Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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88ARCHIMEDIS ductæ ſunt à baſibus ad portiones lineæ a n, a q, quæ angu
los æquales continent cum ipſis baſibus, eandem propor-
tionem habebit q a ad a n, quam l a ad a d.
] _Hoc nos ſu_-
_pra demonstrauimus_.
Aequalis eſt ergo a n ipſi n q. ] _Cum enim q a ad a n ſit_,
11F _ut l a ad a d;
diuidendo, conuertendoq; erit an ad n q, ut a d ad_
_d l.
eſt autem a d æqualis ipſi d l, quoniam d b ponitur diameter_
_portionis.
ergo & a n ipſi n q eſt æqualis_.
2214. quinti
Et a q ipſi m y æquidiſtans. ] _Ex quinta ſecundi libri coni_-
33G _corum.
Apollonĳ_.
Etſecetur b d in punctis k r, ut dictum eſt. ] _In prima_
44H _parte huius propoſitionis.
ſecetur autem in K ita, ut b k ſit dupla ip_-
_ſius k d;
& in r, ut K r ſit æqualis ei, quæ uſque ad axcm_.
Quòd cũ in portionibus æqualibus, & ſimilibus, a p o l,
55K a m q l ab extremitatibus baſium ductæ ſint a o, a q, ita ut
portiones ablatæ faciant cum diametris angulos æquales:
& anguli, qui ad y g: & lineæ y b, g b inter ſe æquales erũt. ]
_Secet linea a q diametrum d b in θ, &
a o ſecet in η. Itaque quo_-
_niam in portionibus æqualibus, &
ſimilibus a p o l, a m q l ab ex_-
_tremitatibus baſium_
_ducũtur a o, a q, quæ_
_æquales angulos con_
_tinent cum ipſis baſi_
_bus:
& anguli ad d_
_utrique ſunt recti_:
_erũt & reliqui a η d_,
_a θ d inter ſe æqua_-
_les.
linea autem p g_
_æquidiſtat lineæ a o_:

_itémq;
m y ipſi a q_:
_&
p s, m c ipſis a d_.
_triágula igitur p g s_,
_m y c triãgulis a η d_
_a θ d, atque inter ſe_
_ſunt ſimilia:
& ut a d ad a η, ita a d ad a θ: & permutando. li_-
664. ſexti.