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

AVT, quoniam notus eſt arcus BC, recto angulo
oppoſitus, & arcus CE: VEL, quia datus eſt angulus CBE, & arcus BE,
vel CE; Nam quando datur arcus CE, conſtat etiam,
an alter arcus BE, circa angulum rectum datus, ma-
ior ſit quadrante, vel minor: AVT denique, quia notus eſt arcus BC, angulo
recto oppoſitus, cum angulo CBE; notus quoq; ſiet, ex ſcholijs in margine citatis angulus BCE; atque idcirco,
addito recto angulo ACE, totus angulus ACB, datus erit. Rurſus ergo om
nes tres anguli trianguli ABC, inuenti ſunt.

607.1.

25. huius.
Schol. 53.
vel 43. huiꝰ
Schol. 51.
vel 45. huiꝰ.
Schol. 44.
vel 48. huiꝰ.
Schol. 55.
vel 41. huiꝰ.
Schol. 55.
vel 41. huiꝰ.
Schol. 44.
vel 48. huiꝰ.
Schol. 51.
vel 45. huiꝰ.
Schol. 42.
huius.
Schol. 47.
huius.

PRAXIS huius problematis petenda eſt ex ſcholijs in margine ci-
tatis. Solum, vt cognoſcantur arcus BF, CF, in primo caſu, & tertio,
ſtatuendi erunt ſinus complementorum arcuum datorum AB, AC, pro
terminis proportionis ſinus arcus BF, ad ſinum arcus CF, & in primo
quidem caſu adhibenda vel prima praxis propoſ. 7. triangulorum recti-
lineorum, vel aliqua ex alijs eiuſdem propoſ. prout res exiget; in tertio
vero caſu adducenda erit prima, vel ſecunda praxis propoſ. 6. triangulo-
rum rectilineorum, & c.

607.1.

Praxis, quã
do duo at-
cus quæſi-
tum angu-
lum conti-
nentes ſunt
inæquales.

QVOD ſi ſolis vti libeat ſinubus, inueſtigandi erunt arcus BF, CF,
in primo caſu, per ſecundam praxim propoſ. 7. triang. rectil. In tertio ve-
ro per praxim tertiam propoſ. 6. Deinde in triangulo BFD, per praxim
ſcholij 1. propoſ. 43. eruendus arcus DF: Et eodem modo in triangulo
CFE, arcus EF; vt reliquus arcus DE, in primo caſu, vel totus arcus
DE, in tertio caſu habeatur, qui quidem eſt arcus anguli A. Poſt hæc per
praxim problematis 1. ſcholij propoſ. 41. inueniendus in triangulo BFD,
angulus DBF: ex quo reliquus duorum rectorum ABC, notus fiet. At-
que eodem pacto in triangulo CFE, eliciendus angulus ECF, ex quo in
primo caſu angulus quoque ACB, ad verticem cognitus erit.

607.1.

Praxis per
ſolos ſinus,
quando @ar
cus duo an
gulũ quæ-
ſitum am-
biẽtes ſunt
inæquales.

AT vero in quarto caſu ex praxi ſcholij 1. propoſ. 43. inueniendus
eſt arcus BD, anguli A, in triangulo BCD: Et eodem modo in quinto ca
ſu arcus CE, anguli eiuſdem A, in triangulo BCE. Deinde in quarto ca-
ſu, per praxim problematis 1. ſcholij propoſ. 41. in triangulo BCD, inda-
gandus angulus BCD; ex quo reliquus duorum rectorum ACB, notus
fiet: Atque eadem ratione in quinto caſu, angulus EBC, in triangulo
BCE, inueniendus. Ad extremum in quarto caſu, per praxim problema-
tis 2. propoſ. 42. in triangulo BCD, exquirendus angulus CBD; ex quo
& ABC, reliquus recti ABD, notus erit: Et ſimiliter in quinto caſu,
eliciendus angulus BCE; qui additus recto angulo ACE, totum angu-
lum ACB, notum exhibebit.

ALITER, & multo breuius. Sint rurſum dati tres arcus trianguli ABC,

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