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

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        <div xml:id="echoid-div820" type="section" level="1" n="460">
          <p style="it">
            <s xml:id="echoid-s9866" xml:space="preserve">
              <pb o="315" file="327" n="327" rhead=""/>
            _180._ </s>
            <s xml:id="echoid-s9867" xml:space="preserve">Quare ſi, vtiam demonſtratum eſt, beneficio buius aggregatimino-
              <lb/>
            ris, & </s>
            <s xml:id="echoid-s9868" xml:space="preserve">proportionis datæ, vtrum arcum, vel angulum inquir amus, & </s>
            <s xml:id="echoid-s9869" xml:space="preserve">
              <lb/>
            vtrumq, inuentum ſigillatim ex grad. </s>
            <s xml:id="echoid-s9870" xml:space="preserve">_180._ </s>
            <s xml:id="echoid-s9871" xml:space="preserve">demamus, noti relinquentur
              <lb/>
            arcus, vel anguli quæſiti.</s>
            <s xml:id="echoid-s9872" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9873" xml:space="preserve">QVOD ſi quando proportio ſinuum data ſit proportio æqualitatis, hoc
              <lb/>
              <note position="right" xlink:label="note-327-01" xlink:href="note-327-01a" xml:space="preserve">Quando fi-
                <lb/>
              nuum pro-
                <lb/>
              portio da-
                <lb/>
              ta eſt {pro}por
                <lb/>
              tio æquali-
                <lb/>
              tatis.</note>
            eſt, ſinus ſint æquales, erunt quoq; </s>
            <s xml:id="echoid-s9874" xml:space="preserve">tam duo arcus, quam duo anguli æqua-
              <lb/>
            les, vt in deſin. </s>
            <s xml:id="echoid-s9875" xml:space="preserve">ſinuum oſtendimus. </s>
            <s xml:id="echoid-s9876" xml:space="preserve">Quapropter ſemiſsis dati aggregati dabit
              <lb/>
            vtrumq; </s>
            <s xml:id="echoid-s9877" xml:space="preserve">arcum, ſiue angulum cognitum. </s>
            <s xml:id="echoid-s9878" xml:space="preserve">Dato igitur aggregato duorum ar-
              <lb/>
            cuum, quorum ſinguli ſemicirculo ſint minores, vel duorum angulorum re-
              <lb/>
            ctilineorum, &</s>
            <s xml:id="echoid-s9879" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9880" xml:space="preserve">vtrumq; </s>
            <s xml:id="echoid-s9881" xml:space="preserve">illorum ſigillatim exhibuimus notum. </s>
            <s xml:id="echoid-s9882" xml:space="preserve">Quod fa-
              <lb/>
            ciendum erat.</s>
            <s xml:id="echoid-s9883" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div831" type="section" level="1" n="461">
          <head xml:id="echoid-head493" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s9884" xml:space="preserve">_SI_ aggregatum duorum arcuum, vel angulorum fuerit præcisè grad. </s>
            <s xml:id="echoid-s9885" xml:space="preserve">_180_ non
              <lb/>
              <note position="right" xlink:label="note-327-02" xlink:href="note-327-02a" xml:space="preserve">Quãdo ag-
                <lb/>
              gregatũ da
                <lb/>
              tũ continet
                <lb/>
              grad. 180.
