Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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ducamus rectam, VN, parallelam ipſi, AB, tranſibit hæc per
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cta lib 7.
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Annot.
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Prop. 3.</
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punctum, E, qui eſt etiam vertex rcſpectu ipſius, AB, igitur ſeca-
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bit, HM, quod eſt abſurdum, nam vtræque ſunt parallelæ eidem,
<
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AB, & </
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<
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xml:space
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">ideò inter ſe ſunt parallelæ, vel, VN, extendetur ſuper, H
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M, & </
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<
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xml:space
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">ſic, HM, tranſiret per, C, in ipſoq; </
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<
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xml:space
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">tangeret figuram con-
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tra ſuppoſitum, quod etiam eſt abſurdum, non igitur, HM, tanget
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<
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xml:space
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">Ex A. De-
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fin. 1. hu-
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ius.</
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figuram, CARB, ſed erit tota extra figuram, ſi nullibi concurrat
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cum ambitu figuræ, vel, tranſiens per aliquem punctum, eandem
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ſecabit, ſi is punctus non ſit ex illis, qui funt vertices ipſius figuræ ex
<
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hac parte, vel ex oppofito reſpectu ipſius, AB; </
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<
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xml:space
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">quod ſimiliter in ſo-
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lidis oſtendemus pro rectis lineis, AB, HM, VN, plana intelligen-
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tes, & </
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<
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xml:space
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">ipſam, CARB, eſſe figuram ſolidam ſupponentes, quæ
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oſtendere opus erat.</
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<
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xml:space
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<
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">_H_Inc patet à quolibet puncto ambitus datæ figuræ planæ, vel ſolidæ
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ductam lineam, vel planum æquidiſtans illi, reſpectu cuius ſumi-
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tur vertex (ſi ſumptus punctus non ſit vnus ex verticalibus dictis) ſeca-
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rè figuram, cum, vt oſtenſum eſt, tangens eſſe non poſſit, & </
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<
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xml:space
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per inter duo oppoſita tangentia, reſpectu regulæ, penes quam ſumitur
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vertex, aſſumpta linea cadet, licet indefinitè producatur.</
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<
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xml:space
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<
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">_E_T quia ſi recta linea, vel planum, ſecat duas parallelas, vel duo
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æquidiſtantia plana, ſecat etiam omnia intermedia illis æquidi-
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ſtantia; </
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<
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xml:space
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">ideò ſi recta linea, vel planum, tranſeat per verticem, & </
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<
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xml:space
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ſiue per oppoſitos vertices datæ figuræ planæ, vel ſolidæ, ſecabit etiam om-
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nes in figura oppoſitis tangentibus æquidiſtantes intra figuram, vel ea-
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ſdem productas extra figuram.</
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<
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reuolutio verſus cylindricum ducta fuerit recta linea
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<
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">D. fin. 3.</
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paralleìa regulæ lateris cylindrici, hæc eritlatus cylindrici
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in talibaſi conſtituti.</
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<
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cumq; </
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