Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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19140DE CENTRO GRAVIT. SOLID. eſſe pun ctum g. Sequitur ergo uticoſahedri centrum gra
uitatis
fit idem, quodipſius ſphæræ centrum.
Sit dodecahedrum a ſin ſphæra deſignatum, ſitque ſphæ
centrum m.
Dico m centrum eſſe grauitatis ipſius do-
decahedri
.
Sit enim pentagonum a b c d e una ex duode-
cim
baſibus ſolidi a f:
& iuncta a m producatur ad ſphæræ
ſuperficiem
.
cadetin angulum ipſi a oppoſitum; quod col-
ligitur
ex decima ſeptima propoſitione tertiidecimilibri
elementorum
.
cadat in f. at ſi ab aliis angulis b c d e per cẽ
trum
itidem lineæ ducantur ad ſuperficiem ſphæræ in pun
cta
g h k l;
cadent in alios angulos baſis, quæ ipſi a b c d
baſi
opponitur.
tranſeant ergo per pentagona a b c d e,
f
g h K l plana ſphæram ſecantia, quæ facient ſectiones cir-
culos
æquales inter ſe ſe poſtea ducantur ex centro ſphæræ
m
perpen diculares ad pla-
142[Figure 142] na dictorum circulorũ;
ad
circulum
quidem a b c d e
perpendicularis
m n:
& ad
circulum
f g h K l ipſa m o,
11corol. pri
ſphæ
ricorum

Theod
.
erunt puncta n o circulorũ
centra
:
& lineæ m n, m o in
ter
ſe æquales:
quòd circu-
li
æquales ſint.
Eodem mo
226. primi
phærico

rum
.
do, quo ſupra, demonſtrabi
mus
lineas m n, m o in unã
atque
eandem lineam con-
uenire
.
ergo cum puncta n o ſint centra circulorum, con-
ſtat
ex prima huius &
pentagonorũ grauitatis eſſe centra:
idcircoq; m n, m o pyramidum a b c d e m, ſ g h _K_ l m axes.
ponatur
a b c d e m pyramidis grauitatis centrum p:
& py
ramidis
f g h K l m ipſum q centrum.
erunt p m, m q æqua-
les
, &
punctum m grauitatis centrum magnitudinis, quæ
ex
ipſis pyramidibus conſtat.
eodẽ modo probabitur qua-
rumlibet
pyramidum, quæ è regione opponuntur,

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