Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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tium, ACBD, AB, CD, & </
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<
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xml:space
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">producantur donec ſibi occurrant, oc-
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current autem, quia hæc planis ſe inuicem ſecantibus ſunt parallela,
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& </
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">ſit ab illis comprehenſum ſolidum, ZF, erit igitur, ZF, paralle-
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ſepipedum, cum eius oppoſita plana ſint inuicem parallela, quæ tan-
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gunt ſolidum, ACBD, vt in punctis, A, C, B, D, E, X, & </
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<
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erit ſolido, ACBD, circumſcriptum, habens plana oppoſita pro-
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">Def. 15.</
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poſitis planis ſe ſecantibus parallela; </
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<
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">_P_Oteſt autem contingere in antecedentis Propoſ. </
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<
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railelogrammum, & </
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">line as rectas ſe ſecantes, qutbus parallelo-
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grammi circumſcriptibilis latera debent eſſe parallela, eſſe ipſa paralle-
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logrammi latera, in quo caſu idem eſſet parallelogrammum circumſcri-
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ptum, & </
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<
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<
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">V eluti hic etiam ſi ſolidum, ACBD,
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eſſet parallelepipedum, cuius oppoſitis planis, plana circum ſcrip tibilis
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deberent eſſe pacallela, tunc enim idem eſſet parallelepipedum circum-
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ſcriptum, & </
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<
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">Contactus autem in antecedenti po-
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teſt etiam eſſe in linea, & </
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">in bac tum in linea, tum in planis, licet con-
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tactus, qui fit in punctis tantum expoſitus fuerit.</
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<
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ta recta linea, in ſolida verò dato plano; </
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nea, vel planum, quod indefinitè productum non tangat fi-
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guram dictam planam, vel ſolidam, in vertice ſumpto reſpe-
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ctu dictæ lineæ, vel plani, vel totum extra, vel aliquid eius
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intra figuram cadit, nempè figuram ſecat, ſi linea lineæ, vel
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planum plano æquidiſtet.</
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">Sit data figura plana, CARB,
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& </
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<
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">in ea recta, AB, ſit vertex vnus
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reſpectuipſius, AB, punctus, C,
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& </
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<
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">ſit recta, HM, parallela ipſi,
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AB, quæ etiam indefinitè produ-
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cta non tangat figuram, ARBC,
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in, C, vertice. </
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totam extra figuram cadere, vel
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eandem ſecare. </
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<
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ſi poſſibile eſt, igitur, HM, tan-
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get figuram, CARB, & </
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<
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C, igitur in alio puncto, vt in, E,
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igitur, E, erit vertex figuræ, CA
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RB, reſpectu ipſius, AB, eſt e-
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huius.</
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tiam, C, vertēx eiuſdem reſpectu eiuſdem, AB, ergo ſi per, </
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