Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 372
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<
s
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xml:space
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">DIFFERENTIA inter quadrata duorum laterum ambientium an-
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xml:space
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triang. re-
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ctil.</
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gulum, à quo perpendicularis demiſſa eſt, diuidatur per latus tertium, produ
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ceturq́; </
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<
s
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">numerus; </
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<
s
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">qui ſi minor fuerit tertio latere, indicabit, perpendicularem
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intra triangulum cecidiſſe; </
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<
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">idemq́; </
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<
s
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xml:space
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">ex tertio eodem latere ſubductus relinquet
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numerum, cuius ſemiſsis dabit minus ſegmentum baſis, hoc autem ex toto ter
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tio latere ſubtractum dabit ſegmentum maius. </
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<
s
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xml:space
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">Idem vero numerus ex diui-
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ſione productus, ſi fuerit maior tertio latere, argumento erit, perpẽdicularem
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extra triangulum cecidiſſe. </
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<
s
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xml:space
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">Quare ſi ex eo tertium latus auſeratur, reliquus
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erit numerus, cuius ſemiſsis dabit rectam extra triangulum inter perpendicu-
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larem, & </
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<
s
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">angulum obtuſum; </
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<
s
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xml:space
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">eadem vero ſemiſsis tertio lateri appoſita dabit
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alteram rectam inter perpendicularem, & </
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<
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">angulum acutum.</
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<
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<
s
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">FIAT, vt tertium latus, in quod demiſſa eſt perpendicularis, ad ſummam
<
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<
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xlink:label
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xml:space
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">Propoſ. 9.
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triang. re-
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ctil.</
note
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aliorum duorum laterum, ita differentia eorundem ad aliud, prouenietq́; </
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<
s
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merus, ex quo rectam inter perpendicularem, & </
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<
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">angulum vtrumq; </
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<
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mus, vt nuper diximus.</
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<
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">CADENTE perpendiculari intra triangulum; </
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">diuidatur ſemiſsis diffe-
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<
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">Schol. pro-
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poſ 9. triãg-
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rectil.</
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rentiæ inter quadratum vttiuſvis laterum ambientium angulum, à quo per-
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pendicularis eſt demiſſa, & </
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<
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">ſummam quadratorum ex alijs duobus lateribus de-
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ſcriptorum, per latus, in quod perpendicularis cadit, produceturq́; </
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<
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tum baſis prope angulum, quem continẽt duo latera, quorum ſumma quadra-
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torum fuit accepta; </
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<
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xml:space
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">hoc autem ſegmentum ex tota baſi detractum relinquet
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alterum ſegmentum.</
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<
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">CADENTE vero perpendiculari extra triangulum, diuidatur ſemiſsis
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differentiæ inter quadratum lateris angulo obtuſo oppoſiti, & </
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<
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dratorum ex alijs duobus lateribus deſcriptorum, per latus, in quod produ-
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ctum perpendicularis cadit, procreabiturq; </
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<
s
xml:id
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">linea extra triangulum inter per-
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pendicularem, & </
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<
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">angulum obtuſum; </
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<
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">hæc vero toti baſi adiecta conficiet alte-
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ram rectam inter perpendicularem, & </
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<
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<
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">Coroll. pro-
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poſ. S. triãg.
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rectil.</
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dicularis baſim bifariam. </
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<
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">Quare dimidiũ baſis dabit vtramq; </
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<
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">rectã quęſitam.</
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<
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<
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duo latera.</
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<
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">10. DATIS omnibus angulis trianguli non
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rectanguli, cum vno latere, inuenire alia duo
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latera.</
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<
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">FIAT, vt ſinus anguli dato lateri oppoſiti ad ſinum vtriusvis reliquo-
<
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<
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xlink:label
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">Propoſ. 10.
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triang. re
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ctil.</
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rum angulorum, ita latus datum ad aliud, inuenieturq́; </
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<
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angulo oppoſitum. </
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<
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">Fiat rurſus, vt ſinus anguli dato lateri oppoſiti ad ſinum
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tertij anguli, ita latus datum ad aliud, produceturq́; </
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<
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tio angulo oppoſitum.</
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</
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<
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<
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">SI triangulum ſit Iſoſceles, vnius tantum lateris inuentione opus eſt, ſi
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vnum datum ſit, cum angulis. </
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<
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">Idem dicendum eſt de Scaleno, ſi duo eius late-
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ra cum angulis data ſint. </
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<
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">In Aequilatero vero, ſi vnum latus detur, data e-
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runt & </
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<
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">reliqua illi æqualia.</
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