Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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neſque ipſorum ſolidorum, LDGF, 3687, ſimiliter ad eandem
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partem diuidentibus, conceptę (vt probatum eſt) inter ſe ſimiles, vt
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ipſæ, DEF, 647, necnon, MK {14/ }, 9 {10/ } {11/ }, & </
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<
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">omnium earundem
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linearum homologarum regulæ duabus quibuſdam, nempe ipſis, O
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E, Φ 4, æquid ſtantes, & </
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<
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">earum incidentes ipſæ, EF, 47, necnon,
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K {14/ }, {10/ } {11/ }, quę omnes incidentes iacent in plano ſiminum figurarum,
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LFG, 378, & </
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<
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">ſunt earum homologæ, æquidiſtantes ipſis, LQ,
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3 {12/ }, communibus ſectionibus planorum incidentium figurarum, L
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FG, 378, & </
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<
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">oppoſitorum tangentium, quarum quidem figurarum
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">26. lib. 1.</
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plana ſunt ad plana tangentia, vt dictum eſt, æquè ad eandem par-
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tem inclinata, & </
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<
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">cum ipſæ, inquam, figuræ, LFG, 378, ſint ſi-
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miles interſe, nam ex. </
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<
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">eſt, EF, ad, 47, vt, OE, ad, Φ 4, ideſt
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">A. Def. 10.
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vt, LG, ad, 38, quæ diuidunt ſimiliter ad eandem partem ipſas, L
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G, 38, (quod etiam de cæteris probabitur) & </
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">cum anguli, LGT,
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38 {13/ }, ſint etiam æquales ſuperius dictis conſequenter, & </
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lib. </
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<
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">ipſæ figuræ, LFG,
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378, & </
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<
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">ipſa iolida, LDGF, 3687, pariter ſimilia erunt.</
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">Nunc ſolidum, 3678, planis, oppoſitis tangentibus parallelis,
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in talia fruſta diuiſum intelligatur, vt quæ in ipſis ducuntur rectæ li-
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neę ipſi, 38, æquidiſtantes, in ciſdem fruſtis ſingulę integrę habean-
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tur .</
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<
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">ita vt ductarum ſic linearum, quæ ad fruſtorum ambientem ſu-
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perficiem terminantur, pars quidein non ſit intra fruſta, pars verò
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extra, ſed totæ intra, vel ſaltem nihil earum extra reperiatur, hanc
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etenim ſectionem ſupponere ſieri poſſe nullam inuoluit repugnan-
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tiam, cum hoc totum ſolidum ex duabus linearum translationibus re-
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ſultans ſit interius integrum, enim vero ſi præfatum ſolidum in fru-
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ſta quæcunque per dicta plana parallela icinderetur, nec in ipſis con-
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tingeret, quod attentamus, denuò facta fruſta planis prædictis pa-
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rallelis continuò reſecaremus, vt tandem omnis lmearum, ipſi, 38,
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æquidiſtanter in d ctis fruſtis ducibilium, fractura tolleretur: </
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tur, quod hoc obtinuerimus per duo plana, 9 {10/ } {11/ }, 647, oppoſitis
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plan@s tangentibus parallela, qu@bus ſolidum, 3678, intria fruſta,
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3647, 6 {11/ }, &</
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">, 9 {10/ } {11/ } 8, ſectum habeatur eius rationis, qualem di-
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ximus, in his ergo ſingul s fruſtis ductæ quæcunque ipſi, 38, æqui-
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diſtantes, & </
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">ad eorum ſuperficiem terminatæ, integræ habebuntur.
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">Sit vlterius in alio ſolido, LDFG, diuifa, LG, ſimiliter ac, 38, in
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punctis, E, K, per quæ tranſeant plana, DEF, MK {14/ }, oppoſitis
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planis tangentibus parallela, quibus ſolidum, LDFG, in tria fru-
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ſta ſcindatur, LDEF, D {14/ }, MK {14/ } G, erunt ergo etiam hęc fruſta
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eius rationis, qualem cupimus .</
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<
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">omnes ductę ipſi, LG, æquidiſtan-
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tes, in ipſis fruſtis conceptæ, integræ erunt; </
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tudine facilè oſtendi poteſt, ſi enim aliqua ex. </
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