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

IN Schemate adhuc Prop. antec. oſtendemus omnia qua-
quadrata figuræ, HBDM, demptis omnibus quadratis
figuræ, BHMF, eſſe ad omnia quadrata ſemiparabolæ, B
DE, vt, DM, MF, ad @ {3/6}. ipſius, FD.

Nam omnia quadrata figuræ, HBDM, demptis omnibus qua-
dratis figuræ, BHMF, ad omnia quadrata figuræ, CBDF, dem-
1137. huius 1 ptis omnibus quadratis trilinei, BCF, oſtenſa ſunt eſſe, vt, DM, M
F, ad, FD, hæc autem ad omnia quadrata ſemiparabolæ, BDE,
ſunt vt {2/3}. FD, ad {1/8}. ipſius, FD, . ſ. vt, FD, ad @ {3/6}. FD, ergo, ex æ-
quali, omnia quadrata figuræ, HBDM, demptis omnibus qua-
dratis figuræ, BHMF, ad omnia quadrata ſemiparabolæ, BDE.
erunt vt, DM, MF, ad @ {3/6}. ipſius, FD, quod oſtendere opus erat.

THEOREMA XXXVIII. PROP. XL.

SI in figuris Propoſ. 32. & 34. ducantur, GP, GV, regu-
lis, DF, DM, parallelæ, oſtendemus (ſi ipſę ſecauerint
parabolam, DBF,) omnia quadrata figuræ, CBDF, dem
ptis omnibus quadratis trilinei, BCF, ad omnia quadrata
figuræ, CBNP, demptis omnibus quadratis quadrilinei,
BCPO. Vel omnia quadrata figuræ, HBDM, demptis
omnibus quadratis figuræ, BHMF, ad omnia quadrata fi-
guræ, HBNV, demptis omnibus quadratis figuræ, HVO
B, eſſe vt parabolam, DBF, ad parabolam, NBO.

Demonſtratio præſentis, Theor. erit conformis demonſtratio.
nibus Prop. 19. 20. Lib. 3. quapropter inde petatur.

COROLLARIVM.

_H_Inc colligemus omnia quadrata ſiguræ, HBDM, demptis omni-
bus quadratis figuræ, BHMF, ad omnia quadrata figuræ, HBN
V, demptis omnibus quadratis figuræ, BHVO, eſſe vt omnia quadra-
ta figuræ, CBDF, demptis omnibus quadratis trilinei, BCF, ad

Table of contents

Text layer

Text normalization

Search