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

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-
gulis æquales erunt. eadem quoqueratione oſtendetur b c
æqualis c d; & a b ipſi
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
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: et

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