Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER III. bunt, eſſe eorundem axes. His autem prædemonſtratis ſequentia Corol-
laria colliguntur, quæ quidem cum Typographo deeſſent conſueti buiu-
ſcemodi caracteres, diuerſis imprimineceſſe fuit.

358.1.

_@6. Lib. 1._
_47. Eiuſd._
_lib. 1._
_46. Lib. 1._
_47. Lib. 1._

359. COROLLARIVMI.

IN Propoſ. prima igitur, ſi ſuppoſuerimus, PRDE, eſſe circu-
lum, vel ellipſim, & axem, ER, & circa eandem in baſi, DP,
parallelogrammum, FP, quę quidem ſit baſis portionis, DEP, re-
ctè ſecans axim, ER, deinde intellexerimus omnes figuras ſimiles
po@@onis, DEP, eſſe circulos diametros in figura genitrice, DEP,
(cui ſut erecti) ſitos habentes, tunc, FP, erit figura genitrix ſolidi
ſimilaris, quod erit cylindrus rectus, & DEP, erit figura genitrix
ſolidi præ@@ ſimilatis, quod erit portio ſphæræ, vel ſphæroidis,
cuius axis, ER, & quia patet ex ſupradictis, quam rationem habeat
ſolidum ſimilare genitum ex, FP, ad ſibi ſimilare genitum ex, DE
P@uxta regulam, DP, ide@ patet ex ſupradictis, quam rationem ha-
beat cylindrus, FP, ad portionem ſphæræ, vel ſphæroidis, DEP,
ſiue, DP, tranſeat per centrum, A, ſiue non. Similiter ſi ſuppoſue-
rimus, EDRP, eſſe ſphæroidem, & , ER, non axim, ſed diame-
trum, & ſecari per ellipſim, DSPR, obliquè ad diametrum, ER,
& circa eandem diametrum, EB, in eadem baſi ellipſi, DSPR,
eſſe cylindricum, FP, ſecari autem cylindricum, & portionem ſphæ-
roidis planis parallelis ipſi ellipſi, DP, quę intelligatur erecta plano,
DEPR, conceptæ in ipſo cylindrico figuræ erunt omnes figuræ ſi-
miles parallelogrammi, FP, & quæ ſiunt in portione ſphæroidis, D
EP, erunt omnes figuræ ſimiles portionis, DEP, omnes inquam
ellipſes ſimiles ellipſi, DP, (eſt enim idem, ſiue intelligas has figu-
ras ſimiles deſcribi omnibus lineis figurarum genitricium, FP, DE
P, ſiue percipias ealdem produci per ſectionem corporum per plana
factam ipſi, DP, parallela) & quia patet ratio harum omnium ſimi-
lium ſigurarum, ſiue ellipſium inter ſe ex ſupradictis, & ſubinde ſoli-
dorum ſimilarium genitorum ex, FP, & portione, DEP, qucrum
vnum eſt cylmdricus, alterum eſt portio ſphæroidis ſecta plano, D
P, ideo patet, quam rationem habeat cylindricus, FP, ad portio-
nem, DEP, . @. eſſeeandem, quam habet compoſita ex ſexta parte,
EB, & dimidia, BR, ad ipſam, BR, & hoc, ſiue, ER, ſit axis,
ſiuenon; Quod ſi, DP, tranſeat per centrum, A, cylindricum, FP,
eſſe ſexquialterum portionis ſphærę, vel ſphęroidis, DEP. Ijſdem
vijs patebit conum, ſiue conicum, EDP, ad portionem ſphærę, vel
ſphæroidis, DEP, eſſe vt, BR, ad compoſitam ex, BR, & dimi-
dia totius, ER, quod ſi, DP, per centrum tran@eat, conum, vel cc-

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