Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
o n ipſi a c. Quoniam enim triangulorum a b k, a d k, latus
b k eſt æquale lateri k d, &
a k utrique commune; anguliq́;
ad k recti baſis a b baſi a d; & reliqui anguli reliquis an-
8. primigulis æquales erunt.
eadem quoqueratione oſtendetur b c
æqualis c d;
& a b ipſi
Figure: /permanent/library/4E7V2WGH/figures/0119-01 not scanned
[Figure 75]
b c.
quare omnes a b,
b c, c d, d a ſunt æqua-
les.
& quoniam anguli
ad a æquales ſunt angu
lis ad c;
erunt anguli b
a c, a c d coalterni inter
ſe æquales;
itemq́; d a c,
a c b.
ergo c d ipſi b a;
& a d ipſi b c æquidi-
ſtat.
Atuero cum lineæ
a b, c d inter ſe æquidi-
ſtantes bifariam ſecen-
tur in punctis e g;
erit li
nea l e k g n diameter ſe
ctionis, &
linea una, ex
demonſtratis in uigeſi-
ma octaua ſecundi coni
corum.
Et eadem ratione linea una m f k h o. Sunt autẽ a d,
b c inter ſe ſe æquales, &
æquidiſtantes. quare & earum di-
midiæ a h, b f;
itemq́; h d, f e; & quæ ipſas coniunguntrectæ
33. primitlineæ æquales, &
æquidiſtantes erunt. æquidiſtãt igitur b a,
c d diametro m o:
& pariter a d, b c ipſi l n æquidiſtare o-
ſtendemus.
Si igitur manẽte diametro a c intelligatur a b c
portio ellipſis ad portionem a d c moueri, cum primum b
applicuerit ad d, cõgruet tota portio toti portioni, lineaq́;
b a lineæ a d; & b c ipſi c d congruet: punctum uero e ca-
det in h;
f in g: & linea k e in lineam k h: & k f in k g. qua
re &
el in h o, et fm in g n. Atipſa lz in z o; et m φ in φ n
cadet.
congruet igitur triangulum l k z triangulo o k z: et

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