Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ ductarum ſic linearum fracta per ſuperficiem ambientem inueniri
poſtet, etiam illi homologa in fruſto, 3647, fracta eſſe deberet, quod
eſt abſurdum, nullam . n. ducibilium ipſi, 38, in ſolido, 3678, ęqui-
diſtanter linearum fractam eſſe iam ex conſtructione manifeſtum eſt,
fruſta autem, 3647, LDEF, eſſe inter ſe ſimilia, ſicut etiam, 6
{11/ }, D {14/ }, necnon, 9 {10/ } {11/ }8, MK {14/ } G 2 ex diffinitione ſimilium ſoli-
dorum liquidò apparet.

211. D. SECTIO IV.

EX his fruſtis autem duo accipiamus, quę ſimul cum homologis
partibus ipſarum, LG, 38, detruncantur, vt ipſa, LDEF,
3647, & ponamus eadem ſeorſim, deinde ex maiori ipſarum, LE,
34, vt ex, LE, abſcindatur æquali minori . ſ. OE, æqualis ipſi, 34,
hoc facto intelligamus ſingulas, quæ tum in figura, LDE, tum in
figura, LFE, ipſi, LE, æquidiſtant, & ſunt exiam dictis totæ in-
terius integræ ſi-
militer, & ad ean-
dem partem diui-
di, ac ſecatur, LE,
in, O, & per di-
ctas ſectiones ex-
tenſas lineas, OD,
OF, vlterius ſecto
ſolido, LDEF,
plano vtcunq; ip-
ſi, LFE, æquidi-
ſtante, quod in eo
producat figuram,
QMY, & in ſigu-
ra, LDE, rectam, QY, in figura verò, DEF, rectam, YM, & in ſuperficie, LDF, lineam, QAM, intelligantur ſingulæ in figu-
ra, QYM, parallelæ ipſi, QY, ſimiliter, & ad eandem partem di-
uidi, ac ſecatur, QY, in, T, & per ipſas ſectiones concipiatur ex-
tenſa linea, TIM; ſie autem fiat in cæteris figuris, quę in ſolido, L
DEF, ipſi, LEF, æquidiſtant, inuentis lineis, qualis eſt ipſa, TI
M, quorum termini erunt in lineis, DTO, DMF, per eaſdem au-
tem lineas ſic ſe habentes intelligamus extenſam ſuperficiem, cuius
termini erunt lineæ, DO, OF, FD, vt habeamus ſolidum, ODE
F, figuris, ODE, OEF, DEF, & ſuperficie, DOF, comprehen-
ſum. Quoniam ergo linea, OF, diuidit omnes ipfi, LE, in figura,
LEF, æquidiſtantes ſimiliter ad eandem partem, ac diuiditur, LE,

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