Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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13. </
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<
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<
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xml:space
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<
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xml:space
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ſinum BD, 38461. </
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<
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AB. # AB. # BD. # # BD.
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13. # 100000. # 5? # fit. # 38461.
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<
s
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xml:space
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">Ex tabula ergo ſinuum dabitur angulus BAD,
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<
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fig-338-01
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183
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338-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/338-01
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grad. </
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<
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<
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<
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<
s
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B, grad. </
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<
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<
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<
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<
s
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xml:space
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">qui eſt vnus angulorum quę-
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ſitorum. </
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<
s
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">Rurſus, quia poſito AC, ſinu toto, CD,
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ſinus eſt anguli CAD, dicemus iterum per regu-
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lam auream. </
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<
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<
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">dat AC, 100000. </
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<
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totum, quid dabit CD, 16? </
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<
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xml:space
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">Inueniemuſq; </
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<
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CD, 80000. </
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<
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xml:space
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AC. # AC. # CD. # # CD.
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20. # 100000. # 16? # fit # 80000.
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<
s
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xml:space
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">Qui ſinus in tabula ſinuum monſtrat angulum
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CAD, grad. </
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<
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<
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<
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<
s
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xml:space
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mentum C, erit grad. </
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<
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">36. </
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<
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<
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<
s
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xml:space
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">qui eſt vnus
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etiam angulorum quæſitorum. </
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<
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xml:space
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guli duorum ſinuum inuentorum, nempe grad. </
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<
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<
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<
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<
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">& </
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<
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</
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<
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8. </
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">ſimul componantur, fiet tertius angulus BAC, grad. </
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<
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<
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<
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<
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te ſi ſumma duorum angulorum B, C, inuentorum ex grad. </
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<
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<
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reliquus fiet tertius angulus BAC, grad. </
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<
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<
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<
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">ITAQVE, (vt totam praxim complectamur) ſi fiat, vt maximum
<
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latus (in quod perpendicularis ducta eſt) ad ſummam aliorum duorum,
<
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ita differentia eorundem duorum ad aliud, reperietur numerus, qui ex
<
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maximo latere ſubductus relinquet numerum, cuius ſemiſſis dabit minus
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ſegmentum baſis, hoc autem ex baſi detractum relinquet maius ſegmen-
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tum, vt conſtat ex ſecunda praxi propoſ. </
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<
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<
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xml:space
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">Quòd ſi rurſum fiat, vt mi-
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nimum latus ad ſinum totum, ita ſegmentum baſis minus ad aliud, inue-
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nietur ſinus, cuius arcus complementum dabit angulum ſupra baſim me-
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dio lateri oppoſitum. </
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<
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xml:space
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">Deinde ſi rurſum fiat, vt medium latus ad ſinum
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totum, ita maius ſegmentum baſis ad aliud, reperietur ſinus, cuius ar-
<
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cus complementum dabit angulum ſupra baſim minimo lateri oppoſitum.
<
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</
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<
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xml:space
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">Tertius vero angulus maximo lateri oppoſitus conflabitur ex duobus il-
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lis arcubus duorum ſinuum inuentorum: </
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<
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tractionem duorum angulorum inuentorum ex duobus rectis.</
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<
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<
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<
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BC, 20. </
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<
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xml:space
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">Demiſſa in maximum latus BC, perpendiculari AD, inuenietur
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ſegmentum BD, 8 {4/5}. </
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<
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<
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riorem propoſ. </
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<
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BC. # AB. AB. # Differ. inter # AB, AC.
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20. # 24. # 2? # fit # 2 {2/5}.
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<
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<
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<
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">cuius ſemiſsis 8 {4/5}. </
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<
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mentum minus BD. </
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<
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">Ergo maius CD, erit 11 {1/5}. </
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<
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