Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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1215DE CENTRO GRAVIT. SOLID. quo ſcilicet ln, om conueniunt. Poſtremo in figura
a p l q b r m s c t n u d x o y centrum grauitatis trian
guli pay, &
trapezii ploy eſtin linea a z: trapeziorum
uero lqxo, q b d x centrum eſtin linea z k:
& trapeziorũ
b r u d, r m n u in k φ:
& denique trapezii m s t n; & triangu
li s c t in φ c.
quare magnitudinis ex his compoſitæ centrū
in linea a c conſiſtit.
Rurſus trianguli q b r, & trapezii q l
m r centrum eſt in linea b χ:
trapeziorum l p s m, p a c s,
a y t c, y o n t in linea χ φ:
trapeziiq; o x u n, & trianguli
x d u centrum in ψ d.
totius ergo magnitudinis centrum
eſtin linea b d.
ex quo ſequitur, centrum grauitatis figuræ
a p l q b r m s c t n u d x o y eſſe punctū _K_, lineis ſcilicet a c,
b d commune, quæ omnia demonſtrare oportebat.
THE OREMA III. PROPOSITIO III.
Cuiuslibet portio-
nis circuli, &
ellipſis,
quæ dimidia non ſit
maior, centrum graui
tatis in portionis dia-
metro conſiſtit.
HOC eodem prorſus
modo demonſtrabitur,
quo in libro de centro gra
uitatis planorum ab Ar-
chimede demonſtratũ eſt,
in portione cõtenta recta
linea, &
rectanguli coni ſe
ctione grauitatis cẽtrum
eſſe in diametro portio-
nis.
Etita demonſtrari po
77[Handwritten note 7]