Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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PROPOSITIO XXVII.
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<
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>Si ſint quotcumque magnitudines, & aliæ illis
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multitudine æquales, quæ binæ commune habe
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ant in eadem recta centrum grauitatis; ſumpto au
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tem ordine ab vno eius lineæ termino, maior ſit
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proportio primæ ad ſecundam in primis, quàm
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primæ ad ſecundam in ſecundis: & ſecundæ ad
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tertiam in primis maior quàm ſecundæ ad ter
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tiam in ſecundis, & ſic deinceps vſque ad vltimas;
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erit omnium primarum ſimul centrum grauitatis
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propinquius prædicto lineæ termino, à quo ſumi
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tur ordo, quàm omnium ſecundarum. </
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>Sint quotcumque magnitudines GHI, & totidem
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LMN. </
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>Sitque maior proportio G ad H, quàm L ad M: &
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H ad I, maior quàm M ad N: in recta autem AB ſint
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communia centra grauitatis, C duarum magnitudinum
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GL, & D duarum HM, & E duarum IN. omnium
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autem primarum GHI ſimul ſit centrum grauitatis K: at
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ſecundarum omnium LMN centrum grauitatis R. </
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<
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co centrum K cadere termino A propinquius quàm cen
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trum R. </
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<
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>Fiat enim vt G ad H, ita DP ad PC: & vt L
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ad M, ita DQ ad QC. </
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<
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>Maior igitur proportio erit DP </
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