Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
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
10. unde
cimi
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
10. unde-
cimi
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
4. ſextiut 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,
Figure: /permanent/library/4E7V2WGH/figures/0126-01 not scanned
[Figure 83]
cadet linea f q in lineam
c g o.
Sed & centrũ gra
per 5. pe-
titionem
Archime
dis.
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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