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

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          <p>
            <s xml:id="echoid-s15387" xml:space="preserve">
              <pb o="438" file="450" n="450" rhead=""/>
            duo circuli maximi EH, GH, ſe mutuo ſecant in H, & </s>
            <s xml:id="echoid-s15388" xml:space="preserve">ex punctis E, F, arcus
              <lb/>
            EH, ad arcum GH, ducti ſunt arcus perpendiculares EG, FI; </s>
            <s xml:id="echoid-s15389" xml:space="preserve">erit, vt ſinus
              <lb/>
              <figure xlink:label="fig-450-01" xlink:href="fig-450-01a" number="310">
                <image file="450-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/450-01"/>
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            totus quadrantis EH, ad ſecantẽ complementi
              <lb/>
              <note position="left" xlink:label="note-450-01" xlink:href="note-450-01a" xml:space="preserve">Theor. 8.
                <lb/>
              ſcholij 40.
                <lb/>
              huius.</note>
            arcus FI, hoc eſt, ad ſecãtem arcus CF, qui com
              <lb/>
            plementum etiam eſt arcus BC, ita ſinus arcus
              <lb/>
            FH, hoc eſt, arcus DE, (eſt enim arcus FH, ar-
              <lb/>
            cui DE, æqualis, ob quadrantes EH, DF, æqua
              <lb/>
            les) qui arcus eſt anguli A, ad ſecantem comple-
              <lb/>
            menti arcus EG, id eſt, ad ſecantem arcus EC,
              <lb/>
            qui complementum quoque eſt arcus AC: </s>
            <s xml:id="echoid-s15390" xml:space="preserve">Et
              <lb/>
            permutãdo, vt ſinus totus ad ſinum arcus DE,
              <lb/>
            hoc eſt, anguli A, ita ſecans complementi arcus BC, ad ſecantem comple-
              <lb/>
            menti arcus AC. </s>
            <s xml:id="echoid-s15391" xml:space="preserve">Non ſecus oſtendemus, ſi aliter figura conſtruatur, ita
              <lb/>
            eſſe ſinum totum ad ſinum anguli C, vt eſt ſecans complementi arcus AB, ad
              <lb/>
            ſecantem complementi arcus AC. </s>
            <s xml:id="echoid-s15392" xml:space="preserve">In omni igitur triangulo ſphærico rectan-
              <lb/>
            gulo, &</s>
            <s xml:id="echoid-s15393" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15394" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s15395" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1246" type="section" level="1" n="588">
          <head xml:id="echoid-head623" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s15396" xml:space="preserve">SEQVITVR ex hoc theoremate ſequens problema, quod aliter etiam abſol-
              <lb/>
            nimus in problemate. </s>
            <s xml:id="echoid-s15397" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15398" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15399" xml:space="preserve">41.</s>
            <s xml:id="echoid-s15400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15401" xml:space="preserve">IN triangulo ſphęrico rectangulo, dato vtrolibet angulorum non
              <lb/>
            rectorum, cum arcu oppoſito, inueſtigare arcum recto angulo op-
              <lb/>
            poſitum, vnà cum tertio arcu, & </s>
            <s xml:id="echoid-s15402" xml:space="preserve">reliquo angulo non recto: </s>
            <s xml:id="echoid-s15403" xml:space="preserve">dummo-
              <lb/>
            do conſtet, num arcus angulo recto oppoſitus ſit maior quadrante,
              <lb/>
            minorve: </s>
            <s xml:id="echoid-s15404" xml:space="preserve">aut an alter angulus non rectus ſit acutus, obtuſusve.</s>
            <s xml:id="echoid-s15405" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15406" xml:space="preserve">IN triangulo ABC, rectum habente angulum C, datus ſit angulus
              <emph style="sc">B</emph>
            , cum ar-
              <lb/>
              <figure xlink:label="fig-450-02" xlink:href="fig-450-02a" number="311">
                <image file="450-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/450-02"/>
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            cu
              <emph style="sc">AC</emph>
            . </s>
            <s xml:id="echoid-s15407" xml:space="preserve">Dico dari quoque arcum AB, vnà cum arcu
              <lb/>
            BC, & </s>
            <s xml:id="echoid-s15408" xml:space="preserve">angulo A. </s>
            <s xml:id="echoid-s15409" xml:space="preserve">Cum namque ſit, vt ſinus totus ad
              <lb/>
              <note position="left" xlink:label="note-450-02" xlink:href="note-450-02a" xml:space="preserve">54.huius.</note>
            ſinum anguli B, dati, ita ſecans complementi arcus da-
              <lb/>
            ti
              <emph style="sc">AC</emph>
            , ad ſecantem complementiarcus
              <emph style="sc">AB</emph>
            :</s>
            <s xml:id="echoid-s15410" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15411" xml:space="preserve">SI fiat, vt ſinus totus ad ſinum dati anguli,
              <lb/>
              <note position="left" xlink:label="note-450-03" xlink:href="note-450-03a" xml:space="preserve">Praxis.</note>
            ita ſecans complementi dati arcus ad aliud, pro-
              <lb/>
            ducetur ſecans complementi arcus recto angulo
              <lb/>
            oppoſiti, qui inquiritur. </s>
            <s xml:id="echoid-s15412" xml:space="preserve">Ex arcubus vero AB,
              <lb/>
            AC, cognitis notus fiet tertius arcus BC, ex problemate propoſ. </s>
            <s xml:id="echoid-s15413" xml:space="preserve">43.
              <lb/>
            </s>
            <s xml:id="echoid-s15414" xml:space="preserve">Item ex arcubus AB, BC, notis cognitus fiet angulus A, ex problema-
              <lb/>
            te 1. </s>
            <s xml:id="echoid-s15415" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15416" xml:space="preserve">41.</s>
            <s xml:id="echoid-s15417" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15418" xml:space="preserve">OPORTET autem hic conſtare, num arcus quæſitus
              <emph style="sc">AB</emph>
            , ſit quadrante ma-
              <lb/>
            ior, an minor: </s>
            <s xml:id="echoid-s15419" xml:space="preserve">Vel an reliquus angulus non rectus
              <emph style="sc">A</emph>
            , ſit acutus, obtuſus ve, alioquin
              <lb/>
            neſciremus, qualis arcus pro
              <emph style="sc">AB</emph>
            , aſſumendus ſit, cum poßit eße maior quadrante, vel
              <lb/>
            minor, vt perſpicuum eſt. </s>
            <s xml:id="echoid-s15420" xml:space="preserve">Id quod ad problema 3. </s>
            <s xml:id="echoid-s15421" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15422" xml:space="preserve">41. </s>
            <s xml:id="echoid-s15423" xml:space="preserve">monuimus: </s>
            <s xml:id="echoid-s15424" xml:space="preserve">Vbi etiam
              <lb/>
            copernici, atque Ioan Regiom. </s>
            <s xml:id="echoid-s15425" xml:space="preserve">errorem aperuimus.</s>
            <s xml:id="echoid-s15426" xml:space="preserve"/>
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