Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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& vt B ad C, ita G ad B; erit ex æquali minor proportio
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H ad B, quam G ad C, ſed vt H ad B, ita erat D, ad
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E: & vt G ad C, ita E ad F; minor igitur proportio erit
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D ad E, quam E ad F. </
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PROPOSITIO VII.
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>Si ſint octo magnitudines quaternæ propor
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tionales: tertiæ autem vtriuſque ordinis inter ſo
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ſint vt primæ; erit vt compoſita ex primis ad com
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poſitam ex ſecundis, ita compoſita ex tertiis ad
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compoſitam ex quartis. </
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>Sint octo magnitudines quaternæ ſum
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ptæ proportionales, vt A ad B, ita C ad
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D. & vt E ad F, ita G ad H. ſit autem vt
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A ad E, ita C ad G. </
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>Dico eſse vt AE, ad
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ABF, ita CG, ad DH. </
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>Quoniam enim
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componendo eſt vt AE, ad E, ita, CG,
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ad G; ſed vt E ad F, ita eſt G, ad H; erit
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ex æquali, vt AE, ad F, ita CG, ad H.
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>Eadem ratione erit vt AE, ad B, ita CG,
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ad D: & conuertendo, vt B ad AE, ita
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D ad CG. ſed vt AE, ad F, ita erat
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CG ad H; ex æquali igitur erit vt B
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ad F, ita D, ad H: & componendo, vt
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BF ad F, ita DH ad H: & conuerten
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do, vt F ad BF, ita H, ad DH. </
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<
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>Sed vt
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AE, ad F, ita erat CG ad H; ex æqua
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li igitur erit vt AE ad BF, ita CG,
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ad DH. </
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>Quod demonſtrandum erat. </
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