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

niatur ergo, per 16. problema, triang. ſphær. arcus AB, recto angulo D, op-
poſitus, ex duobus angulis B, BAD; eritq́; proinde & AC, illi æqualis, cognitus. Deinde, per problema 14. triang. ſphær. ex inuento arcu AB, rectum angulum ſub-
tendente, & dato angulo B, reperiatur arcus BD; eritq́; propterea & CD, illi æqualis, cognitus; ideoq́; & totus
BC, notus. Inuentiq́; iam erunt omnes tres arcus AB,
AC, BC.

665.1.

Quãdo da
ti duo an-
guli ſunt
æquales.
513-01

_PER_ ſolos autem ſinus ita rem exequemur. _P_er 1. praxim
problematis _4._ triang. ſphær. inquiratur arcus _ B D,_ ex duobus
angulis _ B, BA D;_ eritq́; idcirco & _CD,_ illi æqualis, cognitus, proptereaq́; & totus
_ BC ,_ notus. _D_einde, per problema _3._ triang. ſphær. ex arcuinuento _ B D,_ & an-
gulo ei oppoſito _ Bad ,_ reperiatur arcus _ AB ,_ recto angulo oppoſitus: quia præter da-
ta conſtat etiam ſpecies alterius anguli _ B ,_ cum datus ſit: eritq́; propterea & arcus
_ A C,_ ipſi _ Ab ,_ æqualis, cognitus.

665.1.

Per ſolos G
nus, quãdo
duo dati an
guli ſunt
æquales.

18. DATIS omnibus arcubus trianguli non
rectanguli, inueſtigare omnes eius angulos.

665.1.

Quætũtur
omnes an-
guli.

SINT omnes arcus in triangulo ABC, dati, ſitq́; primo loco inquiren
dus angulus A, & duo arcus AB, AC, eum continentes ſint inæquales, quadran
teq́; minores, quicquid ſit de arcu BC. Productis arcubus AB, AC, vt fiant
quadrantes AD, AE, deſcribatur per D, E, arcus circuli maximi DE, occur-
rens arcui BC, producto verſus maiorem arcum, qui ſit AC, in puncto F. Sta-
tuantur ſinus complementorum arcuum datorum AB, AC, pro terminis pro-
portionis ſinus arcus BF, ad ſinum arcus CF. Atque ex hac proportione, & arcu dato BC, qui differentia eſt arcuum BF, CF, inueſtigetur, per proble-
ma 8. triang. rectil. vterque arcus BF, CF. Deinde, per problema 8. triang. ſphær. inue-
ſtigetur tam arcus DF, ex arcu inuento BF,
rectum angulum D, ſubtẽdente, & arcu BD,
qui complementum eſt dati arcus AB; quam
arcus EF, ex arcu inuento CF, rectum angu
lum E, ſubtendente, & arcu CE, qui comple
mentum eſt dati arcus AC. Subducto enim
arcu EF, inuento, ex inuento arcu DF, no-
tus remanebit arcus DE, anguli, A; ac proin
de angulus A, notus erit. Poſt hæc, per pro-
blema 11. triang. ſphæ. ex arcubus notis BD,
DF, circa rectum angulum D, inueniatur an-
gulus DBF, ac proinde & reliquus duorum
rectorum ABC. Eadem denique ratione, ex arcubus CE, EF, notis circa an-
gulum rectum E, eruatur angulus ECF, atque adeo & angulus ACB, ei ad
verticem æqualis. Atque ita iam omnes tres anguli A, B, C, inuenti erunt.

665.1.

Quãdo duo
dati arcus
ſunt inæ-
quales, &
quadrante
minores.
Prop. 63.
triãg. ſphęr.
513-02

_PER_ ſolos ſinus ita progrediemur. Vterque arcus _ B F, CF,_ reperiatur per _3._ praxim problematis _8._ triang. rectil. _D_einde, per _1._ praxim problematis _8._ triang. ſphar. tam arcus _DF,_ ex arcu inuento _ B F,_ rectum angulum _D,_ ſubtendente, & ar-
cu _ B D,_ complemento dati arcus _ Ab ,_ inueniatur, quam arcus _EF,_ ex inuento ar-

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