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

Table of figures

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        <div xml:id="echoid-div1175" type="section" level="1" n="563">
          <head xml:id="echoid-head598" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s14774" xml:space="preserve">HINC colligemus duo ſequentia problemata.</s>
            <s xml:id="echoid-s14775" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1176" type="section" level="1" n="564">
          <head xml:id="echoid-head599" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s14776" xml:space="preserve">IN triangulo ſphærico rectangulo, dato alterutro arcuum circa
              <lb/>
            angulum rectum, cum alterutro angulorum non rectorum, reperire
              <lb/>
            alium arcum circa rectum angulum, & </s>
            <s xml:id="echoid-s14777" xml:space="preserve">reliquum angulum non re-
              <lb/>
            ctum, cum arcu, qui recto angulo opponitur: </s>
            <s xml:id="echoid-s14778" xml:space="preserve">dum modo, quando
              <lb/>
            angulus datus opponitur arcui dato, conſtet, an reliquus arcus circa
              <lb/>
            rectum angulum ſit quadrante minor, maiorve; </s>
            <s xml:id="echoid-s14779" xml:space="preserve">vel an reliquus an-
              <lb/>
            gulus non rectus ſit acutus, obtuſusve.</s>
            <s xml:id="echoid-s14780" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14781" xml:space="preserve">IN triangulo
              <emph style="sc">ABC</emph>
            , cuius angulus
              <emph style="sc">C</emph>
            , rectus, da-
              <lb/>
              <figure xlink:label="fig-435-01" xlink:href="fig-435-01a" number="289">
                <image file="435-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/435-01"/>
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            tus ſit primum arcus AC, cum angulo
              <emph style="sc">A</emph>
            , ſibi adia-
              <lb/>
            cente. </s>
            <s xml:id="echoid-s14782" xml:space="preserve">Dico dari quoque arcum BC, vnà cum angu-
              <lb/>
            lo B, & </s>
            <s xml:id="echoid-s14783" xml:space="preserve">arcu
              <emph style="sc">Ab</emph>
            . </s>
            <s xml:id="echoid-s14784" xml:space="preserve">Quoniam enim eſt, vt ſinus totus
              <lb/>
              <note position="right" xlink:label="note-435-01" xlink:href="note-435-01a" xml:space="preserve">44. huius.</note>
            ad ſinum arcus AC, ita tangens anguli A, ad tangen-
              <lb/>
            tem arcus
              <emph style="sc">BC</emph>
            :</s>
            <s xml:id="echoid-s14785" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14786" xml:space="preserve">SI (quando datur arcus cum angulo adia-
              <lb/>
              <note position="right" xlink:label="note-435-02" xlink:href="note-435-02a" xml:space="preserve">Praxis, cũ
                <lb/>
              datur arcus
                <lb/>
              cum angu-
                <lb/>
              lo adiacẽte.</note>
            cente) fiat, vt ſinus totus ad ſinum dati arcus,
              <lb/>
            ita tangens anguli dati ad aliud, producetur
              <lb/>
            tangens arcus quæſiti. </s>
            <s xml:id="echoid-s14787" xml:space="preserve">Ex eodem vero arcu dato, & </s>
            <s xml:id="echoid-s14788" xml:space="preserve">argulo dato, inue-
              <lb/>
            nietur alter angulus non rectus, et arcus recto angulo oppoſitus, vt in pro-
              <lb/>
            blemate 2. </s>
            <s xml:id="echoid-s14789" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14790" xml:space="preserve">42. </s>
            <s xml:id="echoid-s14791" xml:space="preserve">demonſtrauimus.</s>
            <s xml:id="echoid-s14792" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14793" xml:space="preserve">AN vero arcus quæſitus
              <emph style="sc">BC</emph>
            , ſit quadrante minor, maiorue, indicabit angulus
              <lb/>
            datus
              <emph style="sc">A</emph>
            . </s>
