5636GEOMETRIÆ
planumper, VK, XN, ductum in recta, KN, rurſus diuidatur, H
P, vtcumq; in puncto, G, à quo ducatur ipſi, SP, parallela, GD,
ſecans baſis ambitum in punctis, F, E, C, D, deinde extendatur
planum per, A, verticem, & rectam, DG, quod per conici latera
1116. Huius. tranſibit, & producet triangula ſiueintus, ſiue extra conicum, quæ
ſint, ADC, ACE, AEF, AFG, ſecabitque figuram, VBO, ſe-
cet eius productum planum in recta, BM, quæ ambitum eiuſdem,
VBO, diuidat in punctis, B, R, I, O, habebimus etiam triangula,
ABR, ARI, AIO, AOM, quorum latera erunt portiones late-
rum inferiorum triangulorum, per planum autem, ADG, ſiue per
rectam, AG, ſit ſecta, KN, in puncto, M. Quia ergo plana, quę
28[Figure 28]
per rectas, VK, XN, &
per, TH, SP, tranſeunt
ſunt parallela, & ſecan-
tur à plano, APH, com-
2210. Vnde-
cimi El. munes eorum ſectionese-
runt parallelę. ſ. KN, ipſi,
HP, igitur triangulus, A
MN, æquiangulus erit
triangulo, AGP, & ideo
circa æquales angulos e-
334. Sexti
Elem. runt latera proportiona-
lia, ergo vt, PG, ad, G
A, ſic erit, NM, ad, M
A, eodem modo oſtende-
mus, vt, AG, ad, GH, ita eſſe, AM, ad, MK, ergo ex æquali
PG, ad, GH, erit vt, NM, ad, MK, ſunt igitur, PH, NK, ſi-
militer ad eandem partem diuiſæ in punctis, M, G: Eodem modo
oſtendemus triangulum, AMO, eſſe ęquiangulum ipſi, AGF, & ,
AMI, ipſi, AGE, & , AMR, ipſi, AGC, & tandem, AMB,
ipſi, AGD, igitur, vt, GA, ad, AM, ſic erit, permutando, FG,
ad, OM, vt verò, GA, ad, AM, ſic permutando eſt, PG, ad,
NM, ideſt, PH, ad, NK, ergo, FG, ad, OM, eſt vt, PH, ad,
NK, ſimiliter oſtendemus, EG, ad, IM, & , CG, ad, RM, &
tandem, DG, ad, BM, eſſe vt, PH, ad, NK, & quia, KN, eſt
parallela ipſi, HP, & , NX, ipſi, PS, ideò angulus, KNX, eſt
4410. Vnde-
Fimi El. æqualis angulo, HPS; habemus igitur duas figuras planas, VBO,
TDF, quarum ductæ ſunt oppoſitæ tangentes, VK, XN, vnius,
& , TH, SP, alterius, inuenimus autem rectas, KN, HP, inter
eaſdem poſitas, cum eis ad eandem partem angulos æquales conti-
nentes, ita ſe habere, vt ductis duabus vtcumque ipſis tangentibus
parallelis, quæ diuidant ipſas ſimiliter ad eandem partem,
P, vtcumq; in puncto, G, à quo ducatur ipſi, SP, parallela, GD,
ſecans baſis ambitum in punctis, F, E, C, D, deinde extendatur
planum per, A, verticem, & rectam, DG, quod per conici latera
1116. Huius. tranſibit, & producet triangula ſiueintus, ſiue extra conicum, quæ
ſint, ADC, ACE, AEF, AFG, ſecabitque figuram, VBO, ſe-
cet eius productum planum in recta, BM, quæ ambitum eiuſdem,
VBO, diuidat in punctis, B, R, I, O, habebimus etiam triangula,
ABR, ARI, AIO, AOM, quorum latera erunt portiones late-
rum inferiorum triangulorum, per planum autem, ADG, ſiue per
rectam, AG, ſit ſecta, KN, in puncto, M. Quia ergo plana, quę
per, TH, SP, tranſeunt
ſunt parallela, & ſecan-
tur à plano, APH, com-
2210. Vnde-
cimi El. munes eorum ſectionese-
runt parallelę. ſ. KN, ipſi,
HP, igitur triangulus, A
MN, æquiangulus erit
triangulo, AGP, & ideo
circa æquales angulos e-
334. Sexti
Elem. runt latera proportiona-
lia, ergo vt, PG, ad, G
A, ſic erit, NM, ad, M
A, eodem modo oſtende-
mus, vt, AG, ad, GH, ita eſſe, AM, ad, MK, ergo ex æquali
PG, ad, GH, erit vt, NM, ad, MK, ſunt igitur, PH, NK, ſi-
militer ad eandem partem diuiſæ in punctis, M, G: Eodem modo
oſtendemus triangulum, AMO, eſſe ęquiangulum ipſi, AGF, & ,
AMI, ipſi, AGE, & , AMR, ipſi, AGC, & tandem, AMB,
ipſi, AGD, igitur, vt, GA, ad, AM, ſic erit, permutando, FG,
ad, OM, vt verò, GA, ad, AM, ſic permutando eſt, PG, ad,
NM, ideſt, PH, ad, NK, ergo, FG, ad, OM, eſt vt, PH, ad,
NK, ſimiliter oſtendemus, EG, ad, IM, & , CG, ad, RM, &
tandem, DG, ad, BM, eſſe vt, PH, ad, NK, & quia, KN, eſt
parallela ipſi, HP, & , NX, ipſi, PS, ideò angulus, KNX, eſt
4410. Vnde-
Fimi El. æqualis angulo, HPS; habemus igitur duas figuras planas, VBO,
TDF, quarum ductæ ſunt oppoſitæ tangentes, VK, XN, vnius,
& , TH, SP, alterius, inuenimus autem rectas, KN, HP, inter
eaſdem poſitas, cum eis ad eandem partem angulos æquales conti-
nentes, ita ſe habere, vt ductis duabus vtcumque ipſis tangentibus
parallelis, quæ diuidant ipſas ſimiliter ad eandem partem,