Clavius, Christoph - Geometria practica

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10474GEOMETR. PRACT.11
Vt ſin{us} anguli A D L, \\ differentiæ inter an- \\ gulos obſeruationum \\ ADM, LDM, # ad A L, hoc \\ eſt, ad D E, \\ differentiam \\ ſtationum: # Ita ſin{us} anguli ALD, qui \\ relinquitur, ſi DLM, comple- \\ mentum minoris anguli \\ L D M, obſeruati ex duob{us} \\ rectis ſubtrahatur, # ad AD.

Nam productus numerus offeret hypotenuſam AD. Si ergo rurſus fiat,

2210. triang.
rectil.33
Vt ſin{us} tot{us} an- \\ guli recti M, # ad hypotenuſam \\ AD, inuentam: # Ita ſin{us} maioris anguli \\ obſer uationis ADM, # ad AM,
4410. triang.
rectil.

procreabitur altitudo A M, & c. Siautem fiat,

55
Vt ſin{us} to- \\ t{us} anguli \\ recti M, # ad hypotenuſam AD, \\ proxime inuentam, # Ita ſin{us} anguli D A M, \\ complementi maioris an- \\ guli obſeruationis, # ad DM,

effi cietur diſtantia D M, cognita.

3. Si ſine numeris problema ſoluen dum eſt, recurrendum erit ad ſuperiora,
præſertim ad Num. 6. 8. & 7. problematis 1.

ALTITVDINEM maiorem ex minori cognita, per duas ſtationes
in ſummitate, vel in duabus feneſtris factas, etiamſi ſolum maioris alti-
tudinis vertex cernatur, per Quadrantem adinuenire. Atque hinc
diſtantiam quoque inter altitudines colligere.

40[Figure 40]

PROBLEMA XVI.

1. Maior altitudo ſit AN, minor tur-
ris C O, cognita, ex qua ſolum cacumen
A, non autem baſis N, appareat. Fiantin
ſummitate duæ ſtationes in C, D, menſo-
ris que ſtatura ſit C G, vel D E, & ad A N,
intelligatur ducta perpendicularis G E F.
Atque inſpecto cacumine A, obſeruentur
anguli A E F, AGF. Reliqua fiant, vt in 2.
problemate. Si ergo fiat, ſicut in eo pro-
blemate demonſtrauimus,

66
Vt GM, differentia Tangentium GL, EK, angu- \\ lorum H, I, qui complementa ſunt angulorũ ob- \\ ſeruationum, poſitis ſinub{us} totis HL, IK, # ad GE, diffe- \\ rentiam ſta- \\ tionum: # Ita LH, ſi- \\ n{us} tot{us} # ad FA.

Inuenietur altitudo A F, cuiſi adijciatur F N, conflata ex altitudine turris C O,
& ſtatura menſoris, tota maior altitudo AN, nota euadet. Item ſi fiat,

77
Vt GM, differentiæ Tan- \\ gentium earundem. # ad GE, differenti- \\ am ſtationum: # Ita GL, Tangens complementi \\ minoris anguli obſeruationis # ad GF,

pro creabitur diſtantia GF, à qua ſi dematur latitudo turris C O, reliqua erit di-
ſtantia inter duas turres.

Hæc omnia in 2. problemate demonſtrauimus: & ob hanc cauſam eiſdem
prorſus literis hic vſi ſumus, quas ibivſurpauimus, vt demonſtratio ex illo loco
in hunc transferri poſsit.

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86	56
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89	59
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91	61
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94	64
95	65
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