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-

77[Figure 77] 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]

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Scan	Original
61	25
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63	26
64
65	27
66
67	22
68
69	29
70
71	30
72
73	37
74
75	32
76
77	25
78
79	34
80
81	35
82
83	36
84
85	37
86
87	38
88
89	39
90

Scan	Original
61	25
62
63	26
64
65	27
66
67	22
68
69	29
70
71	30
72
73	37
74
75	32
76
77	25
78
79	34
80
81	35
82
83	36
84
85	37
86
87	38
88
89	39
90