            <s xml:id="echoid-s14794" xml:space="preserve">Nam ſi fuerit acutus, erit arcus
              <emph style="sc">BC</emph>
            , quadrante minor; </s>
            <s xml:id="echoid-s14795" xml:space="preserve">ſi vero obtuſus,
              <lb/>
              <note position="right" xlink:label="note-435-03" xlink:href="note-435-03a" xml:space="preserve">34. huius.</note>
            quadrante maior.</s>
            <s xml:id="echoid-s14796" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14797" xml:space="preserve">SIT deinde datus arcus
              <emph style="sc">AC</emph>
            , cum angulo
              <emph style="sc">B</emph>
            , ſibi oppoſito, conſtetq́; </s>
            <s xml:id="echoid-s14798" xml:space="preserve">præterea de
              <lb/>
            altero arcu
              <emph style="sc">BC</emph>
            , num quadrante minor ſit, an maior; </s>
            <s xml:id="echoid-s14799" xml:space="preserve">vel an alter angulus A, acu-
              <lb/>
            tus ſit, an obtuſus. </s>
            <s xml:id="echoid-s14800" xml:space="preserve">Dico rurſum dari arcum
              <emph style="sc">BC</emph>
            , vnà cum angulo
              <emph style="sc">B</emph>
            , & </s>
            <s xml:id="echoid-s14801" xml:space="preserve">arcu
              <emph style="sc">AB</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s14802" xml:space="preserve">Cum enim ſit, vt tangens anguli
              <emph style="sc">B</emph>
            , ad tangentem arcus
              <emph style="sc">AC</emph>
            , ita ſinus totus ad ſi-
              <lb/>
              <note position="right" xlink:label="note-435-04" xlink:href="note-435-04a" xml:space="preserve">44. huius.</note>
            num arcus
              <emph style="sc">BC</emph>
            :</s>
            <s xml:id="echoid-s14803" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14804" xml:space="preserve">SI (quando datur arcus cum angulo oppoſito) fiat, vt tangens angu-
              <lb/>
              <note position="right" xlink:label="note-435-05" xlink:href="note-435-05a" xml:space="preserve">Praxis. cũ
                <lb/>
              datur arcus
                <lb/>
              cũ angulo
                <lb/>
              oppoſito.</note>
            li dati ad tangentem dati arcus, ita ſinus totus ad aliud, reperietur ſinus
              <lb/>
            arcus quæſiti. </s>
            <s xml:id="echoid-s14805" xml:space="preserve">Ex dato vero arcu, & </s>
            <s xml:id="echoid-s14806" xml:space="preserve">angulo dato dabitur & </s>
            <s xml:id="echoid-s14807" xml:space="preserve">alter angu-
              <lb/>
            lus non rectus, & </s>
            <s xml:id="echoid-s14808" xml:space="preserve">arcus recto angulo oppoſitus, vt in problemate 2. </s>
            <s xml:id="echoid-s14809" xml:space="preserve">pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s14810" xml:space="preserve">42. </s>
            <s xml:id="echoid-s14811" xml:space="preserve">diximus.</s>
            <s xml:id="echoid-s14812" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14813" xml:space="preserve">OPORTET autem conſtare, an arcus
              <emph style="sc">BC</emph>
            , ſit quadrante minor, an maior, vt
              <lb/>
            ſciamus, qualis arcus inuento ſinui reſpondens accipiẽdus ſit, an videlicet minor qua-
              <lb/>
            dr ante, an vero maior. </s>
            <s xml:id="echoid-s14814" xml:space="preserve">Quòd ſi conſtaret de angulo
              <emph style="sc">A</emph>
            , qualis ſit, ſtatim cognoſce-
              <lb/>
            remus, qualis ſit arcus
              <emph style="sc">BC</emph>
            . </s>
            <s xml:id="echoid-s14815" xml:space="preserve">Exiſtente enim angulo A, acuto, erit arcus BC, qua-
              <lb/>
              <note position="right" xlink:label="note-435-06" xlink:href="note-435-06a" xml:space="preserve">34. huius.</note>
            drante minor: </s>
            <s xml:id="echoid-s14816" xml:space="preserve">exiſtente vero obtuſo, quadrante maior. </s>
            <s xml:id="echoid-s14817" xml:space="preserve">Sic etiam, ſi ſciretur, </s>
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