DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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9
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huius.
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29,
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primi.
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4.
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primi.
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Hoc autem aliter quo
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〈que〉 oſtendetur. </
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<
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logrammum ABCD.
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ipſius verò diameter ſit
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<
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B D. triangula
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vti〈que〉
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ABD BDC
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erunt in
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terſe æqualia, & ſimilia.
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quare triangulis inuicem
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coaptatis; centra quo〈que〉
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grauitatis ipſorum inuicem coaptabuntur. </
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<
s
id
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trum grauitatis punctum E; lineaquè BD bifariam ſecetur in H. con
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nectaturquè EH, & producatur. </
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<
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">ſumaturquè FH æqualisipſi HE.
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Ita〈que〉 coaptato triangulo ABD cumtriangulo B DC, poſitoquè latere
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AB in DC,
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hoc eſt A in C, & B in D.
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AD autem
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poſito
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in
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BC;
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A ſcilicet in C, & D in B. vnde & BD cum ipſamet
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DB coaptatur, B ſcilicet in D, & D in B. quia verò pun
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ctum H ſibi ipſi coaptatur, cùm fitmedium lineę BD. & an
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guli EHD FHB ad verticem ſunt æquales; lineaquè EH eſt
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ipſi HF ęqualis;
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congruet etiam recta HE cum recta FH, &
<
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ctum</
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E cum F conueniet, ſed
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quoniam punctum E centrum
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eſt grauitatis trianguli ABD idem punctum E
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cum centro e
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tiam grauitatis trianguli B DC
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conueniet. </
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<
s
id
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cẽ-trum
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trum</
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eſt grauitatis trianguli BDC. Nunc verò intelligantur
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triangula non ampliùs coaptata.
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Quoniam igitur centrum graui
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tatis trianguli ABD eſt punctum E, ipſius verò DBC est punctum F,
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triangulaquè ABD DBC ſunt ęqualia,
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patet magnitudinis ex v
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triſ〈que〉 triangulis compoſit
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centrum grauitatis eſſe medium rectæ lineæ
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EF; quod eſt punctum H,
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vt factum furt. </
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<
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id
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">Quoniam autem dia
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metri cuiuſlibet parallelogrammi ſeſe bifariam diſpeſcunt, e
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rit punctum H, vbi diametri parallelogrammi ABCD con
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currunt. </
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<
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id
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ABCD centrum grauitatis exiſtit. </
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<
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rebat. </
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