Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

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16728DE CENTRO GRAVIT. SOLID. uel coni portionis axis à centro grauitatis ita diui
ditur, ut pars, quæ terminatur ad uerticem reli-
quæ partis, quæ ad baſim, ſit tripla.

Sit pyramis, cuius baſis triangulum a b c; axis d e; & gra
uitatis centrum _K_. Dico lineam d k ipſius _K_ e triplam eſſe.
trianguli enim b d c centrum grauitatis ſit punctum f; triã
guli a d c centrũ g; & trianguli a d b ſit h: & iungantur a f,
b g, c h. Quoniam igitur centrũ grauitatis pyramidis in axe
cõſiſtit: ſuntq; d e, a f, b g, c h eiuſdẽ pyramidis axes: conue
1117. huíus nient omnes in idẽ punctũ _k_, quod eſt grauitatis centrum.
Itaque animo concipiamus hanc pyramidem diuiſam in
quatuor pyramides, quarum baſes ſint ipſa pyramidis
triangula; & axis pun-
88[Handwritten note 8]

123[Figure 123] ctum k quæ quidem py-
ramides inter ſe æquales
ſunt, ut demõſtrabitur.
Ducatur enĩ per lineas
d c, d e planum ſecãs, ut
ſit ipſius, & baſis a b c cõ
munis ſectio recta linea
c e l: eiuſdẽ uero & triã-
guli a d b ſitlinea d h l.
erit linea a l æqualis ipſi
l b: nam centrum graui-
tatis trianguli conſiſtit
in linea, quæ ab angulo
ad dimidiam baſim per-
ducitur, ex tertia deci-
ma Archimedis. quare
221. ſexti. triangulum a c l æquale
eſt triangulo b c l: & propterea pyramis, cuius baſis trian-
gulum a c l, uertex d, eſt æqualis pyramidi, cuius baſis b c l
triangulum, & idem uertex. pyramides enim, quæ ab eodẽ
335. duode-
cimi.

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Scan	Original
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55	22
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61	25
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63	26
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65	27
66
67	22
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71	30
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74
75	32
76
77	25
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79	34
80

Scan	Original
51	20
52
53	21
54
55	22
56
57	23
58
59	24
60
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