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

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4828GEOMETRIÆ ad eandem partem ſecantium planorum exiſtent: Et ſi idem
ſecetur planis parallelis quomodocumq; omnibus eiuſdem
lateribus coincidentibus, conceptæ in cylindrico figuræ e-
runt ſimiles, æquales, & ſimiliter poſitæ.

Conſpiciatur figura Propoſit. 10. in qua iam propoſitas ſectiones
habemus, plana enim, AE, ME, tranſeuntia per cylindrici latera

21[Figure 21] ipſum ſecant, & plana, BNG, COF, omni-
bus eiuſdem lateribus coincidunt, & ſunt paral-
lela. Dico ergo figuras, MZH, EIV, eſſe ſi-
miles, & æquales, & ſimiliter poſitas, quod pa-
tet, nam illæ ſunt cylindrici, MHZI, oppoſi-
tæ baſes; idem eodem modo probabitur de figu-
ris, AMH, DVE, & de, ARH, DXE, &
tandem oſtendemus pariter figuras, BNGK, C
OFL, eſſe ſimiles, æquales, & ſimiliter poſitas,
1111. Huius. quia ſunt cylindrici, BF, oppoſitæ baſes, quod
demonſtrandum erat.

COROLLARIV M.

_H_Inc apparet, quamuis figuram planam ex ſectione plani, oppofi-
tis baſibus cylindrici æquidiſtantis, in eo productam, eiſdem op-
poſitis baſibus eſſe ſimilem, æqualem, & ſimiliter poſitam.

THEOREMA X. PROPOS. XIII.

SI quis cylindricus ſecetur plano per latera, deinde ſece-
tur planis oppoſitis eiuſdem baſibus æquidiſtantibus:
Communes ſectiones plani per latera ducti, & planorum ba-
ſibus æquidiſtantium, erunt lineæ, vellatera homologa fi-
gurarum ſimilium, quæ ex ſectione æquidiſtantium plano-
rum in cylindrico effecta in eodem producuntur.

Sit cylindricus, ADM, cuius oppoſitæ baſes, ABC, TDF, ſe-
cetur autem plano vtcumque per latera ducto, quod in eo producat
parallelogrammum, BF, & alio vtcumque plano oppoſitis baſibus
æquidiſtante, quodin eo producat figuram, YNXO, & in paral-
lelogrammo, BF, rectam, NO. Dicorectas, DF, NO, BC, eſſe
lineas, vellatera homologa figurarum, TDF, YNO, ABC,

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