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

Itaque quoniam duæ lineæ K l, l m ſe ſe tangentes, duabus
lineis ſe ſe tangentibus a b, b c æquidiſtant; nec ſunt in eo-
dem plano: angulus K l m æqualis eſt angulo a b c: & ita an
gulus l m K , angulo b c a, & m K lipſi c a b æqualis prob abi
tur. triangulum ergo K l m eſt æquale, & ſimile triang ulo
a b c. quare & triangulo d e f. Ducatur linea c g o, & per ip
ſam, & per c f ducatur planum ſecans priſma, cuius & paral
lelogrammi a e communis ſectio ſit o p q. tranſibit linea
f q per h, & m p per n. nam cum plana æquidiſtantia ſecen
tur à plano c q, communes eorum ſectiones c g o, m p, f q
ſibi ipſis æquidiſtabunt. Sed & æquidiſtant a b, K l, d e. an-
guli ergo a o c, K p m, d q f inter ſe æquales ſunt: & ſunt
æquales qui ad puncta a k d conſtituuntur. quare & reliqui
reliquis æquales; & triangula a c o, _K_ m p, d f q inter ſe ſimi
lia erunt. Vtigitur ca ad a o, ita fd ad d q: & permutando
ut c a ad fd, ita a o ad d q. eſt autem c a æqualis fd. ergo & a o ipſi d q. eadem quoque ratione & a o ipſi _K_ p æqualis
demonſtrabitur. Itaque ſi triangula, a b c, d e f æqualia & ſimilia inter ſe aptétur,
cadet linea f q in lineam
c g o. Sed & centrũ gra
uitatis h in g centrũ ca-
det. trãſibit igitur linea
f q per h: & planum per
c o & c f ductũ per axẽ
g h ducetur: idcircoq; li
neam m p etiã per n trã
ſire neceſſe erit. Quo-
niam ergo ſh, c g æqua-
les ſunt, & æquidiſtãtes: itemq; h q, g o; rectæ li-
neæ, quæ ipſas cónectũt
c m f, g n h, o p q æqua-
les & æquidiſtãtes erũt.

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