Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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nient hæ lineæ productæ ad partes D, F, vt in puncto G. </
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<
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proportio ſit data maioris inæqualitatis, maior erit ſinus arcus BF, hoc eſt,
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perpendicularis ex B, ad CF, demiſſa, ſinu arcus DF, hoc eſt, perpendiculari
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ex D, ad CF, demiſſa. </
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<
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">Quare minus diſtabit punctum D, à recta CF, quàm pun-
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ctum B; </
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<
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">atque adeo tandem coibunt BD, CF, productæ ad partes D, F. </
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<
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etiam ita probabitur. </
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<
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xml:space
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demiſſæ eſſent æquales, cum ipſæ ſint paral-
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lelæ, eſſent quoque BD, CF, parallelæ. </
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<
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ergo perpendicularis ex D, demiſſa minor
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ſit, eſſicitur, vt conueniant, &</
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<
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de arcu BD, bifariam in A, ſecabit ſemidia-
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meter ducta EA, chordã BD, quoq; </
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in H, ex lemmate ad defin. </
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ſtrato; </
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">& </
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<
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niam vero proportio ſinus arcus BF, ad ſi-
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num arcus DF, eſt, ex hypotheſi, vt 11. </
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5. </
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DF, ita BG, ad DG; </
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DG, vt 11. </
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</
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<
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">ac proinde reliqua BD, 6. </
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<
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">vtraque uero ſemiſsis BH, HD, 3.</
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denique HG, 8. </
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xml:space
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ſis BA, AD, grad. </
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<
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duum quoque 30. </
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<
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">Et quia, poſito ſinu toto EH, recta HD, tangens eſt angu-
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li DEH, & </
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ſecãtium monuimus; </
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HD, partium 57735. </
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">Quapropter, ut tangentem HG, anguli HEG, cognoſ-
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camus, dicemus per auream regulam. </
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proportionis datæ, nempe 3. </
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<
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xml:space
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">dat HD, tangentem ſemiſsis differentiæ datæ
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arcuum BF, FD, uel angulorum BEF, DEF, partium 57735. </
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<
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HG, aggregatum ex ſemiſſe differentiæ terminorum datæ proportionis, & </
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conſequente eiuſdem proportionis, nimirum 8? </
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partium 153960. </
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HD. # HD. # HG. # # HG.
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3. # 57735? # 8? # ſit. # 153960.
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">In tangentium autem tabula hæc tangens inuenta offert angulum AEF, ſiue
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arcum AF, grad. </
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<
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<
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<
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BF, ſiue angulus BEF, grad. </
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<
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grad.</
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<
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<
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<
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nũ minoris eſt maioris inæqualitatis: </
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norum proportionis datæ ad tangentem ſemiſſis differẽtiæ arcuum, vel an-
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gulorum datæ, ita aggregatum ex ſemiſſe differentiæ terminorum propor-
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tionis, & </
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<
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vel anguli, qui ſemiſſi differentiæ arcuum, vel angulorum datæ additus
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componit maiorem arcum, ſeu angulum; </
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ſubducatur, remanet arcus, vel angulus minor.</
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