Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

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190FED. COMMANDINI ctiones circuli ex prima propofitione ſphæricorum Theo
doſii: unus quidem circa triangulum a b c deſcriptus: al-
ter uero circa d e f: & quoniam triangula a b c, d e f æqua-
lia ſunt, & ſimilia; erunt ex prima, & ſecunda propoſitione
duodecimi libri elementorum, circuli quoque inter ſe ſe
æquales. poſtremo a centro g ad circulum a b c perpendi
cularis ducatur g h; & alia perpendicularis ducatur ad cir
culum d e f, quæ ſit g _k_; & iungantur a h, d k. perſpicuum
eſt ex corollario primæ ſphæricorum Theodoſii, punctum
h centrum eſſe circuli a b c, & k centrum circuli d e f. Quo
niam igitur triangulorum g a h, g d K latus a g eſt æquale la
teri g d; ſunt enim à centro ſphæræ ad ſuperficiem: atque
eſt a h æquale d k: & ex ſexta propoſitione libri primi ſphæ
ricorum Theodoſii g h ipſi g K: triangulum g a h æquale
erit, & ſimile g d k triangulo: & angulus a g h æqualis an-
gulo d g _K_. ſed anguli a g h, h g d ſunt æquales duobus re-
1113. primi ctis. ergo & ipſi h g d, d g k duobus rectis æquales erunt.
& idcirco h g, g _K_ una, atque eadem erit linea. cum autem
2214. primi h ſit centrũ circuli, & tri-

141[Figure 141] anguli a b c grauitatis cen
trũ probabitur ex iis, quæ
in prima propoſitione hu
ius tradita funt. quare g h
erit pyramidis a b c g axis.
& ob eandem cauſſam g k
axis pyramidis d e f g. Ita-
que centrum grauitatis py
ramidis a b c g ſit púctum
l, & pyramidis d e f g ſit m.
Similiter ut ſupra demon-
ſtrabimus m g, g linter ſe æquales eſſe, & punctum g graui
tatis centrum magnitudinis, quæ ex utriſque pyramidibus
conſtat. eodem modo demonſtrabitur, quarumcunque
duarum pyramidum, quæ opponuntur, grauitatis

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73	37
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75	32
76
77	25
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79	34
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82
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85	37
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87	38
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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