Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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eſſe pun ctum g. </
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<
s
xml:id
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xml:space
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">Sequitur ergo uticoſahedri centrum gra
<
lb
/>
uitatis fit idem, quodipſius ſphæræ centrum.</
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<
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</
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<
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<
s
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echoid-s4804
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xml:space
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">Sit dodecahedrum a ſin ſphæra deſignatum, ſitque ſphæ
<
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ræ centrum m. </
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>
<
s
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xml:space
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">Dico m centrum eſſe grauitatis ipſius do-
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decahedri. </
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>
<
s
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echoid-s4806
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xml:space
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">Sit enim pentagonum a b c d e una ex duode-
<
lb
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cim baſibus ſolidi a f: </
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<
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xml:space
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">& </
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<
s
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xml:space
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">iuncta a m producatur ad ſphæræ
<
lb
/>
ſuperficiem. </
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<
s
xml:id
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echoid-s4809
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xml:space
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">cadetin angulum ipſi a oppoſitum; </
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>
<
s
xml:id
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echoid-s4810
"
xml:space
="
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">quod col-
<
lb
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ligitur ex decima ſeptima propoſitione tertiidecimilibri
<
lb
/>
elementorum. </
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<
s
xml:id
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xml:space
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">cadat in f. </
s
>
<
s
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"
xml:space
="
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">at ſi ab aliis angulis b c d e per cẽ
<
lb
/>
trum itidem lineæ ducantur ad ſuperficiem ſphæræ in pun
<
lb
/>
cta g h k l; </
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>
<
s
xml:id
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xml:space
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">cadent hæ in alios angulos baſis, quæ ipſi a b c d
<
lb
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baſi opponitur. </
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>
<
s
xml:id
="
echoid-s4814
"
xml:space
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">tranſeant ergo per pentagona a b c d e,
<
lb
/>
f g h K l plana ſphæram ſecantia, quæ facient ſectiones cir-
<
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/>
culos æquales inter ſe ſe poſtea ducantur ex centro ſphæræ
<
lb
/>
m perpen diculares ad pla-
<
lb
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<
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fig-0191-01
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142
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0191-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0191-01
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na dictorum circulorũ; </
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<
s
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xml:space
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">ad
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circulum quidem a b c d e
<
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perpendicularis m n: </
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<
s
xml:id
="
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xml:space
="
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">& </
s
>
<
s
xml:id
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xml:space
="
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">ad
<
lb
/>
circulum f g h K l ipſa m o,
<
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<
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position
="
right
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xlink:label
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xlink:href
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note-0191-01a
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xml:space
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">corol. pri
<
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mæ ſphæ
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ricorum
<
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Theod.</
note
>
erunt puncta n o circulorũ
<
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centra: </
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<
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xml:space
="
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">& </
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>
<
s
xml:id
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xml:space
="
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">lineæ m n, m o in
<
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ter ſe æquales: </
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<
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xml:space
="
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">quòd circu-
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li æquales ſint. </
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<
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">Eodem mo
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<
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right
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xlink:label
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xlink:href
="
note-0191-02a
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xml:space
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">6. primi
<
lb
/>
phærico
<
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/>
rum.</
note
>
do, quo ſupra, demonſtrabi
<
lb
/>
mus lineas m n, m o in unã
<
lb
/>
atque eandem lineam con-
<
lb
/>
uenire. </
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>
<
s
xml:id
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xml:space
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">ergo cum puncta n o ſint centra circulorum, con-
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ſtat ex prima huius & </
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>
<
s
xml:id
="
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xml:space
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">pentagonorũ grauitatis eſſe centra:
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</
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<
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xml:space
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">idcircoq; </
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<
s
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xml:space
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">m n, m o pyramidum a b c d e m, ſ g h _K_ l m axes. </
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<
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<
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ponatur a b c d e m pyramidis grauitatis centrum p: </
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<
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xml:space
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">& </
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<
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xml:space
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">py
<
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ramidis f g h
<
emph
style
="
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emph
>
l m ipſum q centrum. </
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>
<
s
xml:id
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xml:space
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">erunt p m, m q æqua-
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les, & </
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>
<
s
xml:id
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xml:space
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">punctum m grauitatis centrum magnitudinis, quæ
<
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ex ipſis pyramidibus conſtat. </
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>
<
s
xml:id
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xml:space
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">eodẽ modo probabitur qua-
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rumlibet pyramidum, quæ è regione opponuntur, </
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