Casati, Paolo, Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae

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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

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