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

productam, arcus perpendicularis deducatur: ha-
bebunt ſinus angulorum, quos arcus perpendicu-
laris cum duobus arcubus dictum angulum com-
prehendentibus facit, eandem proportionẽ, quam
ſinus complemẽtorum reliquorum duorum trian
guli angulorum.

IN triangulo ABC, deducatur ex angulo A, ad baſin BC, arcus perpen
dicularis AD, cadens ſiue intra triangulum,
ſiue extra. Dico ita eſſe ſinum anguli BAD,
ad ſinum anguli DAC, vt eſt ſinus comple-
menti anguli B, ad ſinum complementi angu
li C. Nam in triangulo ABD, cuius angulus
D, rectus, erit, vt ſinus anguli BAD, ad ſi-
num totum, ita ſinus complementi anguli B,
ad ſinum complementi arcus AD. Item in
triangulo CAD, habente angulum D, rectum,
erit, vt ſinus anguli DAC, ad ſinum totum,
ita ſinus complementi anguli C, (habent au-
tem duo anguli ad C, in ſecundo triangulo
eundem ſinum) ad ſinum complementi arcus
AD: Et conuertendo, vt ſinus totus ad ſinum anguli DAC, ita ſinus com. plementi arcus AD, ad ſinum com-
plementi anguli C. Ex æqualitate
ergo (vt in appoſita formula vides)
erit, vt ſinus anguli BAD, ad ſinum
anguli DAC, ita ſinus complemen-
tianguli B, ad ſinum complementi anguli C. Si igitur ab angulo ſphærici
trianguli ad baſin, & c. Quod oſtendendum erat.

604.1.

469-01
42. huius.
Sin. ang. BAD. # Sin. compl. ang. B.
Sinus totus. # Sin. cõpl. arcus AD.
Sin. ang. DAC. # Sin. compl. ang C.

605. PROBL. 3. PROP. 62.

DATIS omnibus angulis trianguli ſphærici
non rectanguli, omnes tres arcus efficere notos.

IN triangulo ſphærico non rectangulo ABC,
dati ſint omnes anguli A, B, C: ſintq́; primum omnes
tres anguli inæquales. Oportet ex his tres cius arcus
perſcrutari. Quoniam nullus angulus ponitur rectus,
erunt ſaltem duo vel acuti, vel obtuſi: ſint B, C, vel
ambo acuti, vel obtuſi, quicquid ſit de reliquo A, ȧ
quo ad arcum BC, arcus perpendicularis ducatur, qui
neceſſario cadet intra triangulum. Et quia eſt, vt ſi-
nus anguli BAD, ad ſinum anguli DAC, ita ſinus complementi anguli B, ad

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