Clavius, Christoph - Geometria practica

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10070GEOMETR. PRACT. 5. dictum eſt. Deinde per Quadrantem cum dioptra angulus C E D, exquiren-
dus in plano Horizontis. quod fiet, ſi Quadrantis

33[Figure 33] planum erectum tranſeat ſemel per puncta E, C, &
iterum per puncta E, D, vt deſignari poſsint partes
rectarum E C, E D. Quadrantis enim vno latere in-
cumbente rectæ E C, dioptra vero rectæ E D, ſi an-
gulus eſt acutus, indicabit arcus inter illud latus, ac
dioptram, angulum C E D. Quod ſi alterum Qua-
drantis latus rectæ ED, congruet erit angulus CED rectus: Si vero recta ED. vl-
tra alterum latus Quadrantis extiterit, dictus angulus obtuſus erit, qui cogni-
tus erit, ſi recto angulo ad datur reliquus inter alterum latus, & rectam ED: Qui
quidem reliquus angulus per Quadrantem explorabitur vt de acuto diximus in
problemate 7. Atq; ita habebimus triangulum ECD, cuius duo latera nota ſunt
EC, E D, angulumq; notum comprehendunt C E D. Igitur, & 1112. triang.
rectil. C D, cognitum erit.

2. Qvo pacto autem ſine ope numerorum problema perſiciendum ſit, tra-
ditum eſt in problemate 7. Num. 2.

LONGITVDINEM in Horizonte inter turrim aliquam, & aliud
quodpiam ſignum, ex turri per duas ſtationes in faſtigio factas: vel in
duabus feneſtris, quarum vna ſit ſub altera ad perpendiculum, quan-
do ſpatium inter illas feneſtras notum eſt, etiamſi totius turris altitu-
do ignota ſit, demetiri. Atque hinc obiter altitudinem turris patefa-
cere.

PROBLEMA XI.

1. Qvamvis problema hoc ſolutum iam ſit in

34[Figure 34] problemate 3. & 4. occaſione altitu dinis inquirendæ,
libet tamen idem hic per ſe, & paulo aliter expedire.
Sit ergo turris A B CD, & longitudo propoſita C E:
ſtatura autem menſoris B G, vel AF. Inſpecto extre-
mo E, in prima ſtatione per angulum C G E, & in ſe-
cũda per angulum DFE, ducatur FH, ipſi G E, paral-
lela. Et quia in triangulis F D H, G C E, anguli D, C,
2229. primi. recti ſunt, & H, E, æquales latuſque FD, lateri GC. 3334. primi. æquale: erunt quo que & anguli G, DFH, 4426. primi.& latera D H, C E. Poſito autem ſinu toto F D, erit
DE, Tangens maioris anguli obſeruationis D F E, &
D H, Tangens anguli D F H, hoc eſt, anguli æqualis
G, in prima ſtatione obſeruati: ac proinde H E, differentia erit earum Tangen-
tium, quæ quidem æqualis eſt differentiæ ſtationum F G, vel AB, vel DC. 5534. primi. igitur fiat,

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Vt H E, differentia Tan- \\ gentium angulorumob- \\ ſeruationum # Ad CE, Tangentem \\ min@ris anguli ob- \\ ſeruationis CGE. # Ita HE, vel FG, \\ differentia ſtatio- \\ num # ad G E, \\ longitu- \\ dinem, \\ gigne-

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Scan	Original
121	91
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125	95
126	96
127	97
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133	103
134	104
135	105
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Scan	Original
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126	96
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