Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ducantur rectæ GBH, GAF, quæ cum KE, produ
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cta conueniant in punctis F, H: & fiant parallelogramma
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FL, AK. </
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>Quoniam igitur eſt vt N, ad R, ita BC, ad
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CA, hoc eſt AD, ad DB, hoc eſt rectangulum AK, ad
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rectangulum BK; erit permutando vt rectangulum AK,
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ad N, ita rectangulum BK, ad R; ſed rectangulum BK,
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eſt pars quarta ipſius R, ergo & rectangulum AK, erit
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pars quarta ipſius N. </
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<
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>Rurſus quia eſt vt GD, ad D
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K
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,
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ita GA, ad AF, & GB, ad BH: ſed GD eſt æqualis
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DK; ergo & GA, ipſi AF, & GB, ipſi BH, æquales
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erunt & centra grauita
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tis A, quidem rectangu
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li MK, B, vero rectan
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guli KL, & rectangulum
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AK, pars quarta ipſius
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M
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K
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, quemadmodum
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& B
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K
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ipſius KL; ſed
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N, rectanguli AK, qua
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druplum erat, quemad
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modum & R ipſius BK;
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igitur rectangulum MK,
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ſpacio N, & rectangulum
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KL, ſpacio R, æquale
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erit. </
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>Sed vt BC, ad CA,
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ita eſt N, ad R; vt igi
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tur BC, ad CA, ita
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rectangulum MK, ad rectangulum KL; ſed A eſt cen
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trum grauitatis rectanguli MK, & B, rectanguli KL; to
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tius ergo rectanguli FL, hoc eſt duorum rectangulorum
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MK, KL, ſimul centrum grauitatis erit C. </
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<
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>Sed rectan
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gulo MK, æquale eſt ſpacium N; & rectangulo KL, ſpa
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cium R. </
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>Igitur ſi pro rectangulo MK, ſit ſuſpenſum N
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ſpacium ſecundum centrum grauitatis in puncto A, & pro
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rectangulo KL, ſpacium R, ſecundum centrum graui-</
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