Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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fit eas, quæ inter taliter incidentes, & </
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<
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xml:space
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tinentur, eodem ordine ſumptas, eſſe vt ipſas, HP, KN, inciden-
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<
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xml:space
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tes, ſunt igitur figuræ planę, BVO, DTF, inter ſe ſimiles, & </
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<
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mologarum earundem regulæ ipſæ tangentes, dictæ figuræ ſunt in
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planis æquidiſtantibus, quarum incidentes fibi inuicem ęquidiſtant,
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& </
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<
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tium, & </
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<
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xml:space
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partem conſtitutæ, igitur figuræ, VBO, TDF, nedum erunt ſimi-
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les, ſed etiam ſimiliter poſitæ, quod oſtendendum erat.</
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">_E_T quia oſtenſum eſt ipſas tangentes, SP, XN, eſſe bomologárum
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earundem ſimilium figurarum regulas, & </
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<
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patet ſi duxerimus alias duas eiuſdem baſis oppoſitas tangentes, quæ cum
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primò ductis angulos efficient æquales, & </
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<
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<
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extenderimus duo plana (quorum & </
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">plani figuræ, BVO, producti com-
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munes ſectiones erunt aliæ duæ figuræ, BVO, oppoſitæ tangentes) quod
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eodem modo oſtendemus has ſecundas tangentes eſſe homologarum earun-
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dem ſimilium figurarum regulas, & </
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quoq; </
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<
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">incidentes, ſacient autem ſecunda tangentes cum primis angu-
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los æquales, prima. </
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<
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parallela ipſi, SP, primæ tangenti figuræ, DTF, & </
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figuræ, BVO, eſt pariter parallela ſecundæ tangenti figuræ, DTF, nam
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tum primæ, tum ſecundæ tangentes ſunt communes ſectiones æquidiſtan-
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tium planorum, ipſarum nempè figurarum, BVO, DTF, productorum
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planorum, & </
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_cimi El._</
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in figuris, quæ à planis baſi conici parallelis producuntur, ſi babeamus
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bomologas cum àuabus quibuſdam regulis, eaſdem etiam babebimus cum
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duabus quibaſuis alijs angulos æquales cum prædictis ad eandem partem
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continentibus.</
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rarum, quæex ſectione planorum baſi cylindrici, vel conici æqui-
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diſtantium in illis producuntur, vel ſunt oppoſitæ baſes cylindrici, aut
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fruſti conici, poſſibile eſſe inuenire incidentes, quæ ſint & </
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cumq; </
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H, ſumptum eſt vtcumque, & </
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tet, quod, ducta vtcumque in dictis figuris incidente earum </
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