Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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gitaui, quo ſecunda
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hìc in illis tertia facilius ſer
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uiret ijs, in quibus certæ proportionis nomen,
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& quar
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tum terminum ſubobſcurè indicat, vt in ſequenti XII iilud,
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proportio dupla. </
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<
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>Illo autem Lemmate, quod prima propofi
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tio inſcribebatur, nunc ita non egeo, vt primam, &
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ſecundã
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,
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quæ ſecunda, & tertia erant, & facilius demonſtrem, & ea
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rum ſenſum paucioribus comprehendam. </
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<
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>priora ergo ita
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non improbo vt hæc ijs anteponam. </
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PROPOSITIO IIII.
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<
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>Si ſint tres magnitudines ſe ſe æqualiter exce
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dentes, minor erit proportio minimæ ad mediam
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quàm mediæ ad maximam. </
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<
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>Sint tres magnitudines inæquales A, BC, DE, qua
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rum BC æquè excedat ipſam A, ac DE ipſam BC
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Dico minorem eſse proportionem A, ad
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BC, quàm BC, ad DE. </
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<
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>Nam vt eſt
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A ad BC, ita ſit BC ad LH, & au
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feratur BF æqualis A, & DG, & LK
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æquales BC. </
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<
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>Quoniam igitur eſt vt A,
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hoc eſt FB ad BC, ita BC hoc eſt KL
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ad LH; erit diuidendo vt BF ad FC,
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ita LK ad KH: & componendo, ac per
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mutando vt BC ad LH, ita FC ad
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KH. ſed BC eſt minor quàm LH; ergo
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& FC hoc eſt EG erit minor quàm KH.
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</
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<
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>Sed DE, LH, ſuperant BC exceſsibus
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EG, KH; minor igitur erit DE quàm
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LH, & minor proportio BC ad LH,
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quàm BC ad DE. </
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<
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>Sed vt BC ad LH,
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ita eſt A ad BC; minor igitur proportio erit A ad BC,
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quàm BC ad DE. </
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<
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>Quod demonſtrandum erat. </
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