Clavius, Christoph - Geometria practica

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150120GEOMETR. PRACT.

cognita erit diſtantia F G, quæſita in partibus turris notæ.

Si autem vmbra verſa ſecetur in E, & fiat,

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Vt vmbra verſa \\ D E, # ad latus D A, par- \\ tium 1000. # Ita A F, altitudo turris co- \\ gnita # ad F G,

efficietur quo que nota eadem diſtantia F G, in partibus turris cognitæ.

2. Per quadratum ſtabile eandem quo que diſtantiam adipiſceris. Site-
nim rurſus turris quæpiam D E, & diſtantia metienda E G, vel E H, vel E F. Si
igitur dio ptra ſecet latus vmbræ rectæ in I. Et fiat,

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Vt latus quadrati \\ AD, 1000. # ad vmbram \\ rectam D I: # Ita altitudo A E, ex turre & la- \\ tere quadrati A D, conflata. # ad E G,

78[Figure 78]

prodibit diſtantia quæſita E G.

Si autem dioptra per C. tranſeat, erit
diſtantia E H, altitudini A E, notæ æqua-
lis.

Si denique vmbra verſa interſecetur
in K; fiat autem,

33
Vt vmbra verſa \\ B K, # ad latus quadrati \\ 1000. # Ita altitudo nota A E, # ad E F,

inuenietur diſtantia EF, in partibus altitudinis A E,

Hæc enim omnia in 2. problem. Num. 1. & 2. demonſtrata ſunt.

3. Qvod ſi altitudo turris cognita non ſit, inueſtiganda ea primum erit per
problema 8. vel 9. vel potius per ſcholium problem. 9. aut certe, ſi commode
fieri poſsit, per chordam aliquam cum appenſo perpendiculo demiſſam explo-
randa. Deinde procedendum erit, vt Num 1. & 2. dictum eſt.

Vervm ſine cognitione turris idem aſſequemur ea ratione, quain problem.
6. vel 7. altitudinem propoſitam indagauimus, etiamſi diſtantia vſque ad alti-
tudinem ſit ignota. Nam ſi in 6. problemate turris ſit d f, diſtantia autem me-
tien da FG, effi ciemus illud, ſi in haſta aliqua erecta d A, fiant duæ ſtationes o-
culi, in a A. Solum quod ibi dictum eſt de vmbra verſa, hic de recta intelligatur,
& contra.

Pari ratione, ſi in 7. problemate turris ſit d F, & diſtantia metienda F G,
inueniemus eam, ſi in plano ſummitatis turris fiant duæ ſtationes oculi in A, a.
Solum quod ibi dicitur de vmbra verſa, hic etiam de recta intelligatur. Nam ſi
figuræ problem. 6. & 7. hoc eſt, figuræ problem. 3. & 4. inuertantur, vt altitu-
dines fiant A F, A F, latus quadrati D C, ad vmbram rectam, & B C, ad verſam
pertinebit, vt initio huius libri in conſtru ctione quadrati Num. 4. explicauimus.

Sed hanc diſtantiam longè facilius in ſcholio præcedentis problematis in-
uenimus per vnicam ſtationem, vt patuit in diſtantia EF, & c.

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Scan	Original
121	91
122	92
123	93
124	96
125	95
126	96
127	97
128	98
129	99
130	100
131	101
132	102
133	103
134	104
135	105
136	106
137	107
138	108
139	109
140	110
141	111
142	112
143	113
144	114
145	115
146	116
147	117
148	118
149	119
150	120

Scan	Original
121	91
122	92
123	93
124	96
125	95
126	96
127	97
128	98
129	99
130	100
131	101
132	102
133	103
134	104
135	105
136	106
137	107
138	108
139	109
140	110
141	111
142	112
143	113
144	114
145	115
146	116
147	117
148	118
149	119
150	120