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

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        <div xml:id="echoid-div1262" type="section" level="1" n="596">
          <head xml:id="echoid-head631" xml:space="preserve">Inuentio anguli non recti vtriusvis.</head>
          <p>
            <s xml:id="echoid-s15615" xml:space="preserve">Quando datur {1. </s>
            <s xml:id="echoid-s15616" xml:space="preserve">Arcus recto angulo oppoſitus: </s>
            <s xml:id="echoid-s15617" xml:space="preserve">Et \ȧrcus circa angulum rectum quę- \\ ſito angulo oppoſitus. </s>
            <s xml:id="echoid-s15618" xml:space="preserve">\\ 2. </s>
            <s xml:id="echoid-s15619" xml:space="preserve">Arcus circa angulum rectum: </s>
            <s xml:id="echoid-s15620" xml:space="preserve">Et \ȧlter angulus non rectus. </s>
            <s xml:id="echoid-s15621" xml:space="preserve">\\ 3. </s>
            <s xml:id="echoid-s15622" xml:space="preserve">Vterq; </s>
            <s xml:id="echoid-s15623" xml:space="preserve">arcus circa rectum angulum. </s>
            <s xml:id="echoid-s15624" xml:space="preserve">\\ 4. </s>
            <s xml:id="echoid-s15625" xml:space="preserve">Arcus recto angulo oppoſitus: </s>
            <s xml:id="echoid-s15626" xml:space="preserve">Et \ȧrcus circa rectum angulum quę- \\ ſito angulo adiacens. </s>
            <s xml:id="echoid-s15627" xml:space="preserve">\\ 5. </s>
            <s xml:id="echoid-s15628" xml:space="preserve">Arcus recto angulo oppoſitus: </s>
            <s xml:id="echoid-s15629" xml:space="preserve">Et \ȧlter angulus non rectus. </s>
            <s xml:id="echoid-s15630" xml:space="preserve">\\ 6. </s>
            <s xml:id="echoid-s15631" xml:space="preserve">Arcus circa angulum rectum quæ- \\ ſito angulo adiacens: </s>
            <s xml:id="echoid-s15632" xml:space="preserve">Et alter an- \ġulus non rectus huic arcui op- \ṗoſitus: </s>
            <s xml:id="echoid-s15633" xml:space="preserve">Probl 1. </s>
            <s xml:id="echoid-s15634" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15635" xml:space="preserve">41. </s>
            <s xml:id="echoid-s15636" xml:space="preserve">& </s>
            <s xml:id="echoid-s15637" xml:space="preserve">\\ (Probl. </s>
            <s xml:id="echoid-s15638" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15639" xml:space="preserve">55. </s>
            <s xml:id="echoid-s15640" xml:space="preserve">\\ Probl. </s>
            <s xml:id="echoid-s15641" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15642" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15643" xml:space="preserve">42. </s>
            <s xml:id="echoid-s15644" xml:space="preserve">\\ Probl. </s>
            <s xml:id="echoid-s15645" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15646" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15647" xml:space="preserve">44. </s>
            <s xml:id="echoid-s15648" xml:space="preserve">\\ (& </s>
            <s xml:id="echoid-s15649" xml:space="preserve">Probl. </s>
            <s xml:id="echoid-s15650" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15651" xml:space="preserve">48. </s>
            <s xml:id="echoid-s15652" xml:space="preserve">\\ Probl. </s>
            <s xml:id="echoid-s15653" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15654" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15655" xml:space="preserve">45. </s>
            <s xml:id="echoid-s15656" xml:space="preserve">\\ (& </s>
            <s xml:id="echoid-s15657" xml:space="preserve">Probl. </s>
            <s xml:id="echoid-s15658" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15659" xml:space="preserve">51. </s>
            <s xml:id="echoid-s15660" xml:space="preserve">\\ Probl. </s>
            <s xml:id="echoid-s15661" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15662" xml:space="preserve">47. </s>
            <s xml:id="echoid-s15663" xml:space="preserve">\\ Probl. </s>
            <s xml:id="echoid-s15664" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15665" xml:space="preserve">56. </s>
            <s xml:id="echoid-s15666" xml:space="preserve">& </s>
            <s xml:id="echoid-s15667" xml:space="preserve">\\ (Probl. </s>
            <s xml:id="echoid-s15668" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15669" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15670" xml:space="preserve">42.</s>
            <s xml:id="echoid-s15671" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15672" xml:space="preserve">SED quia hactenus de eo ſolum triangulo rectangulo egimus, cuius nullus ar-
              <lb/>
              <note position="right" xlink:label="note-455-01" xlink:href="note-455-01a" xml:space="preserve">Quid agen
                <lb/>
              dũ in trian
                <lb/>
              gulo rectã-
                <lb/>
              gulo, ĩ quo
                <lb/>
              quadrãtes
                <lb/>
              ſunt.</note>
            cuum quadrans eſt, doceamus breuiter, (rem quidem cuilibet perfacilem ex demon-
              <lb/>
            ſtratis) quo pacto nos gerere debeamus in eo, quod duos ſaltem arcus habet quadran
              <lb/>
            tes, & </s>
            <s xml:id="echoid-s15673" xml:space="preserve">duos angulos rectos. </s>
            <s xml:id="echoid-s15674" xml:space="preserve">Nullum enim triangulum eſſe poteſt rectangulum, cuius
              <lb/>
            vnus duntaxat arcus ſit quadrans, ſed vel nullus erit quadrans, vel omnes tres qua-
              <lb/>
              <note position="right" xlink:label="note-455-02" xlink:href="note-455-02a" xml:space="preserve">Coroll. 38.
