11282GEOMETR. PRACT.
PROBLEMA XXIV.
1.
Hoc etiam nihil aliud eſt, niſi altitudinem quampiam ex eius ſum-
mo faſtigio per duas ſtationes dimetiri, vt problemate 4. oſtenſum eſt. Sit enim
vallis inter duosmontes AB, FG, poſita, & terminus ipſius C, ex monte AB,
poſsit conſpici. Ere cta haſta aliqua AE, fiantin D, & E, duæ ſtationes, obſer-
uenturque anguli D, & E, inſpecto termino C, per radios DC, EC. Intelliga-
tur autem recta EA, vſque ad baſem montis extenſa in B: & recta excurrens
AF, ipſi BG, parallela, vel ad EB, perpendicularis: & denique CH ipſi AB, pa-
rallela, quæ altitudini AB, ęqualis erit, ita vt AB, vel HC, ſit profunditas 1134. primi. lis ab A, vſque ad baſem montis, & IC, eius deſcenſus obliquus. Liquidò au-
47[Figure 47] tem eonſtat, profunditatem AB, vel CH, exquiri poſſe, vt problemate 4. alti-
tudo turris AB, ex duabus ſtationibus in haſta AE, factis, vel in duabus fe-
neſtris, vel certè, vtin præcedenti problemate profunditas putei AB, inuen-
tafuit.
mo faſtigio per duas ſtationes dimetiri, vt problemate 4. oſtenſum eſt. Sit enim
vallis inter duosmontes AB, FG, poſita, & terminus ipſius C, ex monte AB,
poſsit conſpici. Ere cta haſta aliqua AE, fiantin D, & E, duæ ſtationes, obſer-
uenturque anguli D, & E, inſpecto termino C, per radios DC, EC. Intelliga-
tur autem recta EA, vſque ad baſem montis extenſa in B: & recta excurrens
AF, ipſi BG, parallela, vel ad EB, perpendicularis: & denique CH ipſi AB, pa-
rallela, quæ altitudini AB, ęqualis erit, ita vt AB, vel HC, ſit profunditas 1134. primi. lis ab A, vſque ad baſem montis, & IC, eius deſcenſus obliquus. Liquidò au-
47[Figure 47] tem eonſtat, profunditatem AB, vel CH, exquiri poſſe, vt problemate 4. alti-
tudo turris AB, ex duabus ſtationibus in haſta AE, factis, vel in duabus fe-
neſtris, vel certè, vtin præcedenti problemate profunditas putei AB, inuen-
tafuit.
Descensvs autem obliquus IC, ita notus euadet.
Quoniam, vt in ante-
cedente problemate monſtratum eſt, angulus DCE, differentia eſt angulorum
BDC, BEC, obſeruatorum: ſi 2210. Triang.
rectil.33
Vt ſin{us} anguli D C E, \\ differentiæ inter angu- \\ losobſeruatos # ad D E, differen- \\ tiam ſtationum \\ oculorum: # ita ſin{us} anguli \\ E, minoris ob- \\ ſeruati # ad DC,
cognita fiet recta DC, ex qua ſi detrahatur DI, (quam facilè ab oculo vſque
cedente problemate monſtratum eſt, angulus DCE, differentia eſt angulorum
BDC, BEC, obſeruatorum: ſi 2210. Triang.
rectil.33
Vt ſin{us} anguli D C E, \\ differentiæ inter angu- \\ losobſeruatos # ad D E, differen- \\ tiam ſtationum \\ oculorum: # ita ſin{us} anguli \\ E, minoris ob- \\ ſeruati # ad DC,
cognita fiet recta DC, ex qua ſi detrahatur DI, (quam facilè ab oculo vſque