Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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        <div xml:id="echoid-div1428" type="section" level="1" n="634">
          <pb o="490" file="502" n="502" rhead=""/>
          <p>
            <s xml:id="echoid-s17741" xml:space="preserve">DIFFERENTIA inter quadrata duorum laterum ambientium an-
              <lb/>
              <note position="left" xlink:label="note-502-01" xlink:href="note-502-01a" xml:space="preserve">Propoſ. 9.
                <lb/>
              triang. re-
                <lb/>
              ctil.</note>
            gulum, à quo perpendicularis demiſſa eſt, diuidatur per latus tertium, produ
              <lb/>
            ceturq́; </s>
            <s xml:id="echoid-s17742" xml:space="preserve">numerus; </s>
            <s xml:id="echoid-s17743" xml:space="preserve">qui ſi minor fuerit tertio latere, indicabit, perpendicularem
              <lb/>
            intra triangulum cecidiſſe; </s>
            <s xml:id="echoid-s17744" xml:space="preserve">idemq́; </s>
            <s xml:id="echoid-s17745" xml:space="preserve">ex tertio eodem latere ſubductus relinquet
              <lb/>
            numerum, cuius ſemiſsis dabit minus ſegmentum baſis, hoc autem ex toto ter
              <lb/>
            tio latere ſubtractum dabit ſegmentum maius. </s>
            <s xml:id="echoid-s17746" xml:space="preserve">Idem vero numerus ex diui-
              <lb/>
            ſione productus, ſi fuerit maior tertio latere, argumento erit, perpẽdicularem
              <lb/>
            extra triangulum cecidiſſe. </s>
            <s xml:id="echoid-s17747" xml:space="preserve">Quare ſi ex eo tertium latus auſeratur, reliquus
              <lb/>
            erit numerus, cuius ſemiſsis dabit rectam extra triangulum inter perpendicu-
              <lb/>
            larem, & </s>
            <s xml:id="echoid-s17748" xml:space="preserve">angulum obtuſum; </s>
            <s xml:id="echoid-s17749" xml:space="preserve">eadem vero ſemiſsis tertio lateri appoſita dabit
              <lb/>
            alteram rectam inter perpendicularem, & </s>
            <s xml:id="echoid-s17750" xml:space="preserve">angulum acutum.</s>
            <s xml:id="echoid-s17751" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1430" type="section" level="1" n="635">
          <head xml:id="echoid-head670" xml:space="preserve">Aliter, & facilius.</head>
          <p>
            <s xml:id="echoid-s17752" xml:space="preserve">FIAT, vt tertium latus, in quod demiſſa eſt perpendicularis, ad ſummam
              <lb/>
              <note position="left" xlink:label="note-502-02" xlink:href="note-502-02a" xml:space="preserve">Propoſ. 9.
                <lb/>
              triang. re-
                <lb/>
              ctil.</note>
            aliorum duorum laterum, ita differentia eorundem ad aliud, prouenietq́; </s>
            <s xml:id="echoid-s17753" xml:space="preserve">nu-
              <lb/>
            merus, ex quo rectam inter perpendicularem, & </s>
            <s xml:id="echoid-s17754" xml:space="preserve">angulum vtrumq; </s>
            <s xml:id="echoid-s17755" xml:space="preserve">inuenie-
              <lb/>
            mus, vt nuper diximus.</s>
            <s xml:id="echoid-s17756" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1432" type="section" level="1" n="636">
          <head xml:id="echoid-head671" xml:space="preserve">Aliter.</head>
          <p>
            <s xml:id="echoid-s17757" xml:space="preserve">CADENTE perpendiculari intra triangulum; </s>
            <s xml:id="echoid-s17758" xml:space="preserve">diuidatur ſemiſsis diffe-
              <lb/>
              <note position="left" xlink:label="note-502-03" xlink:href="note-502-03a" xml:space="preserve">Schol. pro-
                <lb/>
              poſ 9. triãg-
                <lb/>
              rectil.</note>
            rentiæ inter quadratum vttiuſvis laterum ambientium angulum, à quo per-
              <lb/>
            pendicularis eſt demiſſa, & </s>
            <s xml:id="echoid-s17759" xml:space="preserve">ſummam quadratorum ex alijs duobus lateribus de-
              <lb/>
            ſcriptorum, per latus, in quod perpendicularis cadit, produceturq́; </s>
