Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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rum magnitudinum binæ eodem ordine, qui ſu
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mitur ab eodem prædictæ lineæ termino vnain
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primis, & alterain ſecundis inter ſe ſint æquales;
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omnium primarum ſimul, ex quibus primæ cen
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trum grauitatis propinquius eſt prædicto lineæ
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termino quàm primæ ſecundarum, propinquius
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erit prædicto lineæ termino quàm omnium ſecun
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darum ſimul centrum grauitatis. </
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<
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>Sint quotcumque magnitudines ABC primæ, & toti
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dem ſecundæ DEF, quarum centra grauitatis in recta
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linea TV, primarum quidem G ipſius A proximum om
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nium termino T, à quo ſumitur ordo. </
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<
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>Deinde H ipſius B,
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&
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K
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, ipſius C, diſpoſita ſint alternatim ad centra ſecun
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darum; videlicet vt centrum grauitatis L, ipſius D cadat
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inter centra G, H, & M ipſius E inter centra H, K: & N
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inter puncta
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K
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, V: ſint autem æquales binæ AD, BE,
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CF: & omnium ABC ſimul centrum grauitatis P, & om
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nium DEF ſimul centrum grauitatis O. </
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<
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>Dico punctum
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P propinquius eſſe termino T, quàm punctum O.
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<
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>Duarum enim A, B ſit centrum grauitatis R: & S, dua
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rum DB, & Q, duarum DE. </
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<
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>Quoniam igitur Q eſt
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centrum grauitatis duarum magnitudinum DE ſimal; erit
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vt D ad E, hoc eſt ad B, ita MQ, ad QL: hoc eſt HS,
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ad SL. & componendo, vt ML, ad LQ, ita HL, ad
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LS; & permutando, vt ML ad LH, ita LQ ad LS:
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ſed ML eſt maior quàm LH; ergo & LQ erit maior
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quàm LS. </
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<
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