Clavius, Christoph - Geometria practica

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9767LIBER SECVNDVS. BD. Quia ergo in triangulo rectangulo ACG, duo latera AG, GC, per inuen-
tionem nota fa cta ſunt; cognoſcetur quoq; baſis AC, quod eſt propoſitum.

113. triang.
rectil.

5. Manifestvm autem eſt, eodem pacto vtramque diſtantiam AB, AC,
reperiri, etiamſi punctum A, in plano ſit, in quo menſor conſiſtit, nimirum in
Horizonte, qui ponatur tranſire per rectam AG, ita vt ſtatura menſoris ſit B G,
Immo tunc per vnicam ſtationem vtraque diſtantia AB, AG, rep erietur. Nam
poſito ſinu toto B G, ſtatura menſoris; A B, ſecans eſt anguli obſeruationis
ABG, & AG, Tangens. Quo circa ſi fiat,

22
Vt BG, ſinus \\ totus # ad B A, ſecantem anguli obſer- \\ @ationis A B G, # Ita BG, ſtatura \\ menſoris # ad B A,
#### Vel
# ad GA, Tangentem anguli ob- \\ ſeruationis A B G: # # ad G A,

vtraque diſtantia & BA, ab oculo B, & G A, à G, pede menſoris cognita fiet.

6. Iam verò ſine numeris operabimur, vt in præcedentibus, vt manifeſtum
33Quo pacto ꝓ-
blema ſine nu-
meris ſit ſol-
uendum. eſt, ſi rectè figura conſtruatur, quemadmodum Num. 6. & 8. problematis 1. di-
ctum eſt.

INTER VALLVM inter duo puncta in quolibet plano eleuato, ſiuc
illud ad Horizontem rectum ſit, ſiue inclinatum, metiri.

PROBLEMA VII.

1. In plano quolibet eleuato AB. prop oſitum ſit interuallum CD, quod
ex plano EB, inueſtigandum ſit. Poſito oculo in G, vt ſtatura menſoris ſit, GE,
inueſtiget ur per præcedens problema 6. vtraque diſtantia G C, G D, in parti-
bus ſtaturæ menſoris G E, ſiue differentiæ

30[Figure 30] duarum ſtationum, è quibus ipſæ diſtan-
tiæ inueſtigantur. Deinde applicato Qua-
drante ſtabili ad oculum G, ita vt eius pla-
num per puncta CD, tranſeat, & vna eius
ſemidiameter ad punctum D, vergat,
(quod fiet, ſi poſita linea fiduciæ dioptræ
ſupra illam ſemidiametrum, punctum D,
per foramina pinnacidiorum conſpicia-
tur) vertatur dioptra, donec per eam punctum C, appareat, arcuſque in-
ter dictam ſemidiametrum, & lineam fiduciæ interceptus notetur. hic enim
angulum G, metietur. Quod ſi altera ſemidiameter Quadrantis vltra re-
ctam G C, exiſtat, erit angulus acutus C G D: Si verò altera illa ſemidia-
meter citra rectam G C, extiterit, dictus angulus erit obtuſus, qui cogno-
ſcetur, ſi ad rectum adiiciatur reliquus angulus inter alteram illam ſemidia-
metrum, & rectam G C; quem quidem reliquum inueſtigabimus per
Quadrantem, vt de acuto C G D, diximus, ſi videlicet in recta C D,
mente notemus punctum, in quod altera illa ſemidiameter incurre-
ret producta. Si namque tunc ſemidiameter illa rectæ G C,

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92	62
93	63
94	64
95	65
96	68
97	67
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100	70
101	71
102	72
103	73
104	74
105	75
106	76
107	77
108	78
109	79
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111	81
112	82
113	83
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116	86
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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