Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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quæ in cylindricis producant figuras, IM, RT, in conicis verò, O
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M, ST, ſecent verò plana tangentia in rectis, IC, MF, Od; </
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Tp, So, iſtæ ergo erunt ad inuicem parallelæ, & </
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Elem.</
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IM, RT, OM, ST, eadem verò planaſecent plana, BG, Zl, in
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rectis, CF, ℟ p. </
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IM, RT, vel, OM, ST, ſint ſimi-
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les baſibus, & </
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huius.</
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iam oſtenſum fuit, ex quo fit, vt & </
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ipſarum, & </
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fatis ſolidis producibilium ſimilium
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figurarum homologæ duabus qui-
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buſdam regulis, vt ex. </
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<
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Yl, ſemper æquidiſtent. </
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eſt autem, vt probemus, CF, ℟ p,
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vel, dF, op, eſſe prædictarum in-
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cidentes. </
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<
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duabus, LD. </
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guli, ICF, LDG, æquales erunt,
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ſic etiam probabimus eſſe æquales,
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R ℟ p, Xfl, cum verò, IC, ſit e-
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tiam æqualis, LD, & </
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Xf, necnon, CF, ipſi, DG, &</
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℟ p, ipſi, fl, erit, IC, ad, R ℟, vt,
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CF, ad, ℟ p, & </
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MF, R ℟, Tp, ad eundem angu-
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lum ex eadem parte, ergo, CF, ℟
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p, erunt incidentes ſimilium figura-
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rum, IM, RT, & </
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<
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gentium, IC, MF; </
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dem ratione demonſtrabimus, dF,
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op, eſſe incidentes ſimilium figura-
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rum, OM, ST, & </
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<
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gentium, Od, MF; </
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autem, dF, ad, op, vt, dE, ad,
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o &</
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<
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DE, f &</
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partem diuiſæ in punctis, do, (ete-
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Elem.</
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nim altitudines dictorum ſolidorum per plana, IF, Rp, ſimiliter ad
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eandem partem diuiduntur) ergo, dF, op, æquidiſtantes oppoſitis
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tangentibus, BE, DG, Z &</
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lium, EDG, & </
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erunt ipſæ, ED, & </
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