Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

Erit enim, AM, parallelogrammum, vnde, MA, ad, AD, erit
vt, CM, ad, CD, AD, verò ad trian
gulum, FCD; eſt vt, CD, ad, {1/2}, C
D, ergo, AM, ad triangulum, FCD,
erit vt, MC, ad, {1/2}, CD, eſt autem,
AM, ad, FM, vt, CM, ad, MD,
ergo, colligendo, AM, ad, FM, cum
triangulo, FCD, ideſt ad trapezium,
OFCM, erit vt, CM, ad, MD, cum,
{1/2}, DC, quod oſtendendum erat.

223.1.

0169-01
5. huius.
Ex antec.
5. huius

224. COROLLARIVM.

_M_Anifeſtnm eſt autem, ſi, CD, ſit æqualis ipſi, DF, omnes lineas
parallelogrammi, AD, regula, CD, eſſe æquales maximis ab-
ſciſſarum, FD, & omnes lineas trianguli, FCD, regula eadem æquari
omnibus abſciſſis, FD. Nunc ſi intelligamus cuilibet earum, quæ dicun-
tur maximæ abſciſſarum, vel abſciſſæ, adiungirectam, DM, vocantur
tunc maximæ abſciſſarum, vel abſciſſæ adiuncta, DM, hæc autem ſunt
eædem illis, quæ habentur in parallelogrammo, AM, & trapezio, FC
MO, nam ſi produxeris, NE, vſq; ad, OM, in, X, ſiet, EX, adiun-
cta tum ipſi, NE, vni ex maximis abſciſſarum, FD, tum ipſi, HE,
vni ex omnibus abſciſſis, FD, & , EX, adiuncta eſt æqualis ipſi, DM,
vnde omnes linea, AD, adiuncta, DM, ſunt omnes lineæ parallelo-
grammi, AM, & ſunt æquales maximis abſciſſarum ipſius, FD, ad-
iuncta, DM, & omnes lineæ trianguli, FCD, adiuncta, DM, ſunt om-
nes lineæ trapezij, FCMO, & ſunt æquales omnibus abſciſſis ipſius, F
D, adiuncta, DM. Quiaergo, AM, ad trapezium, FCMO, eſt vt, C
M, ad, MD, cum, {1/2}, DC, ideò omnes lineæ, AM, ad omnes lineas
trapezij, FCMO, (regulam hic ſemperintelligeipſam, CM,) . i. ma-
ximæ abſciſſarum, FD, adiuncta, DM, ad omnes abſciſſas, FD, adiun-
cta, DM, erunt vt, CM, compoſita nempè ex propoſita linea, CD, ſiue
ex propoſita, FD, illi æquali, & adiuncta, DM, ad compoſitam ex ad-
iuncta, MD, & , {1/2}, propoſitæ lineæ, CD, vel, DF.

224.1.

_ExCor. 2._
_antec._
_Defin. 7._
_huius._
_3. huius._

225. THE OREMA XXI. PROPOS. XXI.

IN expoſita ſuperioris Propoſ. figura, ſiproducatur, CD,
ad partes, C, vtcunque, vt in, R, & compleatur parallc-
logrammum, GC, oſtendemus trapezium, FGRC, ad tra-

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