Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ ei, quam habet, CO, ad, RZ, vel, CD, ad, RX, cum ſunt æqui-
angula, ergo æqualia parallelogramma baſes habent altitudinibus,
vel lateribus æqualiter baſibus inclinatis reciprocas, quod oſtendere
opus erat.

183.1.

Defin. 12.
lib. 1.
Exantec.

184. THEOREMA VIII. PROPOS. VIII.

SImilia parallelogramma ſunt in dupla ratione laterum
homologorum.

Sint ſimilia parallelogramma, AC, EG. Dico eadem eſſe in du-
plarat one laterum homologorum: Quoniam enim ſunt ſimilia illa
ſunt æquiangula, ſint anguli, BCD, FGH, æquales, & latera ho-
mologa, BC, FG; CD, GH, ſi ergo pro
baſibus ſumpierimus ipſas, BC, FG, erit,
AC, ad, EG, in ratione compoſita ex ea,
quam habet, BC, ad, FG, & ex ea, quam
habet, DC, ad, HG, quæ eſt eadem ei,
quam habet, BC, ad, FG, vel, FG, ad
tertiam proportionalem duaru, primę nem-
pè, BC, & ſecundæ, FG, ergo, AC, ad, EG, erit vt, BC, ad ter-
tiam proportionalem duarum primę, nempè, BC, & @ecundę, FG,
. i. erit in dupla ratione eius, quam habet, BC, ad, FG, vel, CD,
ad, GH, quod oſtendere opus erat.

184.1.

lux diff.
Sex. El.
0140-01
6. huius.
Defin. 10.
5. Elem.

185. COROLLARIVM.

_H_Inc patet, quæ de parallelogrammis in ſuperioribus Propoſitioni-
bus oſtenſa ſunt, eadem de eorundem omnibus lineis cum quibuſ. uis regulis aſſumptis pariter verificari, nam illa ſunt, vt ipſa paralle-
logramma.

185.1.

_3. huius._

186. THEOREMA IX. PROPOS. IX.

PArallelogrammorum in eadem altitudine exiſtentium
omnia quadrata, regula baſi, iuxta quam altitudo ſum-
pta eſt, ſunt inter ſe, vt quadrata baſium.

186.1.

A. Def. 8.
huius.
Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer