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

gulo oppoſitus, cum angulo non recto ACD;

615.1.

Schol. 45.
huius.

reperietur quoque, per ſcholia in margine adducta, arcus CD, circa rectum
angulum: qui vel additus arcui BD, iam dudum inuento, vel ab eo ſubductus,
(prout nimirum arcus perpendicularis AD, intra triangulum ceciderit, vel
extra) dabit arcum BC, in propoſito triangulo ABC, quæſitum.

PORRO nulla ratione alteruter arcuum AD, BD, in hoc caſu, qua-
drans eſſe poteſt: quia alioquin & arcus AB, recto angulo D, oppoſitus eſſet
quadrans, quod eſt contra hypotheſim. Eadem ratione neque CD, quadrans
erit, ne & arcus AC, angulo recto oppoſitus quadrans ſit, quod eſſet etiam
contra hypotheſim.

615.1.

35. huius.

PRAXIS huius problematis petatur ex ſcholijs in margine poſitis.

Praxis per
ſolos ſinus,
quãdoneu-
ter datorũ
arcuum in
ęqualiũ eſt
quadrans.

SED per ſolos ſinus ita problema abſoluetur. Per praxim problema-
tis 2. ſcholij propoſ. 41. inuenietur arcus AD, in triangulo ABD: Et hinc
per praxim problematis ſcholij propoſ. 43. arcus BD. Deinde per praxim
problematis 2. ſcholij propoſ. 42. reperietur angulus BAD.

POST hæc in triangulo ACD, per praxim problematis 1. ſcholij pro-
poſ. 41. cognitus erit angulus ACD, qui e§t vnus quæſitorum, ſi conſtet,
angulum C, eiuſdem eſſe ſpeciei cum angulo dato B; ſi vero diuerſæ, veli-
quus duorum rectorum erit angulus ACB, quæſitus, quia ibi arcus per-
pendicularis intra triangulum cadit, hic vero extra. Rurſus per praxim
problematis ſcholij propoſ. 43, notus efficietur arcus CD, qui in priori
triangulo additus inuento arcui BD, in poſteriori vero ex eodem ſublatus
exhibebit reliquum arcum BC, in propoſito triangulo notum. Ad extre-
mum, per praxim problematis 1. ſcholij propoſ. 41. reperietur angu-
lus CAD, qui additus, vel ſubductus ex inuento angulo BAD, tertium
angulum BAC, qui quæritur, notum efficiet.

615.1.

57. huius.
Quando al
ter duorũ
arcuũ inæ-
qualiũ da-
torum eſt
guadrans.

QVOD ſi alter arcuum datorum inæqualium AB, AC, ſit quadrans; ſi
quidem AB, quadrans fuerit, erit quoque BD, quadrans, & angulus BAD,
rectus, necnon B, polus arcus AD; atque adeo angulus datus B, eundem ar-
cum AD, notum exhibebit, vt in præcedenti propoſ. oſtendimus, quando ar-
cus AB, ponebatur eſſe quadrans. Inuentis igitur arcubus AD, BD, & angu
lo BAD, ſine vllo negotio, reliqua inueniemus, vt prius. Si vero arcus AC,
ſit quadrans, erit eadem ratione CD, quadrans, & angulus CAD, rectus, nec
non C, polus arcus AD; atque adeo inuentus arcus AD, angulum ACD, no-
tum faciet: qui vnus erit ex quæſitis, quando arcus AD,
cadit intra triangulum; ſi vero extra, reliquus duorum re
ctorum dabit angulum quæſitum ACB. Atq; ita inuen-
tus tunc erit, ſine multiplicatione vlla, & arcus CD, & angulus CAD, necnon angulus ACD: ex quibus repe-
rientur reliqua, vt prius.

615.1.

494-01

SINT iam dati duo arcus AB, AC, æquales. Erunt
duo anguli B, C, æquales; & arcus perpendicularis AD, ex
A, in BC, demiſlus intra triangulum cadet; necnon & ar-
cus BD, CD, & anguli ad A, ęquales erunt, vt in vltimo caſu propoſ. 63. oſten

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