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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104	74
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113	83
114	84
115	85
116	86
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126	96
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Scan	Original
101	71
102	72
103	73
104	74
105	75
106	76
107	77
108	78
109	79
110	80
111	81
112	82
113	83
114	84
115	85
116	86
117	87
118	88
119	89
120	90
121	91
122	92
123	93
124	96
125	95
126	96
127	97
128	98
129	99
130	100

Scan	Original
101	71
102	72
103	73
104	74
105	75
106	76
107	77
108	78
109	79
110	80
111	81
112	82
113	83
114	84
115	85
116	86
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118	88
119	89
120	90
121	91
122	92
123	93
124	96
125	95
126	96
127	97
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129	99
130	100