Full text: Bithynius, Theodosius: Theodosii Tripolitae Sphaericorum libri tres

C. # A. # # AB. # # BC.
59996. # 50779. # # 13? # fit # 11. # ferè.
# # Item.
C. # B. # # AB. # # AC.
59996. # 92310. # # 13? # fit # 20. # ferè.
# # Vel.
A. # B. # # BC. # # AC.
50779. # 92310. # # 11? # fit # 20. # ferè.

ITAQVE, datis angulis omnibus, cum vno latere; Si fiat, vt ſi-
nus anguli lateri dato oppoſiti ad ſinum vtriuſuis reliquorum angulorum,
ita latus datum ad aliud, inuenietur latus angulo illi, cuius ſinus acce-
ptus eſt, oppoſitum: Et ſi rurſus fiat, vt ſinus anguli lateri dato oppo-
ſiti ad ſinum tertij anguli, ita datum latus ad aliud, reperietur latus ter
tio angulo oppoſitum, & c.

467.1.

Praxis.
Quãdo triã
gulũ eſt Iſo
ſceles, vel ę-
quilaterũ:
aut quãdo
in ſcaleno
dãtur duo
latera cum
angulis.

QVOD ſi triangulum fuerit Iſoſceles, & dentur anguli: Vel ſi fuerit ſca-
lenum, & duo dentur latera cum angulis, vnius tantum lateris inuentione
opus eſt, vt patet. In æquilatero autem triangulo, ſi detur vnum latus, erunt
& reliqua data, vtpoteilli æqualia.

IAM verò ſi datæ ſint proportiones angulorum, cum vno latere, inue-
ſtigandæ erunt ex illis proportionibus magnitudines angulorum, vt in ſcho-
lio propoſ. 1. demonſtrauimus: Deinde vero reliqua latera exploranda, vt
hic oſtenſum eſt.

467.1.

Quãdo dã-
rur propor
tiones an-
gulorũ, cũ
vno latere.

INVENTIS autem lateribus, liquido conſtat, eorum proportiones
eſſe notas in numeris, in quibus ipſa cognita ſunt. Datis ergo omnibus angu-
lis trianguli non rectanguli, & c. Quod erat faciendum.

468. PROBL. 7. PROPOS. 11.

DATIS omnibus trianguli non rectanguli
lateribus, vel eorum proportionibus, omnes an-
gulos notos efficere.

468.1.

In triãgulo
ex notis la-
teribus, vel
ex eorũ pro
portionibꝰ
notis, angu
li inueniũ-
tur.

IN triangulo priori ABC, ſint data omnia
latera; AB, 13. AC, 20. & BC, 21. Oporter ex
his inueſtigare angulos. In maximum latus BC,
ex oppoſito angulo A, ducatur perpendicularis
AD, quę neceſlario intra triangulum cadet. Cum
enim latus BC, ſit maximum, erit & angulus A,
ipſi oppoſitus, maximus: ac propterea vterq; B,
C, acutus. Ex quo fit, perpendicularem AD, in-
tra triangulum cadere. Primùm itaq; inquiran-
tur rectæ BD, CD. Inuenietur BD, 5. & CD,
16. Quia ergo, poſito ſinu toto AB, recta BD,
ſinus eſt anguli BAD, vt in tractatione ſinuum
oſtendimus, dicemus per auream regulam. Si AB,

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