Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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lh eandem habet proportionem, quam em ad mk, uideli
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cet triplam. </
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<
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">quare linea lm ipſam ef ſecabit in puncto g:
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etenim eg ad gf eſt, ut el ad lh. </
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<
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id
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">præterea quoniam hk, lm
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æquidiſtant, erunt triangula hef, leg ſimilia:
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itemq;
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inter
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ſe ſimilia fek gem: & ut ef ad eg, ita hf ad lg: & ita fK ad
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gm. </
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id
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s.000603
">ergo ut hf ad lg, ita fk ad gm: & permutando ut hf
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ad fK, ita lg ad gm. </
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<
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id
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s.000604
">ſed cum h ſit centrum trianguli abd;
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& k
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abbr
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triãguli
">trianguli</
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bcd
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abbr
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punctũ
">punctum</
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uero f totius quadrilateri abcd
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lb
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centrum: erit ex 8. Archimedis de centro grauitatis plano
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rum hf ad fk ut triangulum bcd ad triangulum abd: ut,
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autem bcd triangulum ad triangulum abd, ita pyramis
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58
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bcde ad pyramidem abde. </
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<
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id
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s.000605
">ergo
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linea lg ad gm erit, ut pyramis
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bcde ad
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abbr
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pyramidẽ
">pyramidem</
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>
abde. </
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id
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s.000606
">ex quo
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ſequitur, ut totius pyramidis
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abcde punctum g ſit grauitatis
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centrum. </
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id
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">Rurſus ſit pyramis ba
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ſim habens pentagonum abcde:
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& axem fg:
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diuidaturq;
">diuidaturque</
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axis in
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pũ
">pun</
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>
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cto h, ita ut fh ad hg triplam habe
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at proportionem. </
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<
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id
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s.000608
">Dico h grauita
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tis
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abbr
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centrũ
">centrum</
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eſſe pyramidis abcdef. </
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<
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id
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s.000609
">iungatur enim eb:
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intelligaturq;
">intelligaturque</
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pyramis, cuius uertex f, & baſis
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triangulum abe: & alia pyramis
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intelligatur eundem uerticem ha
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bens, & baſim bcde
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quadrilaterũ
">quadrilaterum</
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:
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ſit autem pyramidis abef axis fk
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& grauitatis centrum l: & pyrami
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dis bcdef axis fm, & centrum gra
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uitatis n:
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iunganturq;
">iunganturque</
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km, ln;
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quæ per puncta gh tranſibunt. </
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>
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<
s
id
="
s.000610
">Rurſus eodem modo, quo ſup ra,
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demonſtrabimus lineas Kgm, lhn ſibi ipſis æquidiſtare: </
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