Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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tertio lateri adiuncta offeret alteram rectam inter perpendicularem, & </
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angulum acutum.</
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<
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ciendum erat.</
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S_ igitur, in vtraque praxi calculum ipſum monſtrare, num perpendicula
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ris intra triangulum cadat, an vero extra.</
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_ hoc problema abſolui poteſt per propoſ. </
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<
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<
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ucl. </
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pendicularis intra triangulum cadit, vel extra. </
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_AD,_ intra, ſintq́; </
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<
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, 13. </
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_ritq; </
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acutus, propter rectos angulos ad _D._ </
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_
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DC,_ ſint duobus rectis minores. </
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duo quadrata ex _AB,
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C,_ rectangulo bis cõprehenſo ſub _
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D;_ </
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_AC,_ nempe 400. </
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C,_ nimirum ex
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_610._ </
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, BD,_ bis com-
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prehẽſum _210._ </
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ctangulum ſub _
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D,_ comprehenſum: </
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per latus _BC,_ hoc eſt, per _21._ </
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D,_
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_5._ </
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do reperirs poteſt, ſi quadratum lateris _AB,_ ex qua-
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dratis laterum _AC,
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B,_ ſubducatur, &</
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_ſt enim
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& </
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,_
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_
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D,_ bis comprehenſo.</
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DAT_ deinde perpendicularis _AD,_ extra, ſintq́;
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, 20. </
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, 11._ </
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angulus _
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,_ obtuſus: </
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_ABD,_ ſunt duobus rectis minores; </
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<
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D,_
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acutus, cum _D,_ rectus ſit. </
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_
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,_ maius eſt, quàm duo quadrataex _
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B,
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,_ re-
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ctangulo bis comprehenſo ſub _
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B, BD;_ </
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,_
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id eſt, _290._ </
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,_ relinquetur rectangulum bis
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comprehenſum ſub _
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D, 110._ </
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ſub _
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D,_ contentum: </
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,_ prodibit recta _
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D,_ extra
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triangulum, _5._ </
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,_ componet rectam _
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D, 16._</
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<
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differentiæinter quadratum vtriusuis laterum ambientium angulum, à
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quo perpendicularis demiſſa eſt, & </
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duobus lateribus deſcriptorum, diuidatur per latus, in quod perpendicu-
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laris cadit, producetur ſegmentum baſis prope angulum, quem continent
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latera, quorum ſumma quadratorum accepta fuit: </
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ex eadem-baſe det ractum relinquet alterum ſegmentum.</
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diffcrentiæinter quadratum lateris angulo obtuſo oppoſiti, & </
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