Clavius, Christoph - Geometria practica

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137107LIBER TERTIVS. do diſtantia A F, minor eſt altitudine F G: eritque triangulum A B H, triangu-
lo AFG, æquiangulum, vt problemate 3. Num. 3. demonſtrauimus. Igitur erit,
vt BH, ad AB, ita AF, ad F G: ac proinde, ſi fiat,

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Vt vmbra \\ recta B H, # ad AB, lat{us} qua- \\ drati 1000. # Ita diſtantia AF, veldata, vel \\ inuenta per probl. 3. aut 4. # ad F G,

nota euadet FG, cuiſi addetur menſura vel ſtatura menſoris F L, efficietur nota
tota altitudo G L, propoſita.

ALTITVDINEM eandem, etiamſi eius diſtantia ab oculo menſo-
ris neque data ſit, neq; inuenta, per duas ſtationes in plano factas pa-
tefacere auxilio quadrati.

PROBLEMA VI.

1. Proposita ſit altitudo metienda FG, ſecluſa menſoris ſtatura FL. Fi-

65[Figure 65] ant duæ ſtationes, vt in problemate 3. cuius figura 1. hicrepetatur, ſeceturque
primum vmbra verſa in vtraque ſtatione in punctis E, H. Et quia propter ſimili-
tudinem triangulorum ADE, AFG, eſt vt DE, ad A D, ita F G, ad A F: ſi fiat,

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Vt D E, vmbra ver- \\ ſa abſciſſa # ad AD, lat{us} qua- \\ drati 1000. # Ita FG, quaten{us} 1. # ad A F.

hoc eſt, (cum 1. multiplicans latus quadrati 1000. producat idem latus 1000.)
ſi quadrati latus 1000. diuidatur per vmbram verſam D E, prodibit Quotiens
AF, indicans, quoties FG, in AF, contineatur. Eodem pacto ſi fiat,

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Vt vmbra verſa d H, # ad a d, lat{us} quadra, \\ ti 1000. # Ita F G, quaten{us} \\ 1. # ad a F,

hoc eſt, ſi quadrati latus 1000. diuidatur per vmbram verſam d H, gignetur
Quotiens a F, monſtrans, quoties FG, in a F, contineatur. Siigitur poſterior hic
Quotiens a F, ex priori Quotiente a F, detrahatur, relinquetur differentia A a,
cognita in partibus, quarum F G, eſt 1. Siergo fiat,

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Scan	Original
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
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157	127
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Scan	Original
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
151	121
152	122
153	123
154	124
155	125
156	126
157	127
158	128
159	129
160	130