Clavius, Christoph - Geometria practica

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10979LIBER SECVNDVS.

DISTANTIAM accliuem montis à loco menſoris vſque ad baſem
altitudinis monti impoſitæ, etiam non viſam, vna cumipſa altitudine,
quando menſor in aſcenſu montis conſiſtit, prope verum efficere
cognitam, beneficio Quadrantis.

PROBLEMA XXII.

45[Figure 45]

1. Sit turris AB, monti impoſita,
in cuius aſcenſu ſeu latere menſor con-
ſiſtat in C, ex quo loco baſem turris
11In figura duc
rectam F A. videre non poſsit. Erigatur haſta aliqua
C G, ad Horizontem, non autem ad la-
tus montis perpendicularis, ſitque men-
ſoris ſtatura CE. Cogitetur ducta E K,
ad altitudinem perpendicularis: Et in-
ſpecto cacumine A, per angulum A EK,
fiat alia ſtatio ſuperior in F, ductaque
FI, ad altitu dinem perpendiculari, inſpi-
ciatur idem cacumen A, per angulum
2232. primi. A F I, Et quia angulus A F G, duobus angulis FEA, FAE, eſt æqualis: ſi dema-
tur A EF, complementum maioris anguli
A EK, in prima ſtatione obſeruati, reli-
3310. triang.
rectil. quus fiet angulus EAF, Igitur ſi fiat,

44
Vt ſin{us} anguli \\ EAF, differen- \\ tiæ complemen- \\ torũ angulorũ \\ obſeruationum # ad EF, diffe- \\ rentiam ſta- \\ tionum: # Ita ſin{us} anguli AFE, confta- \\ ti ex recto E F I, & minore \\ angulo AFI, in ſeounda ſta- \\ tione obſeruati, # ad A E \\ hypote- \\ nuſam.

efficietur nota hypotenuſa AE. Poſt hæc erigatur alius baculus DH, ad Hori-
zontem rectus, ſumptaque menſoris ſtatura DH, ipſi CE, æquali, & ducta recta
HL, ad altitudinem perpendiculari, inſpiciatur punctum E, per angulum EHL,
& perradium HEM, quiipſi BCD, lateri montis parallelus erit. 5533: primi. enim ſunt tria puncta B, C, D, in vna recta iacere, ac ſi DC, producta ad baſem
turris perueniret. Quia verò angulus EHL, angulo MEK, æqualis eſt: ſi hic 6629. primi. maiori angulo obſeruato AEN, inprima ſtatione dematur, reliquus fiet angulus
AEM. Eſt autem & angulus EAN, cognitus, quippe cum ſit complementum
maioris anguli obſeruati AEN. Igitur & AME, reliquus duorum rectorum cog-
nitus erit: qui quidem etiam relinquitur, ſi complementum anguli M HL, in
ſtatione D, obſeruati ex duobusrectis detrahatur. Igitur ſi fiat,

7710. triang.
rectil.88
Vtſin{us} anguli A M E, qui \\ velinquitur, ſicomplemen- \\ tum poſtremi anguli obſer- \\ uati MHL, ex duob{us} re- \\ ctis dematur # ad hypotenu- \\ ſam A E, \\ nuper inuẽ- \\ tam: # Ita ſin{us} anguli, \\ E A N, comple- \\ mẽti maioris an- \\ guli obſeruati AEN # ad M E,

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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
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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
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