Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER II. neſque ipſorum ſolidorum, LDGF, 3687, ſimiliter ad eandem
partem diuidentibus, conceptę (vt probatum eſt) inter ſe ſimiles, vt
ipſæ, DEF, 647, necnon, MK {14/ }, 9 {10/ } {11/ }, & omnium earundem
linearum homologarum regulæ duabus quibuſdam, nempe ipſis, O
E, Φ 4, æquid ſtantes, & earum incidentes ipſæ, EF, 47, necnon,
K {14/ }, {10/ } {11/ }, quę omnes incidentes iacent in plano ſiminum figurarum,
LFG, 378, & ſunt earum homologæ, æquidiſtantes ipſis, LQ,
3 {12/ }, communibus ſectionibus planorum incidentium figurarum, L
FG, 378, & oppoſitorum tangentium, quarum quidem figurarum
plana ſunt ad plana tangentia, vt dictum eſt, æquè ad eandem par-
tem inclinata, & cum ipſæ, inquam, figuræ, LFG, 378, ſint ſi-
miles interſe, nam ex. g. eſt, EF, ad, 47, vt, OE, ad, Φ 4, ideſt
vt, LG, ad, 38, quæ diuidunt ſimiliter ad eandem partem ipſas, L
G, 38, (quod etiam de cæteris probabitur) & cum anguli, LGT,
38 {13/ }, ſint etiam æquales ſuperius dictis conſequenter, & ijs, quæ
lib. 1. Prop. 26. oſtenia ſunt, ideò, inquam, & ipſæ figuræ, LFG,
378, & ipſa iolida, LDGF, 3687, pariter ſimilia erunt.

210.1.

16. Vnd@
Elem.
Corollat.
24. lib. 1.
24. lib. 1.
Vide ad
finem A.
p. 15. hu-
ius.
3. huius.
0158-01
26. lib. 1.
26. lib. 1.
26. lib. 1.
A. Def. 10.
lib. 1.
26. lib. 1.
Defin. 11.
lib. 1.

Nunc ſolidum, 3678, planis, oppoſitis tangentibus parallelis,
in talia fruſta diuiſum intelligatur, vt quæ in ipſis ducuntur rectæ li-
neę ipſi, 38, æquidiſtantes, in ciſdem fruſtis ſingulę integrę habean-
tur . i. ita vt ductarum ſic linearum, quæ ad fruſtorum ambientem ſu-
perficiem terminantur, pars quidein non ſit intra fruſta, pars verò
extra, ſed totæ intra, vel ſaltem nihil earum extra reperiatur, hanc
etenim ſectionem ſupponere ſieri poſſe nullam inuoluit repugnan-
tiam, cum hoc totum ſolidum ex duabus linearum translationibus re-
ſultans ſit interius integrum, enim vero ſi præfatum ſolidum in fru-
ſta quæcunque per dicta plana parallela icinderetur, nec in ipſis con-
tingeret, quod attentamus, denuò facta fruſta planis prædictis pa-
rallelis continuò reſecaremus, vt tandem omnis lmearum, ipſi, 38,
æquidiſtanter in d ctis fruſtis ducibilium, fractura tolleretur: Eſto igi-
tur, quod hoc obtinuerimus per duo plana, 9 {10/ } {11/ }, 647, oppoſitis
plan@s tangentibus parallela, qu@bus ſolidum, 3678, intria fruſta,
3647, 6 {11/ }, & , 9 {10/ } {11/ } 8, ſectum habeatur eius rationis, qualem di-
ximus, in his ergo ſingul s fruſtis ductæ quæcunque ipſi, 38, æqui-
diſtantes, & ad eorum ſuperficiem terminatæ, integræ habebuntur. Sit vlterius in alio ſolido, LDFG, diuifa, LG, ſimiliter ac, 38, in
punctis, E, K, per quæ tranſeant plana, DEF, MK {14/ }, oppoſitis
planis tangentibus parallela, quibus ſolidum, LDFG, in tria fru-
ſta ſcindatur, LDEF, D {14/ }, MK {14/ } G, erunt ergo etiam hęc fruſta
eius rationis, qualem cupimus . i. omnes ductę ipſi, LG, æquidiſtan-
tes, in ipſis fruſtis conceptæ, integræ erunt; quodex eorum ſimili-
tudine facilè oſtendi poteſt, ſi enim aliqua ex. gr. in fruſto, LDEF,

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