Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

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1152DE CENTRO GRAVIT. SOLID. tur, centrum grauitatis eſt idem, quod circuli cen
trum.

Sit primo triangulum æquilaterum a b c in circulo de-
ſcriptum: & diuiſa a c bifariam in d, ducatur b d. erit in li-
nea b d centrum grauitatis triãguli a b c, ex tertia decima
primi libri Archimedis de centro grauitatis planorum. Et
quoniam linea a b eſt æqualis

70[Figure 70] lineæ b c; & a d ipſi d c; eſtq́;
b d utrique communis: trian-
gulum a b d æquale erit trian
118. primi. gulo c b d: & anguli angulis æ-
quales, qui æqualibus lateri-
bus ſubtenduntur. ergo angu
2213. primi. li ad d utriq; recti ſunt. quòd
cum linea b d ſecet a c biſa-
riam, & ad angulos rectos; in
33corol. p@@
mæ tertii ipſa b d eſt centrum circuli.
quare in eadem b d linea erit
centrum grauitatis trianguli, & circuli centrum. Similiter
diuiſa a b bifariam in e, & ducta c e, oſtendetur in ipſa utrũ
que centrum contineri. ergo ea erunt in puncto, in quo li-
neæ b d, c e conueniunt. trianguli igitur a b c centrum gra
uitatis eſt idem, quod circuli centrum.

Sit quadratum a b c d in cir-

71[Figure 71] culo deſcriptum: & ducantur
a c, b d, quæ conueniant in e. er-
go punctum e eſt centrum gra
uitatis quadrati, ex decima eiuſ
dem libri Archimedis. Sed cum
omnes anguli ad a b c d recti
ſint; erit a b c femicirculus:
4451. tortil. itemq́; b c d: & propterea li-
neæ a c, b d diametri circuli:

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Scan	Original
71	30
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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
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94
95	42
96
97	43
98
99	44
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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