Clavius, Christoph - Geometria practica

Clavius, Christoph, Geometria practica

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9668GEOMETR. PRACT. nor B, à maiori ADF, differt, ad BD, differentiam ſtationum: ita ſinus anguli B,
in remotiori ſtatione. ad D A.

2. Distantia verò à puncto A, ad pedem menſoris C, hoc eſt, recta AC,
cognoſcetur per Problema 12. triang. rectil. cap. 3. lib. 1. cum in triangulo obli-
quangulo ABC, duo latera AB, BC, nota ſint, nimirum diſtantia inuenta, & ſta-
tura menſoris, comprehendantque angulum ABC, notum, vtpote conflatum
ex recto CBD, & angulo obſeruationis ABD.

3. Sit deinde punctum A, vt in muro HI, infra oculum B. Inſpecto pun-
cto A, obſeruetur angulus CBA. quem latus pinnacidiorum cum perpendiculi
filo, vel dio ptræ linea fiduciæ cum BC, facit: Deinde accede verſus A. vſque ad
D, & iterum conſidera angulum EDA: exiſtentque rectæ AB, AD BD, BC, DE,
in vno eodemque plano, in eo videlicet, quod per ſta-

29[Figure 29] turas menſoris BC, DE, & per punctum A, ducitur.
Et quoniam angulus FDA, complementi anguli 1132. primi. ſeruationis in propinquiore ſtatione æqualis eſt duo-
bus DBA, DAB; ſi DBA, angulus complementi an-
guli remotioris ſtationis dematur ex angulo A D F,
complementi anguli ſtationis propinquioris, reliquus
fiet notus BAD. Si ergo fiat,

2210. Triang.
rectil.33
Vt ſinus anguli BAD, dif- \\ ferentiæ inter angulos com \\ plementorum angulorum \\ obſeruationum # ad B D, diffe- \\ rentiam ſta- \\ tionum: # Ita ſinus anguli ADB, con- \\ flati ex recto B D E, & \\ ex angulo obſeruationis \\ A D E, in propinquiore \\ ſtatione # ad AB di- \\ ſtantiam \\ quæſitã.

cognita erit diſtantia A B, quam quærimus, in partibus differentiæ ſtatio-
num B D.

Qvod ſi oculus ponatur in D, & recedatur à puncto D, vſque ad B, repe-
rietur eodem modo diſtantia DA, ſi pro angulo BDA, aſſumes angulum DBA,
complementianguli ABC, obſeruationis in remotiore ſtatione, vt manifeſtum
eſt. Nam eſt, vt ſinus anguli BAD, differentiæ inter angulos 4410. Triang.
rectil. rum angulorum obſeruationum, ad BD, differentiam ſtationum: ita ſinus angu-
li DBA, complementi anguli ABC, in remotiore ſtatione, ad DA.

4. Vt autem diſtantia CA, à pede ad punctum A, inueniatur, ita progredie-
mur. Quoniam in triangulo rectangulo ABG, (ſi ex puncto A, concipiatur
ducta ad BC, ſtaturam menſoris perpendicularis AG,) baſis AB, nota eſt per in-
uentionem, & angulus BAG, notus, quippe cum ſit complementum anguli
obſeruationis ABG; Si fiat,

552. Triang.
rectil.66
Vt ſinus \\ totus # ad baſem A B, proximè \\ inuentam: # Ita ſinus anguli B A G, complemen- \\ ti anguli obſeruationis, # ad B G,

cognoſcetur BG, in partibus baſis AB, hoc eſt, in partibus differentiæ ſtationum
BD, in quibus AB, inuenta fuit. Ablata autem BG, ex menſoris ſtatura BC, no-
ta fiet reliqua CG. Item ſi fiat,

772. Triang.
rectil.88
Vt ſinus to- \\ tus # ad baſem A B, nu- \\ per inuentam: # Ita ſinus anguli obſeruatio- \\ nis A B G, # ad A G,

nota etiam fiet A G, in partibus eiuſdem baſis A B, vel differentiæ

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