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

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6747LIBERI. in Prop. demonſtratum eſt. Et vice verſaſi figuræ ſint ſimiles, & æqua-
les, etiam homologas æquales eſſe, ſi enim inæquales eſſent, etiam ipſæ
figuræ inæquales eſſent, quod eſt abſurdum. Vlterius autem patet, ſi
ſint inuicem ſuperpoſitæ, ita vt ſimiliter ſint conſtitutæ, ac duæ quæuis
homologæ inuicem fuerint congruentes, etiam ipſas figuras fore con-
gruentes, alioquin ſequerentur abſurda ſuperius demonſtrata, cum quę-
uis aliæ homologæ neceſſariò quoque ſint æquales, quæ enim congruerunt
ſunt æquales, & ſubinde etiam incidentes, & quæuis aliæ homologæ in-
ter ſe ſunt æquales.

THEOREMA XXIII. PROPOS. XXVI.

SI duobus parallelis quibuſcumque planis inciderint duo
plana ſe ſe interſecantia, primum nempè, & ſecundum;
fuerint autem alia duo parallela quæcumque plana, quibus
pariter incidant duo alia plana ſe ſe diuidentia, primum ſi-
militer, & ſecundum: Eorum autem cum paralielis planis
communes ſectiones angulos ęquales comprehenderint, nec-
non primorum, ac ſecundorum planorum mutuæ ſectiones
ad communes ſectiones primorum planorum cum planis pa-
rallelis effe ct as angulos æquales conſtituerint, ipſa verò pri-
ma plana ad plana parallela æquè fuerint ad eandem partem
inclinata: Eędem communes ſectiones ad communes ſectio-
nes ſecundorum planorum cum planis parallelis effe ctas an-
gulos pariter conſtituent æquales, necnon ſecunda plana e-
runt ad eadem plana parallela æqualiter ad eandem partem
inclinata.

Sint duo parallela quæcunque plana, BD, HV, quibus incidat
duo plana, HA, primum, AV, ſecundum ſe ſe ſecantia in recta,
AG. Sint nunc alia duo plana quęcunq; parallela, LQ, & Λ, qui-
bus pariter incidant alia duo plana, LY, primum, & , Κ Λ, ſecun-
dum, ſe ſe pariter ſecantia in recta, KY, communes vero ſectiones,
BA, AD; LK, KQ, incidentium planorum cum planis paralle-
lis contineant angulos æquales, ſit nempè, BAD, angulus æqua-
lis angulo, LKQ, (erit. n. & , HGV, ęqualis ipſi, & Υ Λ,) ſimili-
1110. Vnde.
cimi El. ter ipſæ, AG, KY, cum ipſis, GH, Y & , angulos conſtituant æ-
quales, & prima plana, BG, LY, ad plana parallela, BD, HV;
LQ, & Λ, ſint æquè ad eandem partem inclinata. Dico angulos,
AGV, Κ Υ Λ, ęquales eſſe, necnonſecunda plana, AV, Κ Λ,

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