1conſiſtas angulos CAE, CBF obſeruaturus.
29[Figure 29]
Quibus angulis obſer
uatis intellige rectam
BF occurrere Tangen
ti AE in G. In triangu
lo itaque ABG angu
lus AGB eſt notus, vt
pote differentia duo
rum obſeruatorum C
BG, CAG: angulus A
eſt obſeruatus, & data
eſt altitudo BA: ergo
inueniri poteſt quantitas rectæ BG. Iam du
cantur rectæ CF, CE, & ſunt duo triangula
AEC, BFC rectangula, in quibus duo an
guli EAC, ECA ſimul ſunt æquales duo
bus FBC, FCB: Atqui angulus ECA eſt æ
qualis duobus ECF, FCB; ergo tres ECF,
FCB, CAE ſunt æquales duobus FBC, FCB;
& dempto communi FCB, remanet FBC
æqualis duobus ECF, EAC. Eſt igitur ECF
differentia nota duorum obſeruatorum CAE,
CBF. Ducatur demùm recta CG. Et quo
niam GF, GE ſunt tangentes circulum ab
eodem puncto exeuntes, inter ſe æquales
ſunt, ſicut & CF, CE ex centro ductæ; CG
verò eſt vtrique triangulo FCG, ECG com
munis; ergo angulus ECF notus diuiditur à
29[Figure 29]Quibus angulis obſer
uatis intellige rectam
BF occurrere Tangen
ti AE in G. In triangu
lo itaque ABG angu
lus AGB eſt notus, vt
pote differentia duo
rum obſeruatorum C
BG, CAG: angulus A
eſt obſeruatus, & data
eſt altitudo BA: ergo
inueniri poteſt quantitas rectæ BG. Iam du
cantur rectæ CF, CE, & ſunt duo triangula
AEC, BFC rectangula, in quibus duo an
guli EAC, ECA ſimul ſunt æquales duo
bus FBC, FCB: Atqui angulus ECA eſt æ
qualis duobus ECF, FCB; ergo tres ECF,
FCB, CAE ſunt æquales duobus FBC, FCB;
& dempto communi FCB, remanet FBC
æqualis duobus ECF, EAC. Eſt igitur ECF
differentia nota duorum obſeruatorum CAE,
CBF. Ducatur demùm recta CG. Et quo
niam GF, GE ſunt tangentes circulum ab
eodem puncto exeuntes, inter ſe æquales
ſunt, ſicut & CF, CE ex centro ductæ; CG
verò eſt vtrique triangulo FCG, ECG com
munis; ergo angulus ECF notus diuiditur à