11181LIBER SECVNDVS.
prodibitrecta DB, nota, vtproblemate 4.
oſtendimus:
ex qua ſi ſubtrahatur
ſegmentum haſtæ AD. inter orificium, & oculum in prima ſtatione, reliqua fiet
profunditas, ſiue altitudo putei, velædificij AB.
ſegmentum haſtæ AD. inter orificium, & oculum in prima ſtatione, reliqua fiet
profunditas, ſiue altitudo putei, velædificij AB.
ALITER.
2.
Posito ſinu toto BC, fiat.
11 Vt DE, differentia Tangentium BD, \\ BE, quæ complementis angulorum \\ obſeruationum debentur, # ad DB, Tan- \\ gentem mi- \\ norem # ita DE, diffe- \\ rentia ſtatio- \\ nũ oculorum # ad DE,
Nam numerus procreatus notam exhibebit eandem rectam DB, &
c.
ALITER.
3.
Si per ſolos ſinus operarilubeat, ita agendum erit.
Quoniam 2232. primi.
maior obſeruatus BDC, duobus angulis E, DCE, æqualis eſt;
ſi angulus E,
minor obſeruatus tollatur ex maiore BDC, notus remanebit angulus DCE, dif-
ferentia angulorum obſeruatorum.
Igitur ſi 3310. triang.
rectil.44
Vt ſin{us} anguli D C E, \\ differentiæ angulo- \\ rum obſeruatorum. # ad D E, differen- \\ rentiam ſtationũ \\ oculorum: # ita ſin{us} anguli \\ E, minoris ob- \\ ſeruati # ad D C,
proſiliet nota hypotenuſa D C. Quapropter ſi rurſum 5510. triang.
rectil.66
Vt ſin{us} tot{us} \\ anguli re- \\ cti B, # ad hypotenuſam \\ DC, proximè in- \\ uentam: # ita ſin{us} anguli BCD, com- \\ plementi maioris anguli ob- \\ ſeruati # ad D B,
euadet iterum cognita recta DB, & c.
minor obſeruatus tollatur ex maiore BDC, notus remanebit angulus DCE, dif-
ferentia angulorum obſeruatorum.
Igitur ſi 3310. triang.
rectil.44
Vt ſin{us} anguli D C E, \\ differentiæ angulo- \\ rum obſeruatorum. # ad D E, differen- \\ rentiam ſtationũ \\ oculorum: # ita ſin{us} anguli \\ E, minoris ob- \\ ſeruati # ad D C,
proſiliet nota hypotenuſa D C. Quapropter ſi rurſum 5510. triang.
rectil.66
Vt ſin{us} tot{us} \\ anguli re- \\ cti B, # ad hypotenuſam \\ DC, proximè in- \\ uentam: # ita ſin{us} anguli BCD, com- \\ plementi maioris anguli ob- \\ ſeruati # ad D B,
euadet iterum cognita recta DB, & c.
4.
Iam verò ſi latitudo oriſicij AM, vel fundi BC, cognita fuerit, (Non erit
autem diffi cile eam aliqua menſura nota metiri) facilius in cognitionem altitu-
dinis, profunditatiſue AB, veniemus, pervnicam videlicet ſtationem in D, fa-
ctam, hoc modo. Fiat,
77
Vt ſin{us} \\ tot{us} \\ CB, # ad BD, Tangentem anguli BCD, \\ complementi anguli obſeruatio- \\ nis: # ita latitudo co- \\ gnita CB, # ad DB.
Numerus enim procreatus offeret DB, notam, vt ſupra, & c.
autem diffi cile eam aliqua menſura nota metiri) facilius in cognitionem altitu-
dinis, profunditatiſue AB, veniemus, pervnicam videlicet ſtationem in D, fa-
ctam, hoc modo. Fiat,
77
Vt ſin{us} \\ tot{us} \\ CB, # ad BD, Tangentem anguli BCD, \\ complementi anguli obſeruatio- \\ nis: # ita latitudo co- \\ gnita CB, # ad DB.
Numerus enim procreatus offeret DB, notam, vt ſupra, & c.
Vel per ſolos ſinus, ſi 8810. triang.
rectil.99
Vt ſin{us} anguli \\ B D C, obſer- \\ uationis # ad latitudinem co- \\ gnitam BC: # ita ſin{us} anguli BCD, \\ complemeti anguli ob- \\ ſeruationis. # ad DB,
inuenietur rurſus DB, & c.
rectil.99
Vt ſin{us} anguli \\ B D C, obſer- \\ uationis # ad latitudinem co- \\ gnitam BC: # ita ſin{us} anguli BCD, \\ complemeti anguli ob- \\ ſeruationis. # ad DB,
inuenietur rurſus DB, & c.
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