Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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go prima ad ſecundam erit, vt tertia ad quartam, ſcilicet figura ſo-
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5. Elem.</
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lida, A, ad figuram ſolidam, D, erit vt omnia plana, A, ad om-
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nia plana, D, cum quibuſuis regulis aſſumpta, quod & </
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lidis oſtendere opus erat.</
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">_L_Iquet ex hoc, quod, vt inueniamus, quam rationem habeant inter
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ſe duæ figuræ planæ, vel ſolidæ, ſuſſiciet nobis reperire, quam, in
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figuris planis, inter ſe rationem habeant earundem omnes lineæ, &</
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figuris ſolidis, earundem omnia plana iuxta quamuis regulam aſſumpta,
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quod nouæ huius meæ Geometriæ veluti maximum iacio fundamentum,.</
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">SI duæ figuræ planæ, vel ſolidæ, in eadem altitudine fue-
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rint conſtitutæ, ductis autem in planis rectis lineis, & </
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in figuris ſolidis ductis planis vtcumque inter ſe parallelis,
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quorum reſpectu prædicta ſumpta ſit altitudo, repertum fue-
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rit ductarum linearum portiones figuris planis interceptas,
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ſeu ductorum planorum portiones figuris ſolidis interceptas,
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eſſe magnitudines proportionales, homologis in eadem figu-
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ra ſemper exiſtentibus, dictæ figuræ erunt inter ſe, vt vnum
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quodlibet eorum antecedentium, ad ſuum conſequens in a-
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lia figura eidem correſpondens.</
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">Sint primò duæ figurę planæ in eadem altitudine conſtitutæ, CA
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M, CME, in quibus duæ vtcunque rectæ lineæ inuicem parallelæ
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ductæ intelligantur, AE, BD, reſpectu quarum communis altitu-
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do aſſumpta intelligatur, ſint au-
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tem portiones figuris interceptæ
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ipſæ, AM, BR, in fig. </
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&</
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reperiatur autem, vt, AM, ad,
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ME, ita eſſe, BR, ad, RD.
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ram, CME, eſſe vt, AM, ad,
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ME, vel, BR, ad, RD, quoniam enim, BD, AE, vtcumq; </
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ctæ ſunt inter ſe æquidiſtantes, patet, quod quęlibet earum, quę di-
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cuntur omnes lineæ figuræ, CAM, ſumptæ regula altera </
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