Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ reſultantium figurarum termini ſint in ſuperficiebus, AMCG, A
MDG; AMEG ſimiliter in alio ſolido eſto quod plana, quę produ-
xerũt in ſolido, AMEGF, figur. MEGF, NSTV, genuerint figuras,
QRY, ΖλΩ, ad quas illæ habent eandem rationem, ductis autem,
vel aſſumptis rectis, QY, ΖΔ, inter ſe parallelis, illæ producantur
verſus eandem partem, ΔΥ, in ijſq; productis accipiantur quæcũq; æquè multiplices, vel æquales, YX, Δ℟, & idem fiat in cæteris
ipſis parallelis in figuris, QRY, ΖΩΔ, ſic productis, & omnium
termini ſint in lineis, YXR, Δ℟Ω, hæ verò lineæ, ſicut & reliqua-
rum figurarum eodem modo producibilium, ſint in ſuperficiebus,
PYR, PYXR. Manifeſtum eſt autem figuras, MEGF, MDGE, M
CGD, eſſe æqualiter analogas, & ideò inter ſe æquales, ſicut etiã
figuræ, NSTV, NOTS, NBTO, pariter inter ſe ſunt æquales, & quecunq; aliæ ſunt in eodem plano, ex quo habemus etiam ſoli-
da, AMEGF, AMDGE, AMCGD, eſſe æqualiter analoga, & ideò
interſe æqualia. Eodem modo oſtendemus ſolida, PQRY, PRX
Y, pariter inter ſe æqualia eſſe. Quotupiex eſt ergo ſolidum, AM
CGF, extribus, AMCGD, AMDGE, AMEGF, compoſitum, to-
tuplex eſt figura, MCGF, ex tribus, MCGD, MDGE, MEGF, cõ-
poſita, figuræ, MEGF. Similiter quotuplex eſt ſolidum, PQRX,
ex duobus, PQRY, PYRX, compoſitum ipſius, PQRY, totuplex
eſt baſis, QRX, ex duabus, QRY, YRX, compoſita, fig. QRY; ita
vt habeamus æquè multiplices primæ, & tertiæ, necnon ſecundę,
& quartę magnitudinis. Cum autem figuræ, FMCG, VNBT,
ſint æquè multiplices figurarum, MEGF, NSTV, & pariter figu-
ræ, QRX, ΖΩ℟, ſint æquè multiplices figurarum, QRY, ΖΩΔ,

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