Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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">_E_Ademratione, ſi vice quadratorum ſumamus alias figuras ſimiles,
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oſtendemus omnus figuras ſimiles parallelogram morum in eadem,
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">A. Def 8.
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Huius.</
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baſi exiſtentium eſſe, vt altitudines, vel vt latera baſi æqualiter incli-
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nata, dum illa ſunt æquiangula.</
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gulis duobus quibuſuis in eiſdem aſſumptis lateribus,
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habent inter ſe rationem compoſitam exratione
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quadratorum dictorum laterum, & </
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">altitudinum, vel laterum,
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quę cum prędictis ęqualiter inclinãtur, ſi illa ſint ęquiangula.</
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">Sint parallelogramma vtcunq; </
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">AD, FM, in quibus regulæ ex-
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tent latera vtcunque, CD, GM, altitudines autem iuxta dictas re-
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gulas ſumptæ, BV, ON. </
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">Dico omnia quadrata, AD, ad omnia
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quadrata, FM, habere rationem compoſitam ex ea, quam habet
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quadratum, CD, ad quadratum, GM, & </
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">ex ea, quam habet, B
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V, altitudo ad altitudinem, ON, vel etiam, BD, ad. </
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ſint æquiangula, lateraq; </
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">BD, OM, æqualiter ſint inclinata cum
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0143-01
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lateribus, CD, GM; </
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à, BV, verſus, V, ipſa, XV, æ-
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qualis, ON, & </
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P, parallela ipſi, CD, ſecans, BD,
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in, R, erit autem, DR, æqualis
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ipſi, OM, ſi ſint æquiangula, quod
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facilè probari poteſt, erit etiam pa-
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rallelogrammum, PD, in eadem
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baſi cum parallelogrammo, AD,
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ſed in eadem altitudine cum parallelogrammo, FM, omnia ergo
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lib. 1.</
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quadrata parallelogrammi, AD, ad omnia quadrata, FM, habent
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rationem compoſitam ex ea, quam habent omnia quadrata, AD,
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ad omnia quadrata, DP, .</
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">i. </
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">ex ea, quam habet, BV, ad, VX, ſiue,
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ON, vel ex ea, quam habet, BD, ad, DR, ſiue, OM, ſi ſint æ-
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quiangula parallelogramma, AD, DP; </
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<
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">componitur ex ea, quam
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habent omnia quadrata, PD, ad omnia quadrata, FM, .</
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<
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quam habet quadratum, CD, ad quadratum, GM, ergo omnia
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quadrata, AD, ad omnia quadrata, FM, habent rationem </
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