Clavius, Christoph, Geometria practica

Table of contents

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[41.] Rurſus.
Page: 79 (49)
[42.] XVII. PERPENDICVLAREM IN LATVS quodcunque ex angulo oppoſito cadentem. Ex tribus omnibus lateribus efficere notam.
Page: 79 (49)
[43.] FINIS LIBRI PRIMI.
Page: 80 (50)
[44.] GEOMETRIÆ PRACTICÆ LIBER SECVNDVS.
Page: 81 (51)
[45.] PROBLEMA I.
Page: 82 (52)
[46.] ALITER
Page: 83 (53)
[47.] ALITER
Page: 83 (53)
[48.] ALITER
Page: 85 (55)
[49.] LEMMA.
Page: 85 (55)
[50.] SCHOLIVM.
Page: 86 (56)
[51.] COROLLARIVM I.
Page: 86 (56)
[52.] COROLLARIVM II.
Page: 87 (57)
[53.] PROBLEMA II.
Page: 87 (57)
[54.] 2. ITEM ſi fiat.
Page: 88 (58)
[55.] ALITER.
Page: 88 (58)
[56.] Ergo ſi fiat,
Page: 88 (58)
[57.] Si igitur fiat.
Page: 88 (58)
[58.] COROLLARIVM I.
Page: 89 (59)
[59.] COROLLARIVM II.
Page: 89 (59)
[60.] PROBLEMA III.
Page: 89 (59)
[61.] ALITER.
Page: 91 (61)
[62.] PROBLEMA IV.
Page: 92 (62)
[63.] ALITER.
Page: 93 (63)
[64.] ALITER.
Page: 93 (63)
[65.] COROLLARIVM.
Page: 94 (64)
[66.] VEL PER SOLOS SINVS.
Page: 94 (64)
[67.] PROBLEMA V.
Page: 94 (64)
[68.] ALITER.
Page: 95 (65)
[69.] PROBLEMA VI.
Page: 95 (65)
[70.] PROBLEMA VII.
Page: 97 (67)
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9363LIBER SECVNDVS.11
Vt D F, ſin{us} \\ tot{us} # ad F H, Tangentem \\ maiorem: # Ita D B, altitudo inuen- \\ ta # ad B C,
22Diſtantiæ in-
uentio.
inuenta erit diſtantia B C.
ALITER.
2. Posito ſinu toto C B, erit B E, Tangens anguli B C E, complementi
minoris anguli obſeruationis E, & BD, Tangens anguli B C D, complementi
maioris anguli obſeruationis D; ideo que D E, differentia illarum Tangentium.
Quamobrem ſi fiat,
33
Vt D E, differentia Tangen- \\ tium complementorum an- \\ gulorũ obſer uationum # ad D B, tangen- \\ tem minorem: # Ita D E, differentia ſta- \\ tionum oculorum # ad D B,
prodibit altitudo D B, cognita ab oculo in prima ſtatione vſque ad baſem alti-
44Altitudinis
inuentio aliæ. tudinis, & c.
ALITER.
3. Vt per ſolos ſinus inſtituatur operatio, inueſtiganda prius eſt vtraque
hypotenuſa C D, C E, vel alterutra earum, hoc modo. Quoniam 5529. primi. BDC, duobus E, & DCE, æqualis eſt, ſi minor angulus obſeruationis E, ex ma-
iori angulo obſeruationis BDC, ſubtrahatur, notus relinquetur angulus DCE.
Itaque ſi fiat,
6610. triang.
rectil.77
Vt ſin{us} anguli D C E differen- \\ tiæ angulorum obſeruatio- \\ num # ad D E, differen- \\ tiam ſtationum \\ oculorum: # Ita ſin{us} minoris \\ anguli obſeruatio- \\ nis E, # ad C D-
# # Vel
# # Ita ſin{us} anguli \\ E D C, complemen- \\ ti maioris anguli \\ obſeruationis ad \\ duos rectos, # ad C E,
88Hypotenu-
ſarum inuẽ-
tio.
reperietur tam hypotenuſa C D, quam C E, in partibus differentiæ ſtationum
D E. Quapropter ſi iam fiat,
9910. triang.
rectil.1010
Vt ſin{us} to- \\ t{us} anguli \\ vecti B, # ad hypotenu- \\ ſam C D, # Ita ſin{us} anguli B C D, complementi ma- \\ ioris anguli obſeruationis B D C, # ad D B,
# Vel # Vel
# ad hypotenuſam \\ C E, proximè \\ inuentam: # Ita ſin{us} anguli B C E, comple- \\ menti minoris anguli obſerua- \\ tionis E; # ad E B,
cognita erit vtraque altitudo D B, E B, & c. Siautem fiat,
1111Altitudinis
inuentio per
ſolos ſin{us}.1212
Vt ſin{us} tot{us} an- \\ guli recti B, # ad Hypotenuſam \\ C D, # Ita ſin{us} anguli D, maio- \\ ris obſeruati, # ad B C,
# Vel # Vel
# ad hypotenuſam C E, \\ nuper inuentam # Ita ſin{us} anguli E, mino- \\ ris obſeruati. # ad B C,
cognoſcetur quo que diſtantia B C, per ſolos ſinus,
13134. A@s-

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