Clavius, Christoph - Geometria practica

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8353LIBER SECVNDVS.

prodibit diſtantia D F, quæſita, ſiue A B, in eadem menſura differentiæ ſtatio-
num: cui ſi adij ciatur differentia ſtationum E D, cognita etiam fiet diſtantia E F;
vel C B, à remotiori ſtatione.

ALITER

2. Posito ſinu toto G F, erit D F, Tangens anguli D G F, complementi
anguli obſeruationis G D F. quem angulum D G F, in dicat arcus Quadrantis IK,
1129. primi. à perpendiculo verſus oculum, cum angulus D H I, æqualis ſit angulo D G F, externus interno. Eodem modo E F, Tangens erit anguli E G F, complementi
alterius anguli obſeruationis GEF. At ED, differentia inter eas Tangentes exi-
ſtet. Si igitur fiat,

22
vt E D, differentia \\ inter Tangent{es} \\ angulorũ, qui cõ- \\ plemẽta ſunt angu- \\ lorũ obſeruationũ, # ad D F, Tangentem com- \\ plementi anguli obſerua- \\ tionis G D F, in propin- \\ quiore ſtatione, hoc eſt, ad \\ Tangentem minorem: # Ita E D, diffe- \\ rentia ſtatio- \\ num nota in \\ aliqua men- \\ ſura vulgari. # ad aliud \\ hoc eſt, \\ ad DF,
33Diſtantiæ in-
uentio alia
per tangen-
tes.

procreabitur diſtantia minor quæſita DF, vel A B, in eadem menſura differentiæ
ſtationum: cui ſi addatur differentia ſtationum E D, nota quo que fiet diſtantia
maior E F.

444. ſexti.55
#### 3. Rurſus ſi fiat, Vt D N, ſi- \\ n{us} tot{us} # ad N O, Tangentem anguli \\ G D F, in propinquiore ſtatione: # Ita D F, diſtantia \\ inuenta minor # ad aliud, hoc \\ eſt, ad F G;

@ Inuenietur altitudo F G, in menſura diſtantiæ inuentæ D F; minoris, cui ſi ad-
66Altitudinis in
uentio per tã-
gent{es}. datur menſ@ris ſtatura F B, cognita erit tota altitudo B G. Item ſi fiat,

77
Vt E M, ſi- \\ n{us} tot{us} # ad M H, tangentem anguli G E F, \\ in remotiore ſtatione: # ita E F, diſtantia \\ inuenta maior # ad aliud, hoc \\ est, ad FG,
884. ſexti.

reperietur eadem altitudo F G, in menſura diſtantiæ inuentæ E F, maioris, cui ſi
99Altitudinis
inuentio alia
per tangent{es}. addatur ſtatura menſoris FB, nota fiet tota altitudo B G.

ALITER

4. Si per ſolos ſinus idem expedire lubeat, erit operatio aliquando longior.
Primum enim inuenienda eſt vtra que hypotenuſa E G, D G, in aliqua menſura
nota, hoc modo. Quoniam angulus G D F, æqualis eſt duobus angulis 101032. primi. EGD: ſi angulus E, in remotiore ſtatione obſeruatus dematur ex angulo GDF,
in propinquiore ſtatione deprehenſo, reliquus fiet angulus EGD, differentia ni-
miruminter duosangulos obſeruationum. Quod ſi fiat,

111110. Triang.
rectil.1212
Vt ſin{us} anguli E G D, \\ differentiæ inter an- \\ gulos duos obſeruatio- \\ num # ad E D dif- \\ ferentiam \\ ſtationum \\ notam: # Ita ſin{us} anguli D E G, \\ vel. Ita ſin{us} anguli \\ E D G, cõplementian- \\ guli G D F, ad duos rectos, # ad D G, \\ vel \\ ad E G,

pro ducetur tam D G, quam E G, nota in partibus differentiæ ſtationum. Igi-
1313Inuentio Hy-
potenuſarum. tur ſi fiat,

1414
Vt ſin{us} to- \\ t{us} anguli \\ recti F, # ad hypoten@- \\ ſam D G, \\ proxime inuentam # Ita ſin{us} anguli D G F, complementi anguli ob- \\ ſeruationis in propinquiore ſtatione # ad D F,
151510. triang re-
ctil.

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Scan	Original
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
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101	71
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103	73
104	74
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106	76
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109	79
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Scan	Original
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
101	71
102	72
103	73
104	74
105	75
106	76
107	77
108	78
109	79
110	80