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

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3616GEOMETRIÆ

Sit propoſita quæcumque figura plana, AOVE, & in ipſiu@
plano duæ rectæ lineæ, BD, IT, vtcumq; ſe inuicem fecante@
11Def. 14.

10[Figure 10] in puncto; C, oportet illi parallelogrammum
circumſcribere, cuius latera rectis, SD, IT,
ſint parallela. Ducantur ergo oppoſitæ tan-
gentes figuræ, AOVE, reſpectu ipſius, IT,
quæ ſint, KM, HL, & aliæ duæ reſpectu ip-
22Cor. ant. ſius, BD, quæ ſint, KH, ML, quæ cum
prædictis concurrent, nam ſunt parallelæ ip-
ſis, BD, IT, quæ inuicem concurrunr, ſit
ergo concurſus in punctis, K, M, L, H, igi-
tur, KL, erit parallelogrammum, cuius ſin-
gula latera tangent ambitum ſiguræ, vt in
punctis, A, O, V, E, & ideò erit figuræ, AOVE, circumfcri-
33Def. 14. ptum, habens latera duabus datis rectis lineis, BD, IT, in figu-
ræ, AOVE, plano ſe inuicem ſecantibus, parallela; quod effi-
cere, & c.

PROBLEMA III. PROPOS. III.

CVilibet ſolido parallelepipedum circumſcribere, cu-
ius plana oppoſita tribus datis planis, ſe inuicem ſe-
cantibus, ſint parallela.

Sit ſolidum,

11[Figure 11] ACBD, quod-
cumq; in quo
tria plana, A
CBD, AB, C
D, ſe inuicem
fecent, quæli-
bet duo, opor-
tetſolido, AC
44Def. 1@. BD, paralle-
lepipedum cir-
cūſcribere, cu-
ius oppoſita
plana prædi-
ctis planis ſint
parallela. Du-
cātur duo pla-
na oppoſita
55Coroll. 1.
huius. tangentia dictum ſolidum reſpectu cuiuſuis planorum ſe

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