343331
CD. # CD. # BD. # # BD.
16. # 100000. # 12? # fit # 75000.
C. # BAC. # AB. # # BC.
59996. # 92310. # 13? # fit # 20. ferè.
B, vel C. # A. # AB, vel AC. # # BC.
76604. # 98481. # 9? # fit # 11 {43685/76604}.
Addita autem AD, inuenta 5.
ad latus AC, datum 11.
fiet tota CD, 16.
Cum
ergo, poſito ſinu toto CD, recta BD, ſit tangens anguli C; reperietur tan-
gens BD, 75000. vt hic cernis.
11 ergo, poſito ſinu toto CD, recta BD, ſit tangens anguli C; reperietur tan-
gens BD, 75000. vt hic cernis.
CD. # CD. # BD. # # BD.
16. # 100000. # 12? # fit # 75000.
Quæ tangens offeret in tangentium tabula angulum C, grad.
36.
Min.
52.
&
proinde duo anguli A, C, grad. 112. Min. 36. & grad. 36. Min. 52. ex grad.
180. ablatirelinquent angulum ABC, grad. 30. Min. 31. Quoniam tandem
eſt, vt ſinus anguli C, cogniti ad ſinum anguli BAC, dati, ita latus AB, 13.
221. huius. datum ad BC, inuenietur latus BC, 20. ferè. vt hic apparet.
33 proinde duo anguli A, C, grad. 112. Min. 36. & grad. 36. Min. 52. ex grad.
180. ablatirelinquent angulum ABC, grad. 30. Min. 31. Quoniam tandem
eſt, vt ſinus anguli C, cogniti ad ſinum anguli BAC, dati, ita latus AB, 13.
221. huius. datum ad BC, inuenietur latus BC, 20. ferè. vt hic apparet.
C. # BAC. # AB. # # BC.
59996. # 92310. # 13? # fit # 20. ferè.
QVOD ſi quando data duo latera datum angulum ambientia fuerint
44Quado da
ta latera sũt
æqualia. æqualia, facilius erit problema. Sint namq; in triangulo ABC, duo latera
189[Figure 189]
AB, AC, æqualia, quodlibet 9.
&
angulus A, com-
prehenſus grad. 80. Ablato hoc angulo ex grad.
180. dabit ſemiſsis reſidui, quod eſt grad. 100. vtrum-
que angulorum B, C, grad. 50. Si autem fiat, vt ſinus
anguli B, vel C, ad ſinum anguli A, ita latus AC,
vel AB, ad aliud, prodibit latus BC, 11 {43685/76604}.
vt hic vides.
55 44Quado da
ta latera sũt
æqualia. æqualia, facilius erit problema. Sint namq; in triangulo ABC, duo latera
prehenſus grad. 80. Ablato hoc angulo ex grad.
180. dabit ſemiſsis reſidui, quod eſt grad. 100. vtrum-
que angulorum B, C, grad. 50. Si autem fiat, vt ſinus
anguli B, vel C, ad ſinum anguli A, ita latus AC,
vel AB, ad aliud, prodibit latus BC, 11 {43685/76604}.
vt hic vides.
B, vel C. # A. # AB, vel AC. # # BC.
76604. # 98481. # 9? # fit # 11 {43685/76604}.
PROBL. 9. PROPOS. 13.
66In triãgule non rectan
gulo ex da-
tis duobus
lateribꝰ da
tis, vel ex eo
rũ propor-
cũ vno an-
gulo nõ ab
ipſis cõpre-
henſo, ter-
tium latus,
& reliqui
anguli in-
ueſtigãtur.
DATIS duobus lateribus trianguli non re-
ctanguli, vel eorum proportione data, vnà cum
angulo, qui alteri datorum laterum opponitur:
reliquos angulos, & tertium latus in quirere. Opor
tet autem conſtare, num alter angulus reliquo la-
teri dato oppoſitus ſit acutus, an obtuſus, ſi datus
angulus acutus eſt.
ctanguli, vel eorum proportione data, vnà cum
angulo, qui alteri datorum laterum opponitur:
reliquos angulos, & tertium latus in quirere. Opor
tet autem conſtare, num alter angulus reliquo la-
teri dato oppoſitus ſit acutus, an obtuſus, ſi datus
angulus acutus eſt.
SINT in triangulo ABC, data duo latera AB, AC.
13.
&
20.
datusq́;
ſit
acutus angulus C, grad. 36. Min. 52. lateri dato AB, oppoſitus, conſtetq́ue
de angulo B, qui alteri dato lateri AC, opponitur, num acutus ſit, an obtu-
ſus: alias enim nihil certi colligi poſſet, vt ex ſequenti ſcholio patebit. Quo-
niam ergo eſt, vt latus AB, ad latus AC, ita ſinus anguli C, ad ſinum anguli
771. huiun B; ſuntque tria primadata, inuenietur per auream regulam quartum, hoc eſt,
ſinus anguli B, 92302. vt hic liquet.
acutus angulus C, grad. 36. Min. 52. lateri dato AB, oppoſitus, conſtetq́ue
de angulo B, qui alteri dato lateri AC, opponitur, num acutus ſit, an obtu-
ſus: alias enim nihil certi colligi poſſet, vt ex ſequenti ſcholio patebit. Quo-
niam ergo eſt, vt latus AB, ad latus AC, ita ſinus anguli C, ad ſinum anguli
771. huiun B; ſuntque tria primadata, inuenietur per auream regulam quartum, hoc eſt,
ſinus anguli B, 92302. vt hic liquet.