                <lb/>
              huius.</note>
            drantes erunt, vel duo, &</s>
            <s xml:id="echoid-s15675" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15676" xml:space="preserve">Sit ergo triangulum ſphæricum
              <emph style="sc">ABC</emph>
            , in quo angulus
              <lb/>
              <emph style="sc">B</emph>
            , ponatur rectus, & </s>
            <s xml:id="echoid-s15677" xml:space="preserve">arcus
              <emph style="sc">AB</emph>
            , circa angulum rectum quadrans. </s>
            <s xml:id="echoid-s15678" xml:space="preserve">Hoc poſito, erit
              <lb/>
            & </s>
            <s xml:id="echoid-s15679" xml:space="preserve">arcus
              <emph style="sc">AC</emph>
            , recto angulo oppoſitus, quadrans. </s>
            <s xml:id="echoid-s15680" xml:space="preserve">Quare cum duo arcus
              <emph style="sc">AB, AC</emph>
            ,
              <lb/>
              <note position="right" xlink:label="note-455-03" xlink:href="note-455-03a" xml:space="preserve">35. huius.</note>
            quadrantes ſint, erunt duo anguli
              <emph style="sc">B</emph>
            , C, recti; </s>
            <s xml:id="echoid-s15681" xml:space="preserve">ac propte-
              <lb/>
              <note position="right" xlink:label="note-455-04" xlink:href="note-455-04a" xml:space="preserve">25. huius.</note>
            rea
              <emph style="sc">A</emph>
            , polus erit arcus
              <emph style="sc">BC</emph>
            ; </s>
            <s xml:id="echoid-s15682" xml:space="preserve">& </s>
            <s xml:id="echoid-s15683" xml:space="preserve">
              <emph style="sc">BC</emph>
            , arcus anguli
              <emph style="sc">A</emph>
            , ex
              <lb/>
              <note position="right" xlink:label="note-455-05" xlink:href="note-455-05a" xml:space="preserve">Coroll. 26.
                <lb/>
              huius.</note>
              <figure xlink:label="fig-455-01" xlink:href="fig-455-01a" number="315">
                <image file="455-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/455-01"/>
              </figure>
            definitione 6. </s>
            <s xml:id="echoid-s15684" xml:space="preserve">Igitur ſi datus ſit tertius angulus A, datus
              <lb/>
            etiam erit tertius arcus
              <emph style="sc">BC</emph>
            : </s>
            <s xml:id="echoid-s15685" xml:space="preserve">Et contra, ſi datus ſit ter-
              <lb/>
            tius arcus
              <emph style="sc">BC</emph>
            , datus quoque erit tertius angulus
              <emph style="sc">A</emph>
            . </s>
            <s xml:id="echoid-s15686" xml:space="preserve">Eo-
              <lb/>
            dem modo, ſi alter arcus BC, circa angulum rectum qua-
              <lb/>
            drans ponatur, ostendemus & </s>
            <s xml:id="echoid-s15687" xml:space="preserve">arcum
              <emph style="sc">A</emph>
            C, recto angulo
              <lb/>
            oppoſitum quadrantem eſſe, & </s>
            <s xml:id="echoid-s15688" xml:space="preserve">angulum
              <emph style="sc">A</emph>
            , rectum. </s>
            <s xml:id="echoid-s15689" xml:space="preserve">Si ergo
              <lb/>
            detur tertius angulus
              <emph style="sc">C</emph>
            , dabitur quoque tertius arcus
              <lb/>
              <emph style="sc">AB</emph>
            , & </s>
            <s xml:id="echoid-s15690" xml:space="preserve">contra, vt prius. </s>
            <s xml:id="echoid-s15691" xml:space="preserve">Quòd ſi quantitas tertij angu-
              <lb/>
            li, aut arcus datanon fuerit, nihilcerti colligi poterit, licet duo alij anguli recti </s>
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