Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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ad KM: & permutando, maior DH ad F
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K
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, quam LH, ad
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M
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K
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: hoc eſt, quam BG, ad DH: hoc eſt minor propor
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tio BG ad DH, quam DH, ad FK. </
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ſtrandum erat. </
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PROPOSITIO VI.
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>Si ſint tres magnitudines inæquales, & aliæ il
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lis multitudine æquales binæque in duplicata pri
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marum proportione. </
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>Sit autem minor proportio
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primæ ad ſecundam, quam ſecundæ ad tertiam in
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primis; erit minor proportio primæ ad ſecundam,
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quam ſecundæ ad tertiam in ſecundis. </
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<
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>Sint tres magnitudines A, B, C, & aliæ illis multitudine
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æquales D, E, F. quarum ipſius D ad E proportio ſit du
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plicata eius, quæ eſt A ad B: & E ad F, duplicata eius,
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quæ eſt B ad C. ſit autem mi
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nor proportio A ad B, quam
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B ad C. </
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>Dico minorem eſse
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proportionem D ad E, quam
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E ad F. </
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>Sit enim vt C ad B,
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ita B ad G: & vt B ad A, ita
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A ad H. </
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>Igitur G ad C dupli
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cata erit proportio ipſius G ad
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B, hoc eſt B ad C: ſimiliter
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erit H ad B, duplicata propor
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tio ipſius A ad B. </
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<
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>Vt igitur
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eſt H ad B, ita erit D ad E: &
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vt G ad C, ita E ad F. Rur
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ſus, quia minor eſt proportio
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A ad B, quam B ad C, ſed vt A ad B, ita eſt H ad A </
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