Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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513493LIBER VII. tem rectæ, DF, vel nihil eſt ſaltem ad alteram partem, ſi enim ali-
qua illius portio eſſet ad alteram partem rectæ, DF, iam recta, D
F, ſecaret figuram, BAC, quod eſt abſurdum, ergorecta, DF, tan-
git curuam, BAC, igitur poſſibile eſt, & c.

COROLL ARIV M.

_H_Inc manifeſtum eſt quomodo ducenda ſit recta linea datam cur-
uam totam in eodem plano cum ea exiſtentem contingens, quæ
quidem data recta linea ſit æquidiſtans.

SI propoſita quæcumque figura plana vni regulæ paral-
lelis quotcumque lineis ita ſecari poſſit, vt conceptæ
in figura rectæ lineæ integræ ſemper exiſtant: Ipſa ex pa-
rallelogrammis rectilineis, aut curuilineis, ſeu ex figuris
in alteram partem deficientibus, regula eadem, compo-
netur.

Sit quæcumque figura plana, SPFR, talis tamen, vt ſecta quot-
cumq; vni regulæ, vt, FE, parallelis, conceptæ in ipſa rectæ lineę
integræ ſint. Dico ipſam, velex parallelogrammis rectilineis, aut

343[Figure 343] curuilineis, vel ex figuris in al-
teram partem deficientibus,
reg. eadem, FE, componi.
Sint enim ductæ, SA, FE, op-
poſitæ tangentes figuræ, SPF
R, regula eadem, FE, quibus
incidat quomodocumq; recta
linea, AE, moueatur autem, F
111. lib. 1 E, verſus, SA, ſemperæquidi-
ſtanter eidem, SA, donec illi
congruat, interim verò punctum, E, ita in ipſa feratur, vt deſcri-
bat lineam, ENA, cum, AE, figuram, ANE, comprehenden@em,
quæ eidem, SPFR, ſit æqualiter analoga iuxta regulam, FE; in
eadem integris exiſtentibus parallelis ipſi, FE, ad ambitum, ANE,
terminantibus: rurſus feratur recta linea, AE, verſus ambitum, A
NE, ſemper ipſi, AE, æquidiſtanter donec totam pertranſierit fi-
guram, ANE, adnotentur autem contactus lineæ ſic

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