Full text: Clavius, Christoph: Geometria practica

inuenta erit altitudo F A, in partibus differentiæ ſtationum, cuiſi adij ciatur F B,
ſtatura menſoris, tota altitudo AB, nota euadet.

53.1.

Altitudinis
inuentio per
Tangent{es}.

54. 2. ITEM ſi fiat.

Vt G M, differentia Tangen- \\ tium complementorum an- \\ gulorum obſeruationum. # ad G E, diffe- \\ rentiam ſta- \\ tionum: # ita G L, Tangens \\ complementi angu- \\ li obſeruationis in \\ remotiori ſtatione # ad \\ G F,

effi cietur nota G F, diſtantia maior, quando quidem paulo ante demonſtratum
eſt, eſſe GM, ad GE, vt GL, ad GF. Quod ſi ex GF, inuenta detrahatur GE, dif-
ferentia ſtationum, nota relinquetur EF, diſtantia minor.

54.1.

Diſtantiæ in-
uentio.

55. ALITER.

3. Si per ſolos ſinus dimenſio inſtituatur, inueſtiganda primum erit alteru-
tra hypotenuſarum GA, EA, vel vtraque. hoc ſcilicet modo. Quoniam an- gulus A E F, duobus G, G A E, æqualis eſt, ſi angulus G, in remotiore ſtatione
tollatur ex angulo AEF, in ſtatione propinquiore, reliquus fiet angulus GAE,
differentia inter duos angulos G, AEF obſeruationum.

55.1.

32. primi.

56. Ergo ſi fiat,

10. triang.
rectil.
Vt ſin{us} anguli G A E, \\ differentiæ inter duos \\ angulos obſeruationum # ad G E, dif- \\ ferentiam \\ ſtationum: # ita ſin{us} anguli A G E, \\ vel \\ it a ſin{us}( [?] anguli G E A, \\ complementi) [?] anguli \\ A E F, ad duosrectos. # ad AE, \\ ad G A,
Hypotenuſa-
rum inuentio.

nota fiet tam A E, quam A G, in partibus differentiæ ſtationum.

57. Si igitur fiat.

10. triang.
rectil.
Vt ſin{us} to- \\ t{us} anguli \\ recti F, # ad rectam \\ E A: \\ vel \\ ad rectam \\ G A, proxi- \\ mè inuentam # ita ſin{us} anguli AEF, in pro- \\ pinquiore ſtatione, \\ vel \\ ita ſin{us} anguli A G F, in re- \\ motiore ſtatione # ad A F, \\ ad A F,
Altitudinis
inuentio per
ſolos ſin{us}.

gignetur altitudo A F, & ſi adiungetur F B, ſtatura menſoris, tota altitudo AB,
efficietur nota.

Distantia autem vtraque E F, G F, per ſolos etiam ſinus inuenietur, ſi fiat.

57.1.

10. triang.
rectil.
Vt ſin{us} \\ tot{us} an- \\ guli recti \\ F. # ad hypotenu- \\ ſam E A. \\ vel \\ ad hypotenu- \\ ſam G A: # ita ſin{us} anguli E A F, complementi \\ anguli in propinquiore ſtatione, \\ vel \\ ita ſin{us} anguli G A F, complementi \\ anguli in remotiore ſtatione. # ad E F.
Diſtantiæ in-
uẽtis per ſo-
los ſinus.
088-01

4. Sine numerorum multiplicatione ac diui-
ſione eadem inueſtigabuntur, ſi illi figuræ, quam ab
oculo menſoris ad altitu dinem vſque concepimus
eſſe conſtruendam, ſimilem omni diligentia conſti-
tuamus, vt Num. 6. & 8. præcedentis problematis 1.

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