519499LIBER VII.
ſupereretur à, φ2, ergo prima ad ſecundam erit, vt tertia ad quar-
tam. f. figura, Β& ℟ΚΓΔ, ad figuram, Cφλ, erit, vt aggregatum
ex, & ℟, ΓΔ; ad, φλ, vel vt aggregatum ex, HI, LM, ad, NO, ſeu
vt quælibet aliæ duæ ſimiliter ſumptę, quod erat oſtendendum,
Dicantur autem dictę figuræ proportionaliter analogę iuxta regu-
lam, AD, vel, ΧΩ.
tam. f. figura, Β& ℟ΚΓΔ, ad figuram, Cφλ, erit, vt aggregatum
ex, & ℟, ΓΔ; ad, φλ, vel vt aggregatum ex, HI, LM, ad, NO, ſeu
vt quælibet aliæ duæ ſimiliter ſumptę, quod erat oſtendendum,
Dicantur autem dictę figuræ proportionaliter analogę iuxta regu-
lam, AD, vel, ΧΩ.
THEOREMA III. PROPOS. III.
FIguræ ſolidæ quæcumq;
in eiſdem planis parallelis
conſtitutæ, in quibus ductis quibuſcumque planis di-
ctis parallelis æquidiſtantibus, coneeptæ cuiuſcumq; ſic
ducti plani in ipſis ſolidis figurę planę ſunt inter ſe, vt eiuſ-
modi cuiuſlibet alterius plani in eiſdem ſolis conceptæ ſi-
guræ (homologis tamen in eodem ſolido ſemper exiſter ti-
bus) eandem inter ſe, quam dictæ iam-conceptæ cuiuſcũq;
plani figuræ, rationem habebunt. Dicanrur autem figurę
proportionaliter analogæ, iuxta regulas ipſa plana paral-
lela, in quibus exiſtunt.
conſtitutæ, in quibus ductis quibuſcumque planis di-
ctis parallelis æquidiſtantibus, coneeptæ cuiuſcumq; ſic
ducti plani in ipſis ſolidis figurę planę ſunt inter ſe, vt eiuſ-
modi cuiuſlibet alterius plani in eiſdem ſolis conceptæ ſi-
guræ (homologis tamen in eodem ſolido ſemper exiſter ti-
bus) eandem inter ſe, quam dictæ iam-conceptæ cuiuſcũq;
plani figuræ, rationem habebunt. Dicanrur autem figurę
proportionaliter analogæ, iuxta regulas ipſa plana paral-
lela, in quibus exiſtunt.
Sint duę quelibet fig.
ſolidę, AMEGF, PQRY, in eiſdem planis
parallelis conſtitutę; ductis verò quibuſcumq; planis præfatis pa-
rallelis ęquidiſtantibus, eorum conceptę, in ſolidis figurę ſint vnius
plani ex. g. figuræ, NSTV, ΖΩΔ, alteriusautem, MEGF, QRY,
vel contingat has eſſe ſolidorum baſes, ac in altero planorum pa-
rallelorum, ſolida, AMEGF, PQRY, contingentium, ſit verò figu-
ra, MEGF, ad figuram, QRY, vt figura, NSTV, ad figuram, ΖΩ
Δ, homologis nempè in eodem ſolido exiſtentibus. Dico ſolidum,
AMEGF, ad ſolidum, PQRY, eſſe vt, NSTV, figura, ad figuram,
ΖΩΔ, vel vt figura, MEGF, ad figuram, QRY. Ducatur enim in
figura, MEGF, vtcumq; recta, EF, ad illius ambitum terminata,
cui ducta parallela, SV, in figura, NSTV, producantur ambæ in-
definitè verſus puncta, S, E, in quibus ſumantur vtcũq; ęquè mul-
tiplices, BS, CE, ſimiliter in eiſdem figuris ductis ali js eiſ dem, SV.
EF, ęquidiſtantibus, ſumãtur earum pariter ęquè, multiplices iux-
ta prędictarum multiplicitatem, & omnium termini ſint in lineis,
NBT, MICHG, ſicut ipſarum partium termini ſint in lineis, NST,
NOT, NBT, MEG, MDG, MCG, traductis verò alijs quotcumq;
planis pręfatis parallelis, ac ipſa ſolida ſecantibus, hoc idem fiat
circa ipſorum figuras in ipſis ſolidis conceptas, omnium verò
parallelis conſtitutę; ductis verò quibuſcumq; planis præfatis pa-
rallelis ęquidiſtantibus, eorum conceptę, in ſolidis figurę ſint vnius
plani ex. g. figuræ, NSTV, ΖΩΔ, alteriusautem, MEGF, QRY,
vel contingat has eſſe ſolidorum baſes, ac in altero planorum pa-
rallelorum, ſolida, AMEGF, PQRY, contingentium, ſit verò figu-
ra, MEGF, ad figuram, QRY, vt figura, NSTV, ad figuram, ΖΩ
Δ, homologis nempè in eodem ſolido exiſtentibus. Dico ſolidum,
AMEGF, ad ſolidum, PQRY, eſſe vt, NSTV, figura, ad figuram,
ΖΩΔ, vel vt figura, MEGF, ad figuram, QRY. Ducatur enim in
figura, MEGF, vtcumq; recta, EF, ad illius ambitum terminata,
cui ducta parallela, SV, in figura, NSTV, producantur ambæ in-
definitè verſus puncta, S, E, in quibus ſumantur vtcũq; ęquè mul-
tiplices, BS, CE, ſimiliter in eiſdem figuris ductis ali js eiſ dem, SV.
EF, ęquidiſtantibus, ſumãtur earum pariter ęquè, multiplices iux-
ta prędictarum multiplicitatem, & omnium termini ſint in lineis,
NBT, MICHG, ſicut ipſarum partium termini ſint in lineis, NST,
NOT, NBT, MEG, MDG, MCG, traductis verò alijs quotcumq;
planis pręfatis parallelis, ac ipſa ſolida ſecantibus, hoc idem fiat
circa ipſorum figuras in ipſis ſolidis conceptas, omnium verò