DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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Sit portio ABC, qualis dicta est. </
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<
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id
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">ipſius verò diameter ſit BD. cen
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trum autem grauitatis ſit punctum H. oſtendendum eſt BH ipſius HD
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ſeſquialteram eſſe. </
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<
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id
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">Planè inſcribatur in portione ABC triangulum ABC.
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cuius centrum grauitatis ſit punctum E. biſariamquè diuidatur vtra
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què AB BC in punctis FG. & ipſi BD æquidiſtantes ducantur F
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k
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<
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GL. erunt vti〈que〉
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FK GL
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diametri portionum A
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k
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B BLC. ſit ita
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〈que〉 portionis A
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k
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B centrum grauitatis M; portionis verò BLC pun
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ctum N. connectantur〈que〉 FG MN
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k
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L
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, quæ diametrum BD ſe
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cent in punctis OQS. Quoniam igitur puncta MN in
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eadẽ
">eadem</
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proportione diuidunt KF LG, erit KM ad MF, vt LN
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NG. & componendo KF ad FM, vt LG ad GN. &
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per
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mutando KF ad LG, vt FM ad GN. ſuntquè KF LG
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æquales; erit FM ipſi GN ęqualis; & reliqua Mk
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LN æqualis. </
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<
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id
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">& quoniam FM GN, & Mk NL
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ęqui
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diſtantes, erunt FG MN KL inter ſe ęquales, &
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<
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abbr
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æquidiſtã-tes
">æquidiſtan
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tes</
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. & eſt BD æquidiſtans KF, erit igitur SQ ipſi KM æ
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qualis. </
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<
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">quia verò KF BD LG ſunt æquidiſtantes, erit MQ
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QN, vt FO ad OG. Cùm autem ſit BF ad FA, vt BG ad GC, </
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