Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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ductarum ſic linearum fracta per ſuperficiem ambientem inueniri
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poſtet, etiam illi homologa in fruſto, 3647, fracta eſſe deberet, quod
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eſt abſurdum, nullam .</
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<
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<
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">ducibilium ipſi, 38, in ſolido, 3678, ęqui-
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diſtanter linearum fractam eſſe iam ex conſtructione manifeſtum eſt,
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fruſta autem, 3647, LDEF, eſſe inter ſe ſimilia, ſicut etiam, 6
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{11/ }, D {14/ }, necnon, 9 {10/ } {11/ }8, MK {14/ } G 2 ex diffinitione ſimilium ſoli-
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dorum liquidò apparet.</
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">EX his fruſtis autem duo accipiamus, quę ſimul cum homologis
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partibus ipſarum, LG, 38, detruncantur, vt ipſa, LDEF,
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3647, & </
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<
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">ponamus eadem ſeorſim, deinde ex maiori ipſarum, LE,
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34, vt ex, LE, abſcindatur æquali minori .</
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<
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">OE, æqualis ipſi, 34,
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hoc facto intelligamus ſingulas, quæ tum in figura, LDE, tum in
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figura, LFE, ipſi, LE, æquidiſtant, & </
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<
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terius integræ ſi-
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militer, & </
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dem partem diui-
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di, ac ſecatur, LE,
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in, O, & </
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ctas ſectiones ex-
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tenſas lineas, OD,
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OF, vlterius ſecto
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ſolido, LDEF,
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plano vtcunq; </
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ſi, LFE, æquidi-
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ſtante, quod in eo
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producat figuram,
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QMY, & </
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<
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ra, LDE, rectam, QY, in figura verò, DEF, rectam, YM, & </
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in ſuperficie, LDF, lineam, QAM, intelligantur ſingulæ in figu-
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ra, QYM, parallelæ ipſi, QY, ſimiliter, & </
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uidi, ac ſecatur, QY, in, T, & </
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tenſa linea, TIM; </
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<
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">ſie autem fiat in cæteris figuris, quę in ſolido, L
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DEF, ipſi, LEF, æquidiſtant, inuentis lineis, qualis eſt ipſa, TI
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M, quorum termini erunt in lineis, DTO, DMF, per eaſdem au-
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tem lineas ſic ſe habentes intelligamus extenſam ſuperficiem, cuius
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termini erunt lineæ, DO, OF, FD, vt habeamus ſolidum, ODE
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F, figuris, ODE, OEF, DEF, & </
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ſum. </
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<
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">Quoniam ergo linea, OF, diuidit omnes ipfi, LE, in figura,
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LEF, æquidiſtantes ſimiliter ad eandem partem, ac diuiditur, </
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