Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
"/>
terminans in ambientem ſuperficiem bifariam diuidetur ab ipſa, BD,
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xml:space
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vtin, N; </
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">Sie oſtendemus, BD, diuidere cæteras omnes ipfi, EM,
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æquidiſtantes in ſuperficiem ambientem hinc inde terminatas, & </
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<
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quia, BD, ſecat, EM, adangulos rectos, cæteras omnes iam di-
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ctas bifariam, & </
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">ad angulos rectos ſecabit, igitur tunc figura, BED
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M, erit circa axem, BD, ſiue in ſolido rotundo, ſiue in cono: </
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<
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xml:space
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tem triangulus, APQ, non tranſeat per ductam ipſi plano perpen-
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dicularem, tunc eodem modo, quoſupra oſtendemus, BD, ſecare
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omnes ęquidiſtantes ipſi, EM, bifariam, & </
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<
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xml:space
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">quia triangulus, APQ,
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non tranſit per perpendicularem baſi, neque erit erectus ipſi baſi, P
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EQM, ergo angulus, EDB, non erit rectus, nam ſi eſſet rectus,
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cum ſit etiam rectus, EDP, planum circuli, PEQM, eſſet erectum
<
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triangulo, APQ, & </
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<
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">ille huic, quod eſt contra ſuppoſitum, igitur,
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xml:space
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">4. Vndec.
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Elem.</
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BD, ſecabit, EM, & </
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ſtantes bifariam, & </
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erit circa diametrum, & </
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<
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">erit diameter ipſa, BD, ſiue axis, in ſupra-
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dicto caſu tum in cono, tum etiam in ſolido rotundo, quod erat oſten-
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dendum.</
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<
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">_H_Inc colligitur in cono, ſi triangulus per axem ductus ſit erectus
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baſi, fieri dictam figuram circa axem; </
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inclinatus eidem, fieri figuram circa diametrum; </
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tem fieri ſemper figuram circa axem.</
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<
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no ſecante baſim coni ſecundum rectam lineam, quę ad
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baſim trianguli per axem ſit perpendicularis, cuius & </
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guli per axem cõmunis ſectio ſit parallela vni laterum trian-
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guli per axem; </
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<
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">quadrata ordinatim applicatarum ad axim,
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vel diametrum figurę in cono ſecundo plano productę, æqui-
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diſtantium eiuſdem, & </
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vt abíciſſæ per eaidem ordinatim applicatas verſus verticem
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ſumptæ ab eiſdem axibus, vel diametris iam dictis.</
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