Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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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-_
29. primi_riore i σ d.
ergo & a ν d ipſo i σ d minor erit_.
16. primi
_Et quoniam angulus, qui ad χ minor eſt angulo, qui ad_
D_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
5. ſecũdi
conicoiũ
χ æqualis ei, qui ad ν.
ergo angulus ad χ angulo ad σ, uidelicet eo,
29. primi.qui ad n minor erit:
& propterea χ infra n cadet. linea igitur χ b
35. primi
conicorũ
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.
Ergo æquales faciunt angulos a q, a m cum diametris
Eportionum.
] _Hoc demonstrabimus ut in commentarijs in ſecun-_
_dam partem_.
_Similiter demonſtrabitur, portionem, quæ ad humidũ_
F_in grauitate ean-_
Figure: /permanent/library/4E7V2WGH/figures/0094-01 not scanned
[Figure 59]
_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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