Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER VII.
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tem rectæ, DF, vel nihil eſt ſaltem ad alteram partem, ſi enim ali-
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qua illius portio eſſet ad alteram partem rectæ, DF, iam recta, D
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F, ſecaret figuram, BAC, quod eſt abſurdum, ergorecta, DF, tan-
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git curuam, BAC, igitur poſſibile eſt, &</
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">_H_Inc manifeſtum eſt quomodo ducenda ſit recta linea datam cur-
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uam totam in eodem plano cum ea exiſtentem contingens, quæ
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quidem data recta linea ſit æquidiſtans.</
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<
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">SI propoſita quæcumque figura plana vni regulæ paral-
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lelis quotcumque lineis ita ſecari poſſit, vt conceptæ
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in figura rectæ lineæ integræ ſemper exiſtant: </
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">Ipſa ex pa-
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rallelogrammis rectilineis, aut curuilineis, ſeu ex figuris
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in alteram partem deficientibus, regula eadem, compo-
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netur.</
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<
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">Sit quæcumque figura plana, SPFR, talis tamen, vt ſecta quot-
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cumq; </
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<
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">vni regulæ, vt, FE, parallelis, conceptæ in ipſa rectæ lineę
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integræ ſint. </
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">Dico ipſam, velex parallelogrammis rectilineis, aut
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0513-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0513-01
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curuilineis, vel ex figuris in al-
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teram partem deficientibus,
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reg. </
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<
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">eadem, FE, componi.
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<
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">Sint enim ductæ, SA, FE, op-
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poſitæ tangentes figuræ, SPF
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R, regula eadem, FE, quibus
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incidat quomodocumq; </
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linea, AE, moueatur autem, F
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E, verſus, SA, ſemperæquidi-
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ſtanter eidem, SA, donec illi
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congruat, interim verò punctum, E, ita in ipſa feratur, vt deſcri-
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bat lineam, ENA, cum, AE, figuram, ANE, comprehenden@em,
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quæ eidem, SPFR, ſit æqualiter analoga iuxta regulam, FE; </
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eadem integris exiſtentibus parallelis ipſi, FE, ad ambitum, ANE,
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terminantibus: </
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<
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">rurſus feratur recta linea, AE, verſus ambitum, A
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NE, ſemper ipſi, AE, æquidiſtanter donec totam pertranſierit fi-
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guram, ANE, adnotentur autem contactus lineæ ſic </
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