Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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120FED. COMMANDINI triangulum m k φ triangulo n k φ. ergo anguli l z k, o z k,
m φ k, n φ k æquales ſunt, ac recti.
quòd cum etiam recti
æquidiſtabunt lineæ l o, m n axi b d. & ita.
1128. primi. demonſtrabuntur l m, o n ipſi a c æquidiſtare. Rurſus ſi
iungantur a l, l b, b m, m c, c n, n d, d o, o a:
& bifariam di
uidantur:
à centro autem k ad diuiſiones ductæ lineæ pro-
trahantur uſque ad ſectionem in puncta p q r s t u x y:
& po
ſtremo p y, q x, r u, s t, q r, p s, y t, x u coniungantur.
Simili-
ter oſtendemus lineas
p y, q x, r u, s t axi b d æ-
quidiſtantes eſſe:
& q r,
p s, y t, x u æquidiſtan-
tesipſi a c.
Itaque dico
harum figurarum in el-
lipſi deſcriptarum cen-
trum grauitatis eſſe pũ-
ctum k, idem quod &
el
lipſis centrum.
lateri enim a b c d cen-
trum eſt k, ex decima e-
iuſdem libri Archime-
dis, quippe cũ in eo om
nes diametri cõueniãt.
Sed in figura alb m c n
2213. Archi
medis.
d o, quoniam trianguli
alb centrum grauitatis
33Vltima. eſt in linea l e:
trapezijq́; a b m o centrum in linea e k: trape
zij o m c d in k g:
& trianguli c n d in ipſa g n: erit magnitu
dinis ex his omnibus conſtantis, uidelicet totius figuræ cen
trum grauitatis in linea l n:
& o b eandem cauſſam in linea
o m.
eſt enim trianguli a o d centrum in linea o h: trapezij
a l n d in h k:
trapezij l b c n in k f: & trianguli b m c in fm.
cum ergo figuræ a l b m c n d o centrum grauitatis ſit in li-
nea l n, &
in linea o m; erit centrum ipſius punctum k,