Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
Quoniam enim triangula afd, akg, anl ſi-
Figure: /permanent/library/4E7V2WGH/figures/0048-01 not scanned
[Figure 28]
milia ſunt;
itémq; ſimilia efd, h k g, mnl:
erit ut af ad fd, ita ak ad kg; ut autem fd
4. ſexti.ad fe, ita kg ad kh.
quare ex æquali ut af
ad fe, ita ak ad kh:
& per conuerſionem ra-
tionis ut af ad ae, ita ak ad ah.
eodem
modo oſtendetur, ut af ad a e, ita an ad am.
cum igitur an ad am ſit, ut a k ad a h; erit
19. quintireliqua kn ad reliquam h m, hoc eſt ad g q,
uel o p, ut a n ad a m;
hoc estut a f ad a e.
rurſus a k ad a h est, ut a f ad a e. er-
go reliqua f k ad e h reliquam, uidelicet
ad do, ut a f ad a e.
Similiter demonſtrabi-
mus ita eſſe fn ad d p.
quod quidem demonſtra
re oportebat.

LEMMA II.

Sint in eadem linea a b puncta
Figure: /permanent/library/4E7V2WGH/figures/0048-02 not scanned
[Figure 29]
duo r s ita diſpoſita, ut a s ad a r
eandem proportionem habeat, quam
a f ad ae:
& per r ducatur rtipſi
e d æquidiſtans;
per s uero ducatur
s t æquidiſtans fd, ita ut cum r t in
t puncto conueniat.
Dico punctum t
cadere in lineam a c.
Si enim fieri potest, cadat citra: & produca
tur rt uſque ad ipſam a c in u.
deinde per u
ducatur u x ipſi f d æquidiſtans.
Itaque ex
ijs, quæ proxime demonstrauimus a x ad ar

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