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

ARCHIMEDIS _quæ diametrum ſecet in ψ; ſecet autem i m eandem in σ: & a q in_
_v. Dico angulum a ν d angulo i σ d minoré eſſe. angulus enimi ψ d_
_æqualis est angulo a ν d. ſed angulus interior i ψ d minor eſt exte-_
_riore i σ d. ergo & a ν d ipſo i σ d minor erit_.

55.1.

C
0093-01
29. primi
16. primi

_Et quoniam angulus, qui ad χ minor eſt angulo, qui ad_
_n. ]_ Ducantur per o duæ lineæ, o c quidem ad diametrum b d per-
pendicularis: & o χ in puncto o ſectionem contingens, quæ diame
trum ſecet in χ. æquidiſtabit o χ ipſi a q: atque erit angulus ad
χ æqualis ei, qui ad ν. ergo angulus ad χ angulo ad σ, uidelicet eo,
qui ad n minor erit: & propterea χ infra n cadet. linea igitur χ b
maior eſt, quàm n b. Sed cum b c ſit æqualis χ b, & b s ipſi n b: erit b c ipſa b s maior.

55.1.

D
5. ſecũdi
conicoiũ
29. primi.
35. primi
conicorũ

Ergo æquales faciunt angulos a q, a m cum diametris
portionum. ] _Hoc demonstrabimus ut in commentarijs in ſecun-_
_dam partem_.

55.1.

E

_Similiter demonſtrabitur, portionem, quæ ad humidũ_
_in grauitate ean-_
_dem proportio-_
_nem habeat, quã_
_quadratum p fad_
_quadratũ b d; in_
_humidum demiſ-_
_ſam, ita ut baſis ip_
_ſius non cõtingat_
_humidum, incli-_
_natam conſiſtere_
_adeo, ut baſis in_
_uno pũcto humi-_
_di ſuperficiem cõ_
_tingat: & axis cũ_
_ipſa faciat angulũ_
_angulo φ æqualẽ]_
Habeat portio ad humidum in grauitate proportionem eam, quam
p f quadratum ad quadratum b d: & demiſſa in humidum adeo in-

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