            <s xml:id="echoid-s17760" xml:space="preserve">ſegmen-
              <lb/>
            tum baſis prope angulum, quem continẽt duo latera, quorum ſumma quadra-
              <lb/>
            torum fuit accepta; </s>
            <s xml:id="echoid-s17761" xml:space="preserve">hoc autem ſegmentum ex tota baſi detractum relinquet
              <lb/>
            alterum ſegmentum.</s>
            <s xml:id="echoid-s17762" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17763" xml:space="preserve">CADENTE vero perpendiculari extra triangulum, diuidatur ſemiſsis
              <lb/>
            differentiæ inter quadratum lateris angulo obtuſo oppoſiti, & </s>
            <s xml:id="echoid-s17764" xml:space="preserve">ſummam qua
              <lb/>
            dratorum ex alijs duobus lateribus deſcriptorum, per latus, in quod produ-
              <lb/>
            ctum perpendicularis cadit, procreabiturq; </s>
            <s xml:id="echoid-s17765" xml:space="preserve">linea extra triangulum inter per-
              <lb/>
            pendicularem, & </s>
            <s xml:id="echoid-s17766" xml:space="preserve">angulum obtuſum; </s>
            <s xml:id="echoid-s17767" xml:space="preserve">hæc vero toti baſi adiecta conficiet alte-
              <lb/>
            ram rectam inter perpendicularem, & </s>
            <s xml:id="echoid-s17768" xml:space="preserve">acutum angulum baſis.</s>
            <s xml:id="echoid-s17769" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17770" xml:space="preserve">QVOD ſi duo latera circa perpendicularem ſint æqualia, ſecabit perpen
              <lb/>
              <note position="left" xlink:label="note-502-04" xlink:href="note-502-04a" xml:space="preserve">Coroll. pro-
                <lb/>
              poſ. S. triãg.
                <lb/>
              rectil.</note>
            dicularis baſim bifariam. </s>
            <s xml:id="echoid-s17771" xml:space="preserve">Quare dimidiũ baſis dabit vtramq; </s>
            <s xml:id="echoid-s17772" xml:space="preserve">rectã quęſitam.</s>
            <s xml:id="echoid-s17773" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quærũtur
            <lb/>
          duo latera.</note>
        </div>
        <div xml:id="echoid-div1435" type="section" level="1" n="637">
          <head xml:id="echoid-head672" xml:space="preserve">10. DATIS omnibus angulis trianguli non
            <lb/>
          rectanguli, cum vno latere, inuenire alia duo
            <lb/>
          latera.</head>
          <p>
            <s xml:id="echoid-s17774" xml:space="preserve">FIAT, vt ſinus anguli dato lateri oppoſiti ad ſinum vtriusvis reliquo-
              <lb/>
              <note position="left" xlink:label="note-502-06" xlink:href="note-502-06a" xml:space="preserve">Propoſ. 10.
                <lb/>
              triang. re
                <lb/>
              ctil.</note>
            rum angulorum, ita latus datum ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s17775" xml:space="preserve">latus poſteriori huic
              <lb/>
            angulo oppoſitum. </s>
            <s xml:id="echoid-s17776" xml:space="preserve">Fiat rurſus, vt ſinus anguli dato lateri oppoſiti ad ſinum
              <lb/>
            tertij anguli, ita latus datum ad aliud, produceturq́; </s>
            <s xml:id="echoid-s17777" xml:space="preserve">tertium latus huic ter-
              <lb/>
            tio angulo oppoſitum.</s>
            <s xml:id="echoid-s17778" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17779" xml:space="preserve">SI triangulum ſit Iſoſceles, vnius tantum lateris inuentione opus eſt, ſi
              <lb/>
            vnum datum ſit, cum angulis. </s>
            <s xml:id="echoid-s17780" xml:space="preserve">Idem dicendum eſt de Scaleno, ſi duo eius late-
              <lb/>
            ra cum angulis data ſint. </s>
            <s xml:id="echoid-s17781" xml:space="preserve">In Aequilatero vero, ſi vnum latus detur, data e-
              <lb/>
            runt & </s>
            <s xml:id="echoid-s17782" xml:space="preserve">reliqua illi æqualia.</s>
            <s xml:id="echoid-s17783" xml:space="preserve"/>
          </p>
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