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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Scan	Original
31	10
32
33	11
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35	12
36
37	13
38
39	14
40
41	15
42
43	16
44
45	17
46
47	18
48
49	19
50
51	20
52
53	21
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55	22
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57	23
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59	24
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