Clavius, Christoph - Geometria practica

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9161LIBER SECVNDVS. rentiam ſtationum, vt eſt P Q, Tangens maior ad diſtantiam N L, vt paulo an-
te oſtenſum eſt, facilius demonſtrabimus, ſi ducatur recta I T, quæ producta
ſecet N L, in S. Nam in triangulis IP T, K O R, duo latera IP, P T, duobus la-
teribus KO, OR, æqualia ſunt, angulo ſque continent æquales, vtp ote rectos.
Igitur anguli T, R, ęquales ſunt; ideo que KL, IS, parallelæ. Et quia 114. primi. I K, æqualis eſt & ipſi SL, & differentiæ ſtationum HG, vel NM, liquido 2228. primi. ſtat, ita eſſe T Q, differentiam Tangentium ad S L, quæ differentię ſtationum
3334. primi. I K, vel H G, æqualis eſt, vt eſt P Q, Tangens maior ad diſtantiam NL,

44ſchol. 4.
ſext.

ALITER.

3. Per ſolos ſinus ita Problema efficiemus. Primum inquiremus hypote-
5532. primi. nuſas I L, K L, hoc modo. Quoniam angulus L K V, duobus angulis L I K, I L K, æqualis eſt; ſi L I K, angulus complementi maioris anguli obſeruationis
L I N, auferatur ex L K V, angulo complementi minoris anguli obſeruationis
L K M, reliquus fiet angulus I K L. Si ergo fiat.

6610. triang.
rectil.77
Vt ſin{us} anguli I K L, dif- \\ ferentiæ inter duos an- \\ gulos complementorum \\ angulorum obſeruatio- \\ num # ad I K, \\ differẽ- \\ tiam \\ ſtatio- \\ num: # Ita ſin{us} anguli I K L, conflati ex \\ recto, & angulo obſeruationis \\ minore, vel # ad I L,
# # Ita ſin{us} anguli LIK, complemen- \\ ti maioris anguli obſeruationis. # ad K L,
88Hypotenu-
ſarum inuẽ-
tio.

euadet nota tam I L, quam K L, in menſura differentiæ ſtationum. Igitur ſi fiat,

9910. triang.
rectil.1010
Vt ſin{us} tot{us} \\ angulire- \\ cti N, # ad Hypotenuſam \\ proxime inuen- \\ tam I L, # Ita ſin{us} anguli I L N, complementi \\ maioris anguli obſeruationis # ad I N,
#### Vel
Vt ſin{us} tot{us} an- \\ guli recti M, # ad hypotenuſam K L, \\ nuper inuentam: # Ita ſin{us} anguli K L M, complemen- \\ ti minoris anguli obſeruationis # ad \\ K M,
1111Altitudinis
inuentio per
ſolos ſinus.

cognita fiet altitudò I N, vel KM, ex qua ſi dematur ſtatura menſoris, altitudo
quæſita relinquetur H N, vel G M, hoc eſt, E F.

Distantia autem vtraque N L, M L, reperietur, ſi fiat.

121210. triang.
rectil.1313Diſtantiæ in-
uentio per
ſolos ſinus.1414
Vt ſin{us} tot{us} \\ anguli recti \\ N, vel M, # ad Hypotenuſam \\ inuentam I L, \\ vel K L, # Ita ſin{us} anguli maioris ob- \\ ſeruati NIL, vel \\ ad N L, diſtan- \\ tiam
# # Ita ſin{us} anguli minoris ob- \\ ſeruati M K L, # ad M L, diſtan- \\

Sine numeris eædem rectæ IN, N L, IL, K L, & c. reperientur, vt in ſupe-
1515Quo pacto
problema
conficiatur ſi-
ne numeris. rioribus: ſi nimirum (vtemur figura huius problematis, ne nouam conſtruere
cogamur) ſumptarecta IK, tot partium, quot palmi, pedeſuein differentia ſta-
tionum exiſtunt, fiant anguli VKL, VIL, complementorum angulorum MKL,
NIL, obſeruationum, & concurſus L, notetur, ex quo ducatur LN, ipſi IK, pa-
rallela, & ad hanc perpendicularis in I, excitetur IN, & c. Vel ſi angulus rectus
conſtituatur INL, & in aſſumpto puncto L, vbi concurſum eſſe volumus,

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Scan	Original
91	61
92	62
93	63
94	64
95	65
96	68
97	67
98	68
99	69
100	70
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

Scan	Original
91	61
92	62
93	63
94	64
95	65
96	68
97	67
98	68
99	69
100	70
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