Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of figures

< >
[Figure 111]
[Figure 112]
[Figure 113]
[Figure 114]
[Figure 115]
[Figure 116]
[Figure 117]
[Figure 118]
[Figure 119]
[Figure 120]
[Figure 121]
[Figure 122]
[Figure 123]
[Figure 124]
[Figure 125]
[Figure 126]
[Figure 127]
[Figure 128]
[Figure 129]
[Figure 130]
[Figure 131]
[Figure 132]
[Figure 133]
[Figure 134]
[Figure 135]
[Figure 136]
[Figure 137]
[Figure 138]
[Figure 139]
[Figure 140]
< >
page |< < (40) of 213 > >|
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
ræ 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 hæ 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
na dictorum circulorũ;
circulum quidem a b c d e
perpendicularis m n:
circulum f g h K l ipſa m o,
11corol. pri
mæ 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,