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

FED. 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
ſint, qui ad k; æquidiſtabunt lineæ l o, m n axi b d. & ita. 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. quadri-
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
d o, quoniam trianguli
alb centrum grauitatis
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, in

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