Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBERI. fit eas, quæ inter taliter incidentes, & perimetrum figurarum con-
tinentur, eodem ordine ſumptas, eſſe vt ipſas, HP, KN, inciden-
tes, ſunt igitur figuræ planę, BVO, DTF, inter ſe ſimiles, & ho-
mologarum earundem regulæ ipſæ tangentes, dictæ figuræ ſunt in
planis æquidiſtantibus, quarum incidentes fibi inuicem ęquidiſtant,
& homologæ earundem figurarum ſunt ad eandem partem inciden-
tium, & ipſarum incidentium partes homologæ pariter ad eandem
partem conſtitutæ, igitur figuræ, VBO, TDF, nedum erunt ſimi-
les, ſed etiam ſimiliter poſitæ, quod oſtendendum erat.

83.1.

Coroll. 1.
huius.
Penãtes. 1
Corol. an-
teced.
16. Huius.
0056-01
10. Vnde-
cimi El.
4. Sexti
Elem.
10. Vnde-
Fimi El.
A. Def. 10.

84. COROLLARIVMI.

_E_T quia oſtenſum eſt ipſas tangentes, SP, XN, eſſe bomologárum
earundem ſimilium figurarum regulas, & ductæ ſunt vtcumque,
patet ſi duxerimus alias duas eiuſdem baſis oppoſitas tangentes, quæ cum
primò ductis angulos efficient æquales, & per ipſas, & verticem, A,
extenderimus duo plana (quorum & plani figuræ, BVO, producti com-
munes ſectiones erunt aliæ duæ figuræ, BVO, oppoſitæ tangentes) quod
eodem modo oſtendemus has ſecundas tangentes eſſe homologarum earun-
dem ſimilium figurarum regulas, & intra ipſas contineri earundem
quoq; incidentes, ſacient autem ſecunda tangentes cum primis angu-
los æquales, prima. n. ex. gr. tangens figuræ, BVO, quæ eſt, XN, eſt
parallela ipſi, SP, primæ tangenti figuræ, DTF, & ſecundatangens
figuræ, BVO, eſt pariter parallela ſecundæ tangenti figuræ, DTF, nam
tum primæ, tum ſecundæ tangentes ſunt communes ſectiones æquidiſtan-
tium planorum, ipſarum nempè figurarum, BVO, DTF, productorum
planorum, & ideò ſunt parallelæ, & angulos continent æquales, vnde
in figuris, quæ à planis baſi conici parallelis producuntur, ſi babeamus
bomologas cum àuabus quibuſdam regulis, eaſdem etiam babebimus cum
duabus quibaſuis alijs angulos æquales cum prædictis ad eandem partem
continentibus.

84.1.

_10. Vnde-_
_cimi El._

85. COROLLARIVM II.

_P_Atet in ſuper ex bac, & 11. ac 12. huius ſimilium planarum figu-
rarum, quæex ſectione planorum baſi cylindrici, vel conici æqui-
diſtantium in illis producuntur, vel ſunt oppoſitæ baſes cylindrici, aut
fruſti conici, poſſibile eſſe inuenire incidentes, quæ ſint & ductarum vt-
cumq; oppoſitarum earundem tangentium incidentes, & quia punctum,
H, ſumptum eſt vtcumque, & ab ipſo ducta quælibet incidens, HP, pa-
tet, quod, ducta vtcumque in dictis figuris incidente earum tangenti-

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