Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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quibus incidunt ad eundem angulum ex eadem parte, EO, MR, & </
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quę diuidunt ipſas, EO, MR, ſimiliter ad eandem partem exiſten-
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tes parallelæ ipſis, BC, GN, ſunt vtipſæ, EO, MR, ad eandem
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partem eodem ordine inter ipſas, & </
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<
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">circuitum dictarum figurarum
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compræhenſæ, quia quæ ſunt ex vna parte ſunt æquales ipſis, BO,
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GR, & </
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">quæ ex alia ipſis, OC, RN, in triangulis autem ſunt, vt
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ipſæ, BO, GR, vel, OC, RN, .</
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<
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10.</
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incidentes, & </
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">oppoſitarum tangentium dictarum erunt ipſæ, EO,
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MR, quę tangentes ſunt regulæ homologarum ſimilium figurarum,
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AC, FN, vel, EBC, MGN. </
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<
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">Vlterius, quia, BXC, GYN,
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ſunt ſemicirculi, erunt figurę planę ſimiles iuxta meam definitionem,
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quarum & </
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">tangentium, quæ per extrema, BC, GN, ducuntur e-
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ant.</
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runt incidentes ipſi diametri, BC, GN, vt probatum fuit, veluti
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idem patet de ſemicirculis, B ℟ C, GZN, & </
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<
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quæ diuident ipſas, EO, MR, ſimiliter ad eandem partem, & </
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ſequenter diuidunt etiam altitudines eorũdem reſpectu baſium ſum-
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cimi El.</
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ptas ſimiliter ad eandem partem, & </
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">deijs, quæ per extrema, E, M,
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ducuntur, habemus igitur cylindros, AC, FN, ſiue conos, BEC,
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GMN, quorum ducta ſunt plana oppoſita tangentia dictorum ſo-
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lidorum homologis figuris parallela, quæ ſunt plana, B ℟ CX, A
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D; </
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ex eadem parte, illa nempè, in quibus ſunt ipſa parallelogramma,
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AC, FN, vel triangula, BEC, quia ſunt recta ad baſes .</
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tangentia, ipſæ autem ſiguræ .</
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uenta ſunt eſſe ſimilia, quarum homologarum regulæ oppoſitę tan-
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gentes, AD, BC; </
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">FH, GN, quarum ſunt incidentes, EO, MR,
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earum autem lineæ homologæ, ſumptæ regulis dictis tangentibus,
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repertæ ſunt eſſe incidentes figurarum planarum ſimilium, quæ di-
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uidunt altitudines dictorum ſolidorum iam dictas ſimiliter ad ean-
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dem partem, & </
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cuntur per extrema, BC, GN, tangentes circulos, B ℟ CX, GY
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NZ, ſunt ęquidiſtantes, vt facilè conſideranti patebit, ergo cylin-
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dri, AC, FN, vel coni, BEC, GMN, ſunt ſimiles iuxta meam defi-
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nitionem generalem ſimilium ſolidorum, quod oſtendere opus erat.</
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concordat cum definitione generali ſimilium ſolido-
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rum.</
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