Full text: Clavius, Christoph: Geometria practica

DISTANTIAM accliuem montis à loco menſoris vſque ad baſem
altitudinis monti impoſitæ, etiam non viſam, vna cumipſa altitudine,
quando menſor in aſcenſu montis conſiſtit, prope verum efficere
cognitam, beneficio Quadrantis.

92. PROBLEMA XXII.

109-01

1. Sit turris AB, monti impoſita,
in cuius aſcenſu ſeu latere menſor con-
ſiſtat in C, ex quo loco baſem turris
videre non poſsit. Erigatur haſta aliqua
C G, ad Horizontem, non autem ad la-
tus montis perpendicularis, ſitque men-
ſoris ſtatura CE. Cogitetur ducta E K,
ad altitudinem perpendicularis: Et in-
ſpecto cacumine A, per angulum A EK,
fiat alia ſtatio ſuperior in F, ductaque
FI, ad altitu dinem perpendiculari, inſpi-
ciatur idem cacumen A, per angulum
A F I, Et quia angulus A F G, duobus angulis FEA, FAE, eſt æqualis: ſi dema-
tur A EF, complementum maioris anguli
A EK, in prima ſtatione obſeruati, reli-
quus fiet angulus EAF, Igitur ſi fiat,

92.1.

In figura duc
rectam F A.
32. primi.
10. triang.
rectil.
Vt ſin{us} anguli \\ EAF, differen- \\ tiæ complemen- \\ torũ angulorũ \\ obſeruationum # ad EF, diffe- \\ rentiam ſta- \\ tionum: # Ita ſin{us} anguli AFE, confta- \\ ti ex recto E F I, & minore \\ angulo AFI, in ſeounda ſta- \\ tione obſeruati, # ad A E \\ hypote- \\ nuſam.

efficietur nota hypotenuſa AE. Poſt hæc erigatur alius baculus DH, ad Hori-
zontem rectus, ſumptaque menſoris ſtatura DH, ipſi CE, æquali, & ducta recta
HL, ad altitudinem perpendiculari, inſpiciatur punctum E, per angulum EHL,
& perradium HEM, quiipſi BCD, lateri montis parallelus erit. Concipienda enim ſunt tria puncta B, C, D, in vna recta iacere, ac ſi DC, producta ad baſem
turris perueniret. Quia verò angulus EHL, angulo MEK, æqualis eſt: ſi hic ex maiori angulo obſeruato AEN, inprima ſtatione dematur, reliquus fiet angulus
AEM. Eſt autem & angulus EAN, cognitus, quippe cum ſit complementum
maioris anguli obſeruati AEN. Igitur & AME, reliquus duorum rectorum cog-
nitus erit: qui quidem etiam relinquitur, ſi complementum anguli M HL, in
ſtatione D, obſeruati ex duobusrectis detrahatur. Igitur ſi fiat,

92.1.

33: primi.
29. primi.
10. triang.
rectil.
Vtſin{us} anguli A M E, qui \\ velinquitur, ſicomplemen- \\ tum poſtremi anguli obſer- \\ uati MHL, ex duob{us} re- \\ ctis dematur # ad hypotenu- \\ ſam A E, \\ nuper inuẽ- \\ tam: # Ita ſin{us} anguli, \\ E A N, comple- \\ mẽti maioris an- \\ guli obſeruati AEN # ad M E,

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