7959LIBER I.
lelas, ac (ſi ſint inclinatę, incidantque ipſis in punctis, C, N, iun-
ganturque, CB, CD, NP, NO,) pyramides, ACDB, HNO
P, ſimiles eſſe. Sumatur ergo in, AD, etiam quantumuis protenſa
vbicumq; punctum, F, & accipiatur in, HO, producta, ſi opus ſit,
HL, ęqualis, AF, & indefinitè extenſis lineis, AC, AB, HN, H
11Vidi dicta
lib.7. An-
not. Pro-
poſ.3. P, ducantur in planis, FAC, FAG, LHN, LHP, à punctis, F,
41[Figure 41]
L, ipſis, AF, HL, per-
pendiculares, FE, FG,
LI, LM, occurrentes
ipſis, AE, AG, HI, H
M, in punctis, E, G, I,
M, & iungantur, EG,
IM. Quoniam ergo duo
anguli, AFG, HLM,
recti, & , FAG, LH
M, ſunt æquales, & la-
tera, AF, HL, ęqua-
lia, erunt etiam, FG,
2226.Primi
Elem. LM, GA, MH, ęqua-
lia; eodem modo oſten-
demus æqualia eſſe, F
E, LI, EA, IH, vnde cum ſint ęquales, EA, IH, AG, HM, &
334. Primi
Elem. anguli, EAG, IHM, pariter ęquales, etiam baſes, EG, IM, æ-
quales erunt, & pyramides, AEFG, HILM, ſimiles, & ęquales
ad inuicem exiſtent. Suſpendatur nunc pyramis, AEFG, & pona-
44Defin. 10.
vndec. El. tur punctum, F, in, L, demittaturque, FG, ſuper, LM, cui con-
gruet, ſed & triangulo, EFG, cadente ſuper, ILM, punctum, F,
erit in, I, ac latus, AF, in, HL, alioquin duę eidem plano, ILM,
557. Pri. El. perpendiculares eſſent eductæ ab eodem puncto, L, quod eſt abſur-
dum (ſunt autem, AF, HL, perpendiculares planis, EFG, ILM,
6613. Vnd.
Elem. hoc eſt ſolo plano, ILM, cum ſuperponuntur, ex eo, quod duabus,
IL, IM, ſint perpendiculares in puncto, L,) ergo, FA, cadet ſu-
per, LH, & punctum, A, in, H, vnde etiam, EA, cadet in, IH,
774. Vnd. El.& , AG, in, HM, punctum, B, verò eſto, quod ſit in, T, D, in,
S, & , C, in, V, erit et@am, DB, congruens ipſi, ST, CD, VS,
& , CB, ipſi, VT, & quia angulus, ABD, æquatur ipſi, HPO,
ABD, autem eſt etiam æqualis, HTS, ergo, HTS, HPO, ſunt
æquales, & , ST, parallela, OP. Dico etiam triangulum, VST,
884. Primi
Elem. æquidiſtare ipſi, NOP, ſi . n. hoc non ſit, quia, ST, eſt parallela
ipſi, OP, poterit per, ST, duci planum ipſi, NOP, parallelum,
ducatur, & producat in pyramide triangulum, KST, acta autem à
puncto, H, ipſi, OP, perpendiculari, quę ſit, HQ, ſecante,
ganturque, CB, CD, NP, NO,) pyramides, ACDB, HNO
P, ſimiles eſſe. Sumatur ergo in, AD, etiam quantumuis protenſa
vbicumq; punctum, F, & accipiatur in, HO, producta, ſi opus ſit,
HL, ęqualis, AF, & indefinitè extenſis lineis, AC, AB, HN, H
11Vidi dicta
lib.7. An-
not. Pro-
poſ.3. P, ducantur in planis, FAC, FAG, LHN, LHP, à punctis, F,
pendiculares, FE, FG,
LI, LM, occurrentes
ipſis, AE, AG, HI, H
M, in punctis, E, G, I,
M, & iungantur, EG,
IM. Quoniam ergo duo
anguli, AFG, HLM,
recti, & , FAG, LH
M, ſunt æquales, & la-
tera, AF, HL, ęqua-
lia, erunt etiam, FG,
2226.Primi
Elem. LM, GA, MH, ęqua-
lia; eodem modo oſten-
demus æqualia eſſe, F
E, LI, EA, IH, vnde cum ſint ęquales, EA, IH, AG, HM, &
334. Primi
Elem. anguli, EAG, IHM, pariter ęquales, etiam baſes, EG, IM, æ-
quales erunt, & pyramides, AEFG, HILM, ſimiles, & ęquales
ad inuicem exiſtent. Suſpendatur nunc pyramis, AEFG, & pona-
44Defin. 10.
vndec. El. tur punctum, F, in, L, demittaturque, FG, ſuper, LM, cui con-
gruet, ſed & triangulo, EFG, cadente ſuper, ILM, punctum, F,
erit in, I, ac latus, AF, in, HL, alioquin duę eidem plano, ILM,
557. Pri. El. perpendiculares eſſent eductæ ab eodem puncto, L, quod eſt abſur-
dum (ſunt autem, AF, HL, perpendiculares planis, EFG, ILM,
6613. Vnd.
Elem. hoc eſt ſolo plano, ILM, cum ſuperponuntur, ex eo, quod duabus,
IL, IM, ſint perpendiculares in puncto, L,) ergo, FA, cadet ſu-
per, LH, & punctum, A, in, H, vnde etiam, EA, cadet in, IH,
774. Vnd. El.& , AG, in, HM, punctum, B, verò eſto, quod ſit in, T, D, in,
S, & , C, in, V, erit et@am, DB, congruens ipſi, ST, CD, VS,
& , CB, ipſi, VT, & quia angulus, ABD, æquatur ipſi, HPO,
ABD, autem eſt etiam æqualis, HTS, ergo, HTS, HPO, ſunt
æquales, & , ST, parallela, OP. Dico etiam triangulum, VST,
884. Primi
Elem. æquidiſtare ipſi, NOP, ſi . n. hoc non ſit, quia, ST, eſt parallela
ipſi, OP, poterit per, ST, duci planum ipſi, NOP, parallelum,
ducatur, & producat in pyramide triangulum, KST, acta autem à
puncto, H, ipſi, OP, perpendiculari, quę ſit, HQ, ſecante,