Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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quàm rectanguli BFE, ad rectangulum BDE. </
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<
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rectangulum BQE ad rectangulum BFE, ita eſt quadra
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tum SQ ad quadratum
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F: & vt rectangulum BFE
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ad rectangulum BDE, ita quadratum
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F, ad quadra
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tum AD; minor igitur proportio erit quadrati SQ, ad
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quadratum
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F, quàm quadrati
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F ad quadratum AD.
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</
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<
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>Sed vt quadratum SQ ad quadratum
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F, ita eſt qua
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dratum SZ ad quadratum
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<37>: & vt quadratum
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F ad
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quadratum AD ita quadratum
<
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ad quadratum
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AC; minor igitur proportio erit quadrati SZ ad quadra
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tum
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, quàm quadrati
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, ad quadratum AC, hoc eſt
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circuli SZ ad circulum
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<37>, quàm circuli
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<37>, ad cir
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culum AC; qui circuli ſunt ſectiones conoidis ABC
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poſiti vt in propoſitionibus lemmaticis dicebamus. </
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<
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>Rurſus
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quoniam ſunt quatuor primæ proportionales; vt rectangu
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lum DBE ad rectangulum FBE, ita MD quadratum
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ad quadratum
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F: & totidem ſecundæ, vt quadratum
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BD, ad quadratum BF, ita quadratum DK, ad quadra
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tum F
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, ob ſimilium triangulorum latera proportionalia:
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ſed vt EB, ad BD, hoc eſt rectangulum DBE prima in
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primis ad quadratum BD primam in ſecundis, ita eſt
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quadratum MD tertia in primis ad quadratum DK ter
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tiam in ſecundis; vt igitur compoſita ex primis ad com
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poſitam ex ſecundis, ità erit compoſita ex tertijs ad com
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poſitam ex quartis; videlicet vt rectangulum DBE
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vnà cum quadrato BD, hoc eſt rectangulum BDE
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ad rectangulum BFE, hoc eſt vt quadratum AD, ad
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quadratum
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F, ità compoſitum ex quadratis MD, DK,
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ad compoſitum ex quadratis
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F, F
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: & quadrupla vtro
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rumque, vt quadratum AC, ad quadratum
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<37>, ità com
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poſitum ex quadratis MN, KL, ad compoſitum ex qua
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dratis
<
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; hoc eſt eorum circulorum, qui ſunt ſectio
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nes ſolidorum, vt circulus AC, ad circulum
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<37>, ità com
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poſitum ex circulis MN, KL, ad compoſitum ex circu</
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