Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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135115LIBER II. go prima ad ſecundam erit, vt tertia ad quartam, ſcilicet figura ſo-
11Def. Qui.
5. Elem. lida, A, ad figuram ſolidam, D, erit vt omnia plana, A, ad om-
nia plana, D, cum quibuſuis regulis aſſumpta, quod & in figuris ſo-
lidis oſtendere opus erat.

COROLLARIVM.

_L_Iquet ex hoc, quod, vt inueniamus, quam rationem habeant inter
ſe duæ figuræ planæ, vel ſolidæ, ſuſſiciet nobis reperire, quam, in
figuris planis, inter ſe rationem habeant earundem omnes lineæ, & , in
figuris ſolidis, earundem omnia plana iuxta quamuis regulam aſſumpta,
quod nouæ huius meæ Geometriæ veluti maximum iacio fundamentum,.

THEOREMA IV. PROPOS. IV.

SI duæ figuræ planæ, vel ſolidæ, in eadem altitudine fue-
rint conſtitutæ, ductis autem in planis rectis lineis, &
in figuris ſolidis ductis planis vtcumque inter ſe parallelis,
quorum reſpectu prædicta ſumpta ſit altitudo, repertum fue-
rit ductarum linearum portiones figuris planis interceptas,
ſeu ductorum planorum portiones figuris ſolidis interceptas,
eſſe magnitudines proportionales, homologis in eadem figu-
ra ſemper exiſtentibus, dictæ figuræ erunt inter ſe, vt vnum
quodlibet eorum antecedentium, ad ſuum conſequens in a-
lia figura eidem correſpondens.

Sint primò duæ figurę planæ in eadem altitudine conſtitutæ, CA
M, CME, in quibus duæ vtcunque rectæ lineæ inuicem parallelæ
ductæ intelligantur, AE, BD, reſpectu quarum communis altitu-

75[Figure 75] do aſſumpta intelligatur, ſint au-
tem portiones figuris interceptæ
ipſæ, AM, BR, in fig. CAM,
& , ME, RD, in fig. CME,
reperiatur autem, vt, AM, ad,
ME, ita eſſe, BR, ad, RD.
Dico figu am, CAM, ad figu-
ram, CME, eſſe vt, AM, ad,
ME, vel, BR, ad, RD, quoniam enim, BD, AE, vtcumq; du-
ctæ ſunt inter ſe æquidiſtantes, patet, quod quęlibet earum, quę di-
cuntur omnes lineæ figuræ, CAM, ſumptæ regula altera

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