Clavius, Christoph - Geometria practica

Clavius, Christoph, Geometria practica

Table of figures

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9565LIBER SECVNDVS.

2. Per ſolos ſinus eandem altitudinem G F, adipiſcemur, ſi prius hypote-
nuſam G D, venabimur, hoc modo. Fiat,

1110. triang.
rectil.22
Vt ſin{us} anguli D G E, diffe- \\ rentiæ angulorum obſer- \\ uationum # ad D E, ſpa- \\ tium cogni- \\ tum # Ita ſin{us} anguli E, com- \\ plementi maioris an- \\ guli obſeruationis # ad hypotenu- \\ ſam G D,

Numerus enim productus dabit hypotenuſam GD, in partibus ſpatii DE, no-
tam. Si ergo rurſus fiat,

3310. triang.
rectil.44
Vt ſin{us} tot{us} an- \\ guli recti F, # ad hypotenuſam \\ G D, proximè \\ inuentam: # Ita ſin{us} anguli D, comple- \\ menti minoris anguli ob- \\ ſeruationis # ad G F, altitu- \\ dinem,

producetur altitudo GF, in partibus hypotenuſæ GD, ſiue ſpatij DE, nota.

55Solutio pro-
blematis ſine
numeris.

3. Sine numeris agendum erit, vt in problemate 1. declaratum eſt.

DISTANTIAM ab oculo, vel pede menſoris ad quoduis punctum
in aliqua altitudine notatum, per duas ſtationes in plano factas me-
tiri.

1 Sit inqui@enda diſtantia puncti A, in muro G H, ſiue perpendiculari ad
Horizontem, ſiue inclinato, vel etiam in tecto quo piam; ab oculo B, vel pe-
de C, poſita ſtatura menſoris B C. Concipiatur ducta B D, ipſi plano C E, pa-
ſallela, ſitque primo punctum A, altius,

28[Figure 28] quam oculus B. Inſpecto puncto A, no-
tetur angulus ABD, quem latus pinnaci-
diorum in quadrante pendulo, vel linea
fiduciæ in dioptra Quadrantis ſtabilis
cum recta BD, facit. Deinde accede ver-
ſrus punctum A, quotlibet palmis aut pe-
dibus vſque ad D, vt BD, differentia ſta-
tionum nota ſit. Rurſumque ex D, pun-
ctum A, inſpiciatur, notato diligenter angulo ADF: exiſtentque rectæ AB, AD,
B D, B C, D E, in eodem plano, in eo videlicet, quod per ſtaturas menſoris B C,
D E, & per punctum A, ducitur, Et quia angulus A D F, duobus B, & B A 6632. primi. eſt æqualis: ſi angulus B, in remotiore ſtatione auferatur ex angulo D, in pro-
pinquiore, notus fiet reliquus angulus A. Siigitur fiat,

7710. triang.
rectil.88
Vt ſin{us} anguli \\ A, quo angu- \\ l{us} minor B, à \\ maiori differt, # ad B D, diffe- \\ rentiam ſta- \\ tionum: # Ita ſin{us} anguli A D B, qui comple- \\ mentum eſt maioris anguli D, ad \\ duos rectos, # ad A B, di- \\ ſtantiã quæ- \\ ſitam,

reperta erit quæſita diſtantia A B, in partibus differentiæ ſtationum.

Qvod ſi oculus exiſtat in D, & recedatur à puncto D, vſque ad B, inue-
nietur eadem arte diſtantia D A, ſi loco anguli A D B, ſumatur angulus B, in
9910. triang,
rectil. remotiore ſtatione, vt liquet. Eſt enim vt ſinus anguli A, quo angulus

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