Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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C ad B, ita fiat HM, ad
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& vt B ad A, ita QM, ad
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MP, & ipſi GK, parallelæ TPR, VQS, ducantur.
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<
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>Quoniam igitur eſt vt C, ad duplam ipſius F, ita GH, ad
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HK; erit vt C ad F, ita eſt par llelogrammum GM, ad
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triangulum MHK: ſed vt C, ad B, ita eſt HM, ad
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hoc eſt parallelogrammum GM, ad parallelogrammum
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MV: & vt F, ad E, ita triangulum MHK, ad triangu
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lum MQS, ob duplicatam proportionem eius, quæ eſt
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HM ad
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hoc eſt ipſius C ad B; vt igitur trapezium
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NK, ad NS trapezium, ita erit, per præcedentem, CF,
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ſimul ad BE ſimul. </
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<
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>Rurſus quoniam eſt conuertendo, vt
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parallelogrammum MV, ad parallelogrammum GM, ita
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B ad C. ſed vt parallelogrammum GM, ad triangulum
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KHM, ita erat C, ad F: & vt triangulum KHM, ad
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triangulum QSM, ita F ad E; erit ex æquali, vt paral
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lelogrammum MV, ad triangulum SQM, ita B, ad E.
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>Similiter ergo vt ante erit vt trapezium NS, ad NR tra
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pezium, ita EB, ſimul ad AD, ſimul. </
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æque excedit LV, ipſam LT, atque LG, ipſam LV;
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minor erit proportio LT ad LV, quam LV, ad LG: eſt
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autem trianguli LTR ad triangulum LVS, duplicata
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proportio ipſius LT, ad LV, & trianguli LVS, ad trian
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gulum LGK, duplicata ipſius LV, ad LG, propter ſi
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militudinem triangulorum; minor igitur proportio erit
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trianguli LTR, ad triangulum LVS, quam trianguli
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LVS, ad triangulum LGK; dempto igitur triangulo
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LNM, communi, minor erit proportio trapezij NR, ad
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trapezium NS, quam trapezij NS, ad trapezium NK.
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<
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>Sed vt trapezium NR, ad trapezium NS, ita eſt conuer
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tendo AD ſimul ad BE, ſimul: & vt trapezium NS, ad
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trapezium NK, ita BE, ſimul ad CF, ſimul; minor igi
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tur proportio erit AD, ſimul ad BE ſimul, quam BE ſi
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mul ad CF, ſimul. </
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<
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