6444GEOMETRIÆ
cuitum figurarum eodem ordine ſumptas, ita ſe habere, ve-
lut illæ, quæ dictis tangentibus inciderunt, iſtæ, quæ illis
inciderunt, erunt tum ſimilium propoſitarum figurarum, tum
ductarum tangentium, incidentes.
lut illæ, quæ dictis tangentibus inciderunt, iſtæ, quæ illis
inciderunt, erunt tum ſimilium propoſitarum figurarum, tum
ductarum tangentium, incidentes.
Sint duę quęcumq;
ſimiles planę figurę, ACEI, MTVS, qua-
rum ſint ductæ oppoſitæ tangentes homologarum earundem regu-
læ, AB, EF, figuræ, AE, & , MN, VR, figurę, MV, incidant
autem eiſdem ad eundem angulum ex eadem parte duæ, BF, NR,
& ductæ ſint quædam duæ ipſis tangentibus parallelæ, CD, TO,
ſecantes ipſas, BF, NR, (& coniequenter incidentes, vt facilè
patet) ſimiliter ad eandem partem, reperiamus, CD, ad, TO, &
pariter, ID, ad, SO, eſſe vt, BF, ad, NR. Dico ipſas, BF, N
R, eſſe incidentes ſimilium figurarum, AE, MV, & ductarum op-
32[Figure 32]
poſitarum tangentium, VR, MN;
EF, AB. Ex dictis igitur ipſę, CI, T
11C. 10. defi.
mitionis. S, erunt homologę earundem ſimilium
figurarum, AE, MV, & quia, CD,
22Ex cor. 2.
19. & 22.
huius. ad, TO, eſt vt, BF, ad, NR, & , B
F, ad, NR, vt, ID, ad, SO, erit, C
D, ad, TO, vt, ID, ad, SO, igitur
puncta, D, O, reperientur in duabus
dictarum fimilium figurarum, & op-
poſitarum tangentium, incidentibus,
ſint illæ ipſæ, HG, PL, quę cum ip-
ſis, TO, CD, æquales angulos ad
eandem partem continebunt. Dico ta-
men etiam ipſas, NR, BF, eſſe ea-
rundem figurarum, & tangentium, in-
cidentes: Sint puncta contactus tangentium, FE, RV, proxima ip-
ſis, NR, BF, ipſa, V, E. Dico, EF, ad, VR, eſſe vt, FB, ad,
333. Defin.
10. RN, nam, EL, ad, VG, eſt vt, LP, ad, GH, quia verò angu-
lus, CDP, æquatur angulo, TOH, & , CDB, ipſi, TON, re-
liquus, PDB, ęquabitur reliquo, HON, & ſic etiam, FDL, ipſi,
ROG, eſt etiam angulus, PLE, ęqualis angulo, HGV, ideò re-
444. Sexti
Elem. liquus in triangulo, DFL, ideſt angulus, DFL, erit ęqualis angu-
lo, ORG, & ſic triangula, FDL, ORG, erunt æquiangula, vt
etiam probabimus triangula, DPB, OHN, eſſe ęquiangula, ſicut
ſunt ęquiangula inter ſetriangula, FDL, PDB, & , ROG, HO
N, vnde vt, LD, ad, DF, ſic erit, PD, ad, DB, permutando,
LD, ad, DP, erit vt, FD, ad, DB, componendo, LP, ad, PD,
erit vt, FB, ad, BD, permutando, LP, ad, FB, erit vt, PD,
rum ſint ductæ oppoſitæ tangentes homologarum earundem regu-
læ, AB, EF, figuræ, AE, & , MN, VR, figurę, MV, incidant
autem eiſdem ad eundem angulum ex eadem parte duæ, BF, NR,
& ductæ ſint quædam duæ ipſis tangentibus parallelæ, CD, TO,
ſecantes ipſas, BF, NR, (& coniequenter incidentes, vt facilè
patet) ſimiliter ad eandem partem, reperiamus, CD, ad, TO, &
pariter, ID, ad, SO, eſſe vt, BF, ad, NR. Dico ipſas, BF, N
R, eſſe incidentes ſimilium figurarum, AE, MV, & ductarum op-
EF, AB. Ex dictis igitur ipſę, CI, T
11C. 10. defi.
mitionis. S, erunt homologę earundem ſimilium
figurarum, AE, MV, & quia, CD,
22Ex cor. 2.
19. & 22.
huius. ad, TO, eſt vt, BF, ad, NR, & , B
F, ad, NR, vt, ID, ad, SO, erit, C
D, ad, TO, vt, ID, ad, SO, igitur
puncta, D, O, reperientur in duabus
dictarum fimilium figurarum, & op-
poſitarum tangentium, incidentibus,
ſint illæ ipſæ, HG, PL, quę cum ip-
ſis, TO, CD, æquales angulos ad
eandem partem continebunt. Dico ta-
men etiam ipſas, NR, BF, eſſe ea-
rundem figurarum, & tangentium, in-
cidentes: Sint puncta contactus tangentium, FE, RV, proxima ip-
ſis, NR, BF, ipſa, V, E. Dico, EF, ad, VR, eſſe vt, FB, ad,
333. Defin.
10. RN, nam, EL, ad, VG, eſt vt, LP, ad, GH, quia verò angu-
lus, CDP, æquatur angulo, TOH, & , CDB, ipſi, TON, re-
liquus, PDB, ęquabitur reliquo, HON, & ſic etiam, FDL, ipſi,
ROG, eſt etiam angulus, PLE, ęqualis angulo, HGV, ideò re-
444. Sexti
Elem. liquus in triangulo, DFL, ideſt angulus, DFL, erit ęqualis angu-
lo, ORG, & ſic triangula, FDL, ORG, erunt æquiangula, vt
etiam probabimus triangula, DPB, OHN, eſſe ęquiangula, ſicut
ſunt ęquiangula inter ſetriangula, FDL, PDB, & , ROG, HO
N, vnde vt, LD, ad, DF, ſic erit, PD, ad, DB, permutando,
LD, ad, DP, erit vt, FD, ad, DB, componendo, LP, ad, PD,
erit vt, FB, ad, BD, permutando, LP, ad, FB, erit vt, PD,
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