Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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_180._ </
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ris, & </
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<
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">proportionis datæ, vtrum arcum, vel angulum inquir amus, & </
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vtrumq, inuentum ſigillatim ex grad. </
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<
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<
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arcus, vel anguli quæſiti.</
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<
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">QVOD ſi quando proportio ſinuum data ſit proportio æqualitatis, hoc
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xml:space
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">Quando fi-
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nuum pro-
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portio da-
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ta eſt {pro}por
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tio æquali-
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tatis.</
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eſt, ſinus ſint æquales, erunt quoq; </
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<
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">tam duo arcus, quam duo anguli æqua-
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les, vt in deſin. </
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<
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">ſinuum oſtendimus. </
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<
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vtrumq; </
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<
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">arcum, ſiue angulum cognitum. </
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<
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xml:space
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">Dato igitur aggregato duorum ar-
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cuum, quorum ſinguli ſemicirculo ſint minores, vel duorum angulorum re-
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ctilineorum, &</
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ciendum erat.</
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<
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">_SI_ aggregatum duorum arcuum, vel angulorum fuerit præcisè grad. </
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gregatũ da
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tũ continet
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grad. 180.
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problema
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ſolui non
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poteſt.</
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poterunt arcus illi, vel anguli cognoſci, etiam ſi proportio, quam eorum ſinus habent,
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data ſit. </
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">Nam quomodocunq; </
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eorum ſinus proportionem æqualitatis, cum vnus, & </
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<
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ad defin. </
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ſe, vel maius, quam grad. </
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rentia data
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duorum, ar
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cuũ, quorũ
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quilibet ſe-
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micirculo
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minor ſit,
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vel duorũ
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angulorũ,
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vna cũ pro
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portione,
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quã eorum
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ſinus ha-
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bent, vter
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cognoſcit.</
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<
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ſinguli ſemicirculo ſint minores, vel duorum an-
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gulorum rectilineorum, vna cum proportione,
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quam eorum ſinus habent: </
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<
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latim notum efficere.</
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<
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">IN circulo ABCD, cuius centrum E, ſuperet arcus BF, ſemicirculo
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<
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">Quãdo ſi-
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nꝰ maioris
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arcus, vel
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anguli ad
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ſinum mi-
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noris ha-
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bet propor
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tionẽ maio
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ris inęqua-
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litatis.</
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minor arcum DF, arcu BD, vel angu-
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lus BEF, angulum DEF, angulo BED,
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ſitque differentia hæc, nempe arcus BD, vel
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angulus BED, data grad. </
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<
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quoque ſinus maioris arcus BF, vel angu-
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li BEF, ad ſinum arcus minoris DF, vel
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anguli DEF, ſit primo maioris inæqualita-
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tis data, eadem, quæ 11. </
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<
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<
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contingit, quando duo arcus BF, DF, ſemi-
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circulo ſunt minores ſimul ſumpti. </
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<
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ex his vtrumque arcum BF, DF, ſiue vtrum-
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que angulum BEF, DEF, cognitum facere.
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</
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<
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