Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER I. tium, ACBD, AB, CD, & producantur donec ſibi occurrant, oc-
current autem, quia hæc planis ſe inuicem ſecantibus ſunt parallela,
& ſit ab illis comprehenſum ſolidum, ZF, erit igitur, ZF, paralle-
ſepipedum, cum eius oppoſita plana ſint inuicem parallela, quæ tan-
gunt ſolidum, ACBD, vt in punctis, A, C, B, D, E, X, & ideò
erit ſolido, ACBD, circumſcriptum, habens plana oppoſita pro-
poſitis planis ſe ſecantibus parallela; quod efficere opus erat.

Def. 1@.
Coroll. 1.
huius.
Def. 15.

55.SCHOLIVM.

_P_Oteſt autem contingere in antecedentis Propoſ. figura ipſam eſſepa-
railelogrammum, & line as rectas ſe ſecantes, qutbus parallelo-
grammi circumſcriptibilis latera debent eſſe parallela, eſſe ipſa paralle-
logrammi latera, in quo caſu idem eſſet parallelogrammum circumſcri-
ptum, & cui circumſcriberetur: V eluti hic etiam ſi ſolidum, ACBD,
eſſet parallelepipedum, cuius oppoſitis planis, plana circum ſcrip tibilis
deberent eſſe pacallela, tunc enim idem eſſet parallelepipedum circum-
ſcriptum, & cui cir cumſcriberetur: Contactus autem in antecedenti po-
teſt etiam eſſe in linea, & in bac tum in linea, tum in planis, licet con-
tactus, qui fit in punctis tantum expoſitus fuerit.

56.THEOREMA I. PROPOS. IV.

DAta quacumq; figura plana, vel ſolida, & in plana da-
ta recta linea, in ſolida verò dato plano; qualibet li-
nea, vel planum, quod indefinitè productum non tangat fi-
guram dictam planam, vel ſolidam, in vertice ſumpto reſpe-
ctu dictæ lineæ, vel plani, vel totum extra, vel aliquid eius
intra figuram cadit, nempè figuram ſecat, ſi linea lineæ, vel
planum plano æquidiſtet.

Sit data figura plana, CARB,
& in ea recta, AB, ſit vertex vnus
reſpectuipſius, AB, punctus, C,
& ſit recta, HM, parallela ipſi,
AB, quæ etiam indefinitè produ-
cta non tangat figuram, ARBC,
in, C, vertice. Dico, HM, vel
eandem ſecare. Neutrum efficiat
ſi poſſibile eſt, igitur, HM, tan-
get figuram, CARB, & non in,
C, igitur in alio puncto, vt in, E,
igitur, E, erit vertex figuræ, CA
RB, reſpectu ipſius, AB, eſt e-
tiam, C, vertēx eiuſdem reſpectu eiuſdem, AB, ergo ſi per, C,

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