Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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guli ABC, quatuor rectæ inter ſe parallelæ AD, BE,
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CF, NM, tres autem magnitudines æquales habeant cen
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tra grauitatis G, H, K, in tribus AD, BE, CF. </
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<
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>Di
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co trium magnitudinum ſimul, quarum centra grauitatis
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G, H, K, eſſe in linea NM. </
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<
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>Iungantur enim rectæ GH,
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H
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K
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, GK, BNP; & per punctum P, recta PL, ipſi MN,
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parallela, & iungatur LH. </
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<
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>Quoniam igitur rectæ BP, LH,
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iungunt duas parallelas LP, BH; erunt quatuor rectæ BH,
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LP, BP, LH, in eodem plano. </
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<
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>Et
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quoniã
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planum quadran
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guli PH, ſecat planum trianguli ABC, à communi autem
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ſectione BP, ſurgunt
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duæ parallelæ PL, MN;
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quarum PL, eſt in pla
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no quadranguli PH,
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erit etiam MN, in eo
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dem plano quadranguli
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PH: & ſecabit LH. ſe
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cet in puncto O: qùare
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vt LO, ad OH, ita erit
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PN, ad NB, propter
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parallelas: ſed PN, eſt
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dimidia ipſius NB; er
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go & LO, eſt dimidia ip
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ſius OH. </
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<
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>Eadem ratio
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ne, quoniam AP, æqua
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lis eſt PC, erit & GL, æqualis LK. </
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<
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>Duarum igitur
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magnitudinum G, K, ſimul centrum grauitatis erit L: ſed
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reliquæ magnitudinis, quæ ad H, eſt centrum grauitatis
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H; & vt compoſitum ex duabus magnitudinibus G,
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K, ad magnitudinem H, ita ex contraria parte eſt HO,
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ad OL; Trium igitur magnitudinum G, H, K, ſimul cen
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trum grauitatis erit O, & in linea MN. </
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<
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>Quod demon
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ſtrandum erat. </
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