Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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ſeuntis, vt ipſius, BDFO, quod ſemper eſt trapezium, & </
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<
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BO, TDF, ſiue eiſdem æquidiſtantium inter eaſdem ductarum, eſſe ea-
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rundem lineas, vel latera homologa, vnde patet communes ſectiones
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planiper latera fruſti conici ducti, & </
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<
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xml:space
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">eiuſdem baſium oppoſitarum, ſiue
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eiſdem æquidiſtantium inter eas productarum figurarum, eſſe earundem
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lineas, vel latera homologa; </
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<
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">lineas, inquam, cum ſunt intra figuras,
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nec ſumuntur in plano tangente: </
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<
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">latera, cum ſunt in earum circuitu,
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cum nempè ſunt in eodem plano tangente, in eo præcisè, quod eſt pla-
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num contactus fruſti conici (contactus ſcilicet cius plani, quod per ver-
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ticem ducitur) quod ſemper erit trapezium, vel trapezia, vt patere po-
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teſt in trapezijs, BDCR, IEFO, quæ eſſent planum contactus fruſti
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conici, ſiidem fruſtum tangeretur à plano trianguli, ADF.</
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">SI duæ figuræ planę ſimiles, non exiſtentes in eodem pla-
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no, fuerint inæquales, & </
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<
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">erunt cuiu-
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ſdam fruſticonici oppoſitæ baſes.</
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">& </
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">ſint duæ figuræ planæ quæ-
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cumque ſimiles, inæquales, & </
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">ſimiliter poſitę, non tamen exiſten-
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tesin eodem plano, ipſæ, VBO, TDF. </
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<
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">Dico, quod erunt am-
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bæ cuiuſdam fruſti conici oppoſitę baſes. </
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<
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xml:space
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">Quoniam ergo figure, V
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BO, TDF, ſunt ſimiliter poſitæ, & </
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">non in eodem plano, erunt in
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huius.</
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planis ęquidiſtantibus, & </
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oppoſitarum tangentium, quæ ſunt earundem homologarum regu-
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læ, ipſæ, KN, HP; </
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<
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">KN, ipſius, VBO, &</
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<
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">, HP, ipſius, TDF,
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& </
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<
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">prædictæ tangentes figuræ, VBO, ſint ipſæ, VK, XN, & </
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guræ, TDF, ipſæ, TH, SP, erunt ergo ipſæ, KN, HP, æqui-
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diſtantes, & </
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<
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">quia ad tangentes, quæ ſunt regulæ homologarum, illę
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">Conuerla
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10. Vnde-
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cimi El</
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efficiunt ad eandem partem angulos æquales, erit angulus, KNX,
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æqualis angulo, HPS, & </
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<
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">quia, KN, eſt parallela ipſi, HP, erit
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etiam, XN, parallela ipſi, SP. </
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<
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">Eodem pacto oſtendemus, VK,
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eſſe parallelam ipſi, TH; </
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<
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">ducantur in figuris, VBO, TDF, duæ
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earum homologæ regulis dictis tang entibus, quæ ſint ipſæ, BR, I
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O, DC, EF, ſint autem totæ, BO, DF, productæ, ſi opus ſit, vt
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ſecent ipſas, KN, HP, quas diuident ſimiliter ad eandem partem,
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vt in punctis, M, G, & </
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">quia figuræ propoſitæ ſunt inæquales, ſit
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maior ipſa, TDF, igitur etiam maior erit, DC, ipſa, BR, vel, E
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F, ipſa, IO, ſi, n. </
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">eſſent eiſdem æquales, etiam reliquæ homologæ
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his parallelæ eſſent ęquales, cum omnes ſint proportionales (ſunt.</
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<
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