Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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[Figure 81]
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[Figure 82]
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[Figure 83]
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eſſe punctum g. </
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<
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uitatis ſit idem, quod ipſius ſphæræ centrum.</
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13. primi</
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14. primi</
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<
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">Sit dodecahedrum af in ſphæra deſignatum, ſitque ſphæ
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ræ centrum m. </
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<
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id
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">Dico m centrum eſſe grauitatis ipſius do
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decahedri. </
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<
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id
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s.000850
">Sit enim pentagonum abcde una ex duode
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cim baſibus ſolidi af: & iuncta am producatur ad ſphæræ
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ſuperficiem. </
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<
s
id
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">cadet in angulum ipſi a oppoſitum; quod col
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ligitur ex decima ſeptima propoſitione tertiidecimi libri
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elementorum. </
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<
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">cadat in f. </
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<
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id
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">at ſi ab aliis angulis bcde per
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abbr
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cẽ
">cen</
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trum itidem lineæ ducantur ad ſuperficiem ſphæræ in pun
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cta ghkl; cadent hæ in alios angulos baſis, quæ ipſi abcd
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baſi opponitur. </
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<
s
id
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s.000854
">tranſeant ergo per pentagona abcde,
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fghKl plana ſphæram ſecantia, quæ facient ſectiones cir
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culos æquales inter ſe ſe: poſtea ducantur ex centro ſphæræ
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m perpendiculares ad pla
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na dictorum
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abbr
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circulorũ
">circulorum</
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; ad
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circulum quidem abcde
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perpendicularis mn: & ad
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circulum fghKl ipſa mo,
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erunt puncta no
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circulorũ
">circulorum</
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centra: & lineæ mn, mo in
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ter ſe æquales: quòd circu
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li æquales ſint. </
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<
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">Eodem mo
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do, quo ſupra, demonſtrabi
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mus lineas mn, mo in
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abbr
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unã
">unam</
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atque eandem lineam con
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uenire. </
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<
s
id
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s.000856
">ergo cum puncta no ſint centra circulorum, con
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ſtat ex prima huius &
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pentagonorũ
">pentagonorum</
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grauitatis eſſe centra:
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idcircoq;
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mn, mo pyramidum abcdem, fghklm axes. </
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<
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id
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">ponatur abcdem pyramidis grauitatis centrum p: & py
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ramidis fghklm ipſum q centrum. </
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<
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id
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">erunt pm, mq æqua
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les, & punctum m grauitatis centrum magnitudinis, quæ
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ex ipſis pyramidibus conſtat. </
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eodẽ
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modo probabitur qua
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rumlibet pyramidum, quæ è regione opponuntur,
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centrũ
">centrum</
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