
ctis _K_ r, ut ſuperius dictum eſt: & ducatur n f quidem ipſi
a z æquidiſtans, & contingens coni ſectionem in pũcto n; n t uero æquidiſtans ipſi b d: & n s ad eandem perpendi-
cularis. Quoniam igitur portio ad humidum in grauitate,
cam habet proportionem, quam quadratum, quod fit à χ

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