Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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guli ACB, duplicatus dabit latus AB, in partibus ſemidiametri AD,
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&</
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<
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">Latus autem recto angulo oppoſitum perpetuò eſt diameter circuli
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circunſcripti triangulo. </
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<
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">quare ſi ſemidiameter, ſinus ve totus duplicetur,
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cognitum fiet ipſum latus. </
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<
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<
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bitur, ſi vterq; </
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<
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ſis accipiatur. </
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<
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notum. </
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ACB, ABC: </
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<
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betur, &</
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<
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<
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ex datis {pro}-
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portionibꝰ
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omniũ an-
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gulotũ triã
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guli cogno
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ſcantur ipſi
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anguli.</
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mus nihilominus proportiones laterum, ſi prius ex angulorum proportionibus datis
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eorundem magnitudines inueſtigemus, hocmodo. </
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<
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huius ſcholij ponatur proportio anguli _C,_ ad angulum _B,_ eadem, quæ _12._ </
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anguli _B,_ ad angulum _A,_ quæ _20._ </
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<
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xml:space
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">quæ duæ proportiones notæ ſatis ſunt, e-
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tiamſi proportio anguli _A,_ ad angulum _C,_ ignota ſit. </
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meris _6. </
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<
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nem habeant, quam anguli _C, B,_ hoc
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eſt, quam numeri _12. </
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mi non ſint; </
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<
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dem proportionem habentibus, quam
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anguli _B, A,_ ſiue numeri _20. </
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memus tres hoſce numeros deinceps
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minimos _6. </
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<
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numerorum minimorum _6. </
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<
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</
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<
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">qui ſi non eſſent deinceps minimi, in-
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quirendi eſſent tres minimi, per ea, quæ ab Euclide demonſtrata ſunt lib. </
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<
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ergo angulus _C,_ vt _6. </
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">_A,_ vt _7._ </
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<
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">quos in gradibus per regulam Societatum
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ita notos efficiemus. </
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auream regulam. </
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">dant grad. </
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<
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<
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eſt, duo recti, æquiualent.) </
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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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,_ grad. </
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<
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<
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<
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poitiones
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angulorũ
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notæ non
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ſunt conti-
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nuatę, quid
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agendum.</
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tæ proportiones angulorum non ſint continuatæ, vt in dato exemplo, continuandæ
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erunt. </
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<
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<
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<
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portio anguli _A,_ ad angulum _
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,_ vt _28._ </
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<
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<
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vtraq; </
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<
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<
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_C,_ ad _
<
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,_ eſſe vt _12._ </
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<
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<
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<
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<
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,_ ad _A,_ vt _20._ </
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<
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<
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<
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guli _C,_ ad _
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,_ eſt vt _12._ </
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<
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<
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<
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<
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bimus eas, ponendo proportionem _A,_ ad _C,_ vt _28._ </
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<
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<
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<
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,_ vt _12._ </
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<
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</
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<
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<
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<
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,_ eſt vt _12._ </
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<
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<
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<
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