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
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121	5
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123	6
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127	8
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129	9
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136
137	13
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Scan	Original
111
112
113	1
114
115	2
116
117	3
118
119	4
120
121	5
122
123	6
124
125	7
126
127	8
128
129	9
130
131	10
132
133	11
134
135	12
136
137	13
138
139	14
140