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

AC. # AC. # AD. # # AD.
20. # 100000. # 12? # fit # 60000.

Eſt ergo angulus C, grad. 36. Min. 52. & proinde reliquus duorum rectorum
BAC, grad. 30. Min. 31. Latus BC, inuenietur 11. vt prius. Igitur, Datis
duobus lateribus trianguli non rectanguli, & c. Quod faciendum erat.

472. SCHOLIVM.

Quãdo da-
tus angu-
lus eſt acu-
tus, cur cõ-
ſtare de-
beat, num
alter angu
lus ſit acu-
tus, vel ob-
tuſus.

QVOD _autem nihil certi colligi poſsit, quando datus angulus vni datorum la-_
_terum oppoſitus acutus eſt, niſi prius cognitum ſit, num angulus alteri dato la-_
_teri oppoſitus ſit acutus, obtuſusue, vt in propoſ. diximus, ita per ſpicuum faciemus._ _Sint in triangulo_ Abc , _data latera_ Ab , A C, _vna cum angulo acuto_ B . _Du-_
_cta ex_ A, _ad_ B C, _perpendiculari_ AD, _ignorabitur, num ea cadat extra trian-_
_gulum, an intra, niſi ſciatur, angulum alterum_ ACB, _eſſe_
_obtuſum, acutumue. Sumpta quoque recta_ DE, _ex altera_
_parte perpendicularis_ A D, _ipſi_ DC, _æqualis, ductaq́; recta_
AE ; _erit_ Ae , _ipſi_ A C, _æqualis: propterea quòd latera_
DC, Da , _lateribus_ De , Da , _æqualia ſunt, angulosq́; com_
_prehendunt æquales, vtpote rectos. Itaque etiamſinota ſint_
_latera_ Ab , AC, _vel_ AB, AE, _& angulus acutus_ B, _non_
_tamen idcirco reliquum latus notum erit, aut reliqui an-_
_guli; cum reliquum latus poſsit eſſe vel_ B C, _vel_ B E; _ac_
_propterea reliqui anguli vel_ BCA, B AC, _vel_ B EA,
B AE: _niſi prius conſtet, angulum_ B CA, _obtuſum eſſe, vel acutum._ H_oc enim co-_
_gnito, ſciemus, quando perpendicularis_ AD, _extra triangulum cadit, & quando_
_intra; & c._

472.1.

346-01
4. primi.

EX _quibus conſtat, Nicolaum Copernicum, alioquin diligentißimum, hallucina-_
_tum fuiſſe lb._ 1. _Reuo lutionum propoſ._ 6. _triangulorum rectilineorum, dum ſimplici-_
_ter proponit: Si duo latera trianguli data ſint, & angulus vni eorum oppoſitus datus_
_etiam, reliquum latus, & reliquos angulos dari poſſe. Hoc etenim fieri non poteſt, vt_
_demonſtrauimus, quando datus angulus eſt acutus, niſi conſtet, num angulus alteri_
_laterum daterum oppoſitus ſit acutus, an obtuſus._

472.1.

Error Nico
lai Coper-
nici,

473. FINIS TRIANGVLORVM
RECTILINEORVM.

346-02

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