                <lb/>
              problema
                <lb/>
              ſolui non
                <lb/>
              poteſt.</note>
            poterunt arcus illi, vel anguli cognoſci, etiam ſi proportio, quam eorum ſinus habent,
              <lb/>
            data ſit. </s>
            <s xml:id="echoid-s9886" xml:space="preserve">Nam quomodocunq; </s>
            <s xml:id="echoid-s9887" xml:space="preserve">ſemicirculus in duos arcus ſecetur, habebunt ſemper
              <lb/>
            eorum ſinus proportionem æqualitatis, cum vnus, & </s>
            <s xml:id="echoid-s9888" xml:space="preserve">idem ſinus ſit vtriuſq; </s>
            <s xml:id="echoid-s9889" xml:space="preserve">arcus, vt
              <lb/>
            ad defin. </s>
            <s xml:id="echoid-s9890" xml:space="preserve">ſinuum demonſtrauimus. </s>
            <s xml:id="echoid-s9891" xml:space="preserve">_Ne_ceſſe eſt ergo, aggregatum datum vel minus eſ-
              <lb/>
            ſe, vel maius, quam grad. </s>
            <s xml:id="echoid-s9892" xml:space="preserve">_180._ </s>
            <s xml:id="echoid-s9893" xml:space="preserve">vt in propoſitione expreſſum eſt.</s>
            <s xml:id="echoid-s9894" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div833" type="section" level="1" n="462">
          <head xml:id="echoid-head494" xml:space="preserve">PROBL. 4. PROPOS. 7.</head>
          <note position="right" xml:space="preserve">Ex diffe-
            <lb/>
          rentia data
            <lb/>
          duorum, ar
            <lb/>
          cuũ, quorũ
            <lb/>
          quilibet ſe-
            <lb/>
          micirculo
            <lb/>
          minor ſit,
            <lb/>
          vel duorũ
            <lb/>
          angulorũ,
            <lb/>
          vna cũ pro
            <lb/>
          portione,
            <lb/>
          quã eorum
            <lb/>
          ſinus ha-
            <lb/>
          bent, vter
            <lb/>
          cognoſcit.</note>
          <p>
            <s xml:id="echoid-s9895" xml:space="preserve">DATA differentia duorum arcuum, quorum
              <lb/>
            ſinguli ſemicirculo ſint minores, vel duorum an-
              <lb/>
            gulorum rectilineorum, vna cum proportione,
              <lb/>
            quam eorum ſinus habent: </s>
            <s xml:id="echoid-s9896" xml:space="preserve">vtrumq; </s>
            <s xml:id="echoid-s9897" xml:space="preserve">illorum ſigil-
              <lb/>
            latim notum efficere.</s>
            <s xml:id="echoid-s9898" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9899" xml:space="preserve">IN circulo ABCD, cuius centrum E, ſuperet arcus BF, ſemicirculo
              <lb/>
              <figure xlink:label="fig-327-01" xlink:href="fig-327-01a" number="173">
                <image file="327-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/327-01"/>
              </figure>
              <note position="right" xlink:label="note-327-04" xlink:href="note-327-04a" xml:space="preserve">Quãdo ſi-
                <lb/>
              nꝰ maioris
                <lb/>
              arcus, vel
                <lb/>
              anguli ad
                <lb/>
              ſinum mi-
                <lb/>
              noris ha-
                <lb/>
              bet propor
                <lb/>
              tionẽ maio
                <lb/>
              ris inęqua-
                <lb/>
              litatis.</note>
            minor arcum DF, arcu BD, vel angu-
              <lb/>
            lus BEF, angulum DEF, angulo BED,
              <lb/>
            ſitque differentia hæc, nempe arcus BD, vel
              <lb/>
            angulus BED, data grad. </s>
            <s xml:id="echoid-s9900" xml:space="preserve">60. </s>
            <s xml:id="echoid-s9901" xml:space="preserve">Proportio
              <lb/>
            quoque ſinus maioris arcus BF, vel angu-
              <lb/>
            li BEF, ad ſinum arcus minoris DF, vel
              <lb/>
            anguli DEF, ſit primo maioris inæqualita-
              <lb/>
            tis data, eadem, quæ 11. </s>
            <s xml:id="echoid-s9902" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s9903" xml:space="preserve">quod quidem
              <lb/>
            contingit, quando duo arcus BF, DF, ſemi-
              <lb/>
            circulo ſunt minores ſimul ſumpti. </s>
            <s xml:id="echoid-s9904" xml:space="preserve">Oportet
              <lb/>
            ex his vtrumque arcum BF, DF, ſiue vtrum-
              <lb/>
            que angulum BEF, DEF, cognitum facere.
              <lb/>
            </s>
            <s xml:id="echoid-s9905" xml:space="preserve">Ducta chorda BD, & </s>
            <s xml:id="echoid-s9906" xml:space="preserve">diametro CF, </s>
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    </echo>
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