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
71	41
72	42
73	43
74	44
75	45
76	46
77	47
78	48
79	49
80	50
81	51
82	52
83	53
84	54
85	55
86	56
87	57
88	58
89	59
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91	61
92	62
93	63
94	64
95	65
96	68
97	67
98	68
99	69
100	70

Scan	Original
71	41
72	42
73	43
74	44
75	45
76	46
77	47
78	48
79	49
80	50
81	51
82	52
83	53
84	54
85	55
86	56
87	57
88	58
89	59
90	60
91	61
92	62
93	63
94	64
95	65
96	68
97	67
98	68
99	69
100	70