Clavius, Christoph, Geometria practica

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8757LIBER SECVNDVS. ſeruationis GDF, & diſtantiam DF, quam per angulum obſeruationis GEF, &
diſtantiam
EF.
Vtroque enim modo inuenta eſt altitudo GF.
1. Sit inquirenda altitudo AB, ſiue ea turris ſit, ſiue mons, ſiue aliquid ali-
ud
, licetnon cernatur eius perpendiculi infimus terminus B, vt in omni monte
contingit
:
planum autem, cui perpendicularis eſt altitudo, ſit CB. Statura mẽ-
ſoris
D E.
Ducta autem cogitatione per E, ipſi CB, parallela GF, fiat prima ſta-
tio
in D, propinquior, ſecunda vero in G, remotior, vt differentia ſtationum ſit
GE
.
Deinde per radios viſuales EA, GA, ad verticem A, directos diligenter ob-
ſeruentur
anguli AEF, AGF, ſiue per quadrantem pendulum, vt Num.
1. pro-
blematis
præcedentis do cuimus, ſiue per ſtabilem, vt Num.
5. eiuſdem proble-
matis
præcepimus.
Eodem enim ſemper modo dicti anguli obſeruantur, quan-
do
è loco inferiori altitu dinis faſtigium inſpicitur.
Cogitetur quo que ducta HI,
23[Figure 23] ipſi G F, parallela, vt demiſſæ perpendiculares H L, I K, 2234. prim. parallelogrammo LI, ſint æquales, pro ſinubus totis:
quo-
rum
tangentes ſunt EK, GL, angulis, I, H, qui complemen-
ta
ſunt angulorum obſeruationum E, G, debitæ.
Et quo-
niam
angulus G A F, maior eſt angulo E A F, eſt que 3329. primi. angulus G H L, &
poſteriori angulus E I K, æqualis: erit
quo
que GHL, maior quam EIK, ideo que tãgens G L, ma-
ior
Tangente EK, quòd ſinus toti H L, I K, æquales ſint.
Ab-
ſcindatur
LM, ipſi EK, æqualis, vt GM, ſit differẽtia Tangẽ-
tium
G L, E K, Et quia eſt vt G L, ad L H, ita G F, ad F A, erit permutando, 444. ſexti. GL, ad GF, ita LH, vel IK, ad FA;
Vtautem IK, ad F A, ita quoque eſt EK, 554. ſexti &
permutando
EF.
Igitur erit, vttota GL, ad totam GF, ita EK, vel LM, ex GL, ablata, ad EF,
ex
GF, ablatam:
ac proinde erit etiam vt GM, ex GL, reliqua ad G E, ex G 6619. quinti reliquam, ita tota G L, ad totam G F, hoc eſt, ita L H, ſinus totus, a d F A. 774 ſexti &
permutando
.
Quamobrem ſi fiat.
88
Vt
G M, differentia Tangentium \\ G L, E K, complementorum an- \\ gulorum obſeruationum # ad G E, diffe- \\ rentiam ſt a- \\ tionum. # ita L H, \\ ſin{us} io- \\ t{us}. # ad FA,

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