Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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1194DE 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-
118. primi gulis æquales erunt.
eadem quoqueratione oſtendetur b c
æqualis
c d;
& a b ipſi
75[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
2233. primit lineæ 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:

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