Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

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1257DE CENTRO GRAVIT. SOLID. metrum habens e d. Quoniam igitur circuli uel ellipſis
a e c b grauitatis centrum eſt in diametro b e, & portio-
nis a e c centrum in linea e d: reliquæ portionis, uidelicet
a b c centrum grauitatis in ipſa b d conſiſtat neceſſe eſt, ex
octaua propoſitione eiuſdem.

THEOREMA V. PROPOSITIO V.

SI priſma ſecetur plano oppoſitis planis æqui
diſtante, ſectio erit figura æqualis & ſimilis ei,
quæ eſt oppoſitorum planorum, centrum graui
tatis in axe habens.

Sit priſma, in quo plana oppoſita ſint triangula a b c,
d e f; axis g h: & ſecetur plano iam dictis planis æquidiſtã
te; quod faciat ſectionem K l m; & axi in pũcto n occurrat.
Dico _k_ l m triangulum æquale eſſe, & ſimile triangulis a b c
d e f; atque eius grauitatis centrum eſſe punctum n. Quo-
niam enim plana a b c

82[Figure 82] K l m æquidiſtantia ſecã
1116. unde-
cimi. tur a plano a e; rectæ li-
neæ a b, K l, quæ ſunt ip
ſorum cõmunes ſectio-
nes inter ſe ſe æquidi-
ſtant. Sed æquidiſtant
a d, b e; cum a e ſit para
lelogrammum, ex priſ-
matis diffinitione. ergo
& al parallelogrammũ
erit; & propterea linea
2234. prim@ _k_l, ipſi a b æqualis. Si-
militer demonſtrabitur
l m æquidiſtans, & æqua
lis b c; & m K ipſi c a.

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Scan	Original
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73	37
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75	32
76
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79	34
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84
85	37
86
87	38
88
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Scan	Original
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
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100

Scan	Original
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
91	40
92
93	41
94
95	42
96
97	43
98
99	44
100