161141LIBER II.
in, O, ideò, vt vna ad vnam, ſic omnes ad omnes.
i.
vt, LE, ad, E
11Coroll. 4.
huius. O, ſic omnes lineæ figuræ, LEF, erunt ad omnes lineas figuræ, O
EF, regula, LE, . i. vt, LE, ad, EO, ita figura, LEF, ad figu-
ram, OEF; eodem modo oſtendemus, vt, QY, ad, YT, ſic eſſe
224. huius. figuram, QYM, ad figuram, TYM, eſt autem vt, QY, ad, YT,
ita, LE, ad, EO, ergo figura, LEF, ad, OEF, erit vt, QYM,
ad, TYM, & ſic erit quælibet alia figura in ſolido, LEDF, ipſi,
334. huius. LEF, æquidiſtans, ad eius portionem in ſolido, OEDF, manen-
tem, ergo vt vna ad vnam, ſic omnes ad omnes . i. vt figura, LEF,
ad figuram, OEF, ſic omnia plana ſolidi, LEDF, ad omnia pla-
443. huius. na ſolidi, OEDF, regula plano, LEF, & ita ſolidum, LEDF,
ad ſolidum, OEDF, eſt autem figura, LEF, ad figuram, OEF,
vt, LE, ad, EO, vel ad, 34, ergo ſolidum, LEDF, ad ſolidum,
OEDF, erit vt, LE, ad, 34, quod pariterſerua.
11Coroll. 4.
huius. O, ſic omnes lineæ figuræ, LEF, erunt ad omnes lineas figuræ, O
EF, regula, LE, . i. vt, LE, ad, EO, ita figura, LEF, ad figu-
ram, OEF; eodem modo oſtendemus, vt, QY, ad, YT, ſic eſſe
224. huius. figuram, QYM, ad figuram, TYM, eſt autem vt, QY, ad, YT,
ita, LE, ad, EO, ergo figura, LEF, ad, OEF, erit vt, QYM,
ad, TYM, & ſic erit quælibet alia figura in ſolido, LEDF, ipſi,
334. huius. LEF, æquidiſtans, ad eius portionem in ſolido, OEDF, manen-
tem, ergo vt vna ad vnam, ſic omnes ad omnes . i. vt figura, LEF,
ad figuram, OEF, ſic omnia plana ſolidi, LEDF, ad omnia pla-
443. huius. na ſolidi, OEDF, regula plano, LEF, & ita ſolidum, LEDF,
ad ſolidum, OEDF, eſt autem figura, LEF, ad figuram, OEF,
vt, LE, ad, EO, vel ad, 34, ergo ſolidum, LEDF, ad ſolidum,
OEDF, erit vt, LE, ad, 34, quod pariterſerua.
DVcatur nunc intra ſolidum, OEDF, planum ipſi, DEF, æ-
quidiſtans, quod in eo producat figuram, CNX, quæ ſecet
figuram, ODE, in recta, CN, & , OFE. in recta, NX, & ſuper-
ficiem, ODF, in linea, CX, ſecet autem & lineas, DO, in, C, O
E, in, N, & , OF, in, X, ſimiliter in ſolido, 3467, ducatur pla-
num ipſi, 647, æquidiſtans, quod abipſa, 34, abſcindat, 35, æqua-
lem ipſi, ON, & producat in eo figuram, RSP; vlterius per pun-
cta, C, X, ducantur, BH, G Ω, parallele ipſi, LE, & occurrentes
lineis, DL, LF, in, B, G, & rectis, DE, EF, in, H, Ω, deinde
à puncto, B, ducatur, BV, parallela ipſi, DE, ſiue, CN, (nam,
DE, CN, ſunt communes ſectiones planorum æquidiſtantium, C
NX, DEF, & plani, ODE, eadem ſecantis, vnde, CN, DE, ſunt
parallelæ, veluti patebit etiam, NX, æquidiſtare ipſi, EF,) & iun-
gatur, VG, quia ergo, NX, eſt parallela ipſi, Ε Ω, & , Χ Ω, ipſi,
NE, erit, Χ Ω, æqualis ipſi, NE, & quia, LE, ad, EO, eſt vt, B
H, ad, HC, . i. vt, VE, ad, EN, eſt autem, G Ω, ad, Ω Χ, vt,
LE, ad, EO, quia eſt illi parallela, & ſecatur à linea, OF, in, X,
ergo, G Ω, ad, Ω Χ, erit vt, VE, ad, EN, ſunt autem, Ω Χ, EN,
inter ſe æquales, ergo & , G Ω, VE, erunt æquales, & ſunt paralle-
læ, ergo etiam eas iungentes, VG, Ε Ω, erunt æquales, & paralle-
læ. Sumatur nunc intra lineam, CX, vtcunq; punctum, I, per quod
ipſi, LE, parallela ducatur, AK, quæ ſuperficiei, LDF, occurrat
in, A, & plano, DEF, in, K, quia ergo, AK, æquidiſtat ipſi, L
55Exis: @@
Elem. E, poterit per, AK, planum duci æquidiſtans plano, LEF, ſit du-
ctum idem, quod prius, quod adhuc ſecet figura, LDE, in
quidiſtans, quod in eo producat figuram, CNX, quæ ſecet
figuram, ODE, in recta, CN, & , OFE. in recta, NX, & ſuper-
ficiem, ODF, in linea, CX, ſecet autem & lineas, DO, in, C, O
E, in, N, & , OF, in, X, ſimiliter in ſolido, 3467, ducatur pla-
num ipſi, 647, æquidiſtans, quod abipſa, 34, abſcindat, 35, æqua-
lem ipſi, ON, & producat in eo figuram, RSP; vlterius per pun-
cta, C, X, ducantur, BH, G Ω, parallele ipſi, LE, & occurrentes
lineis, DL, LF, in, B, G, & rectis, DE, EF, in, H, Ω, deinde
à puncto, B, ducatur, BV, parallela ipſi, DE, ſiue, CN, (nam,
DE, CN, ſunt communes ſectiones planorum æquidiſtantium, C
NX, DEF, & plani, ODE, eadem ſecantis, vnde, CN, DE, ſunt
parallelæ, veluti patebit etiam, NX, æquidiſtare ipſi, EF,) & iun-
gatur, VG, quia ergo, NX, eſt parallela ipſi, Ε Ω, & , Χ Ω, ipſi,
NE, erit, Χ Ω, æqualis ipſi, NE, & quia, LE, ad, EO, eſt vt, B
H, ad, HC, . i. vt, VE, ad, EN, eſt autem, G Ω, ad, Ω Χ, vt,
LE, ad, EO, quia eſt illi parallela, & ſecatur à linea, OF, in, X,
ergo, G Ω, ad, Ω Χ, erit vt, VE, ad, EN, ſunt autem, Ω Χ, EN,
inter ſe æquales, ergo & , G Ω, VE, erunt æquales, & ſunt paralle-
læ, ergo etiam eas iungentes, VG, Ε Ω, erunt æquales, & paralle-
læ. Sumatur nunc intra lineam, CX, vtcunq; punctum, I, per quod
ipſi, LE, parallela ducatur, AK, quæ ſuperficiei, LDF, occurrat
in, A, & plano, DEF, in, K, quia ergo, AK, æquidiſtat ipſi, L
55Exis: @@
Elem. E, poterit per, AK, planum duci æquidiſtans plano, LEF, ſit du-
ctum idem, quod prius, quod adhuc ſecet figura, LDE, in