518498GEOMETRIÆ
348[Figure 348]
ca tantum, &
per omnium terminos ex parte, 2, tranſeat linea, C
P2, ſimiliter in alia figura, Β& Δ, ſumantur quotcumq; in ipſa, Δ& ,
producta verſus, & , æquales ipſis, & ℟ΓΔ, fimul ſumptis, & pro-
ductis reliquis in fig. Β& Δ, ipſi, & Δ, parallelis, aliæ tot æquales
ſuis productis in directum capiantur, per quorum omnium termi-
nos tranſeant lineæ, BGZ, BFY. Quoniam ergo figurę, BFYZG,
BGZ& H, Β& ℟κΓΔ, ſunt in eiſdem parallelis, AD, ΧΩ; & ductis
in eiſdem quomodocumq; ipſis, AD, ΧΩ, parallelis, interceptæ in
figuris portiones ſunt æquales, ideò ip@æ figuræ, BYZ, BZ& , Β&
℟κΓΔ, æqualiter analogæ, & ſubinde æquales, erunt: Quo pa-
11Per ant. cto etiam oſtendemus figuras, Φ λ, λC2, æquales eſſe: Quotu-
plex ergo eſt aggregatum ex, Υ℟, ΓΔ, aggregati ex, & ℟, ΓΔ, to-
tuplex erit aggregatum ex figuris, BYZ, BZ& , Β& ℟κΓΔ, ſeu figu-
ra, ΒΥ℟κ @Δ, figuræ, Β& ℟κΓΔ; ſimiliter quotuplex erit, Φ2, ipſi-
us, φλ, totuplex erit aggregatum ex figuris, Cφλ, Cλ2, hoc eſt figu-
ra, CΦ2, ipſius figuræ, CΦλ, habemus ergo æquè multiplices pri-
mæ, & tertiæ vtcumq; aſſumptas, ſimiliter & æquè multiplices ſe-
cundæ, & quartæ. Quoniam verò ex. g. Υ℟, ΓΔ; FI, LM, ſunt
æquè multiplices ipſarum, & ℟, ΓΔ; HI, LM, ſimiliter, 2Φ, PN,
ſunt æquè multiplices ipſarum, Φλ, NO, ipſę verò, & ℟, ΓΔ, HI,
LM, φλ, NO, ſunt proportionales, ideò ſi aggregatum ex, Υ℟, ΓΔ,
adæquabitur ipſi, φ2, etiam aggregatum ex, FI, LM, adæquabitur
ipſi, NP, vt & reliquæ omnes ſimiliter ſumptæ, & conſequenter
22Ex ant. etiam figura, ΒΥ℟κΓΔ, adæquabitur figuræ, Cφ2, ſi verò aggre-
gutum ex, Υ℟, ΓΔ; ſuperet, φ2, eodem modo patebit figuram, ΒΥ
℟κΓΔ, ſuperare figuram, Cφ2, vel ſuperari ab eadem, ſi, Υ℟, ΓΔ;
P2, ſimiliter in alia figura, Β& Δ, ſumantur quotcumq; in ipſa, Δ& ,
producta verſus, & , æquales ipſis, & ℟ΓΔ, fimul ſumptis, & pro-
ductis reliquis in fig. Β& Δ, ipſi, & Δ, parallelis, aliæ tot æquales
ſuis productis in directum capiantur, per quorum omnium termi-
nos tranſeant lineæ, BGZ, BFY. Quoniam ergo figurę, BFYZG,
BGZ& H, Β& ℟κΓΔ, ſunt in eiſdem parallelis, AD, ΧΩ; & ductis
in eiſdem quomodocumq; ipſis, AD, ΧΩ, parallelis, interceptæ in
figuris portiones ſunt æquales, ideò ip@æ figuræ, BYZ, BZ& , Β&
℟κΓΔ, æqualiter analogæ, & ſubinde æquales, erunt: Quo pa-
11Per ant. cto etiam oſtendemus figuras, Φ λ, λC2, æquales eſſe: Quotu-
plex ergo eſt aggregatum ex, Υ℟, ΓΔ, aggregati ex, & ℟, ΓΔ, to-
tuplex erit aggregatum ex figuris, BYZ, BZ& , Β& ℟κΓΔ, ſeu figu-
ra, ΒΥ℟κ @Δ, figuræ, Β& ℟κΓΔ; ſimiliter quotuplex erit, Φ2, ipſi-
us, φλ, totuplex erit aggregatum ex figuris, Cφλ, Cλ2, hoc eſt figu-
ra, CΦ2, ipſius figuræ, CΦλ, habemus ergo æquè multiplices pri-
mæ, & tertiæ vtcumq; aſſumptas, ſimiliter & æquè multiplices ſe-
cundæ, & quartæ. Quoniam verò ex. g. Υ℟, ΓΔ; FI, LM, ſunt
æquè multiplices ipſarum, & ℟, ΓΔ; HI, LM, ſimiliter, 2Φ, PN,
ſunt æquè multiplices ipſarum, Φλ, NO, ipſę verò, & ℟, ΓΔ, HI,
LM, φλ, NO, ſunt proportionales, ideò ſi aggregatum ex, Υ℟, ΓΔ,
adæquabitur ipſi, φ2, etiam aggregatum ex, FI, LM, adæquabitur
ipſi, NP, vt & reliquæ omnes ſimiliter ſumptæ, & conſequenter
22Ex ant. etiam figura, ΒΥ℟κΓΔ, adæquabitur figuræ, Cφ2, ſi verò aggre-
gutum ex, Υ℟, ΓΔ; ſuperet, φ2, eodem modo patebit figuram, ΒΥ
℟κΓΔ, ſuperare figuram, Cφ2, vel ſuperari ab eadem, ſi, Υ℟, ΓΔ;