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

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        <div xml:id="echoid-div503" type="section" level="1" n="246">
          <pb o="179" file="191" n="191" rhead=""/>
          <p>
            <s xml:id="echoid-s6688" xml:space="preserve">PRAETEREA, cum latus trianguli æquilateri in circulo deſcripti ſit
              <lb/>
              <note position="right" xlink:label="note-191-01" xlink:href="note-191-01a" xml:space="preserve">12. tertij-
                <lb/>
              dec.</note>
            potentia triplum ſemidiametri eiuſdem circuli, efficitur, vt quadratum ſe-
              <lb/>
            midiametri triplicatum det quadratum lateris triãguli 300000000000000. </s>
            <s xml:id="echoid-s6689" xml:space="preserve">cu-
              <lb/>
            ius radix quadrata idem latus exhibebit partium 17320508.</s>
            <s xml:id="echoid-s6690" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6691" xml:space="preserve">SIT inſuper AB, ſemidiameter circuli cuiuſuis, qua diuiſa ſecundum ex-
              <lb/>
              <note position="right" xlink:label="note-191-02" xlink:href="note-191-02a" xml:space="preserve">30.ſexti.</note>
            tremam ac mediam rationem
              <lb/>
              <figure xlink:label="fig-191-01" xlink:href="fig-191-01a" number="141">
                <image file="191-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/191-01"/>
              </figure>
            in C, vt maius ſegmentum ſit
              <lb/>
            BC; </s>
            <s xml:id="echoid-s6692" xml:space="preserve">producta autem AB, & </s>
            <s xml:id="echoid-s6693" xml:space="preserve">
              <lb/>
            abſciſſa BD, quæ maiori ſeg-
              <lb/>
            mento BC, ſit æqualis; </s>
            <s xml:id="echoid-s6694" xml:space="preserve">erit
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s6695" xml:space="preserve">AD, in B, diuiſa ſecundum extremam ac mediam rationem, maiusq́;
              <lb/>
            </s>
            <s xml:id="echoid-s6696" xml:space="preserve">
              <note position="right" xlink:label="note-191-03" xlink:href="note-191-03a" xml:space="preserve">5. terrijdec.
                <lb/>
              coroll. 15.6
                <lb/>
              Schol. 9. 13</note>
            ſegmentum erit AB: </s>
            <s xml:id="echoid-s6697" xml:space="preserve">quod cum ſit latus hexagoni in circulo, cuius ſemidia-
              <lb/>
            meter AB; </s>
            <s xml:id="echoid-s6698" xml:space="preserve">erit BD, latus decagoni in eodem circulo. </s>
            <s xml:id="echoid-s6699" xml:space="preserve">Quod hac ratione
              <lb/>
            notum efficietur. </s>
            <s xml:id="echoid-s6700" xml:space="preserve">Secta AB, bifariam in E, erit quadratum rectæ DE, com-
              <lb/>
            poſitæ ex minori ſegmento DB, & </s>
            <s xml:id="echoid-s6701" xml:space="preserve">dimidio BE, maioris ſegmenti BA, quin-
              <lb/>
              <note position="right" xlink:label="note-191-04" xlink:href="note-191-04a" xml:space="preserve">3. tertijdec.</note>
            tuplum quadrati rectæ BE, quæ cognita eſt, cum ſit ſemiſsis ſemidiametri
              <lb/>
            AB, ac proinde partium 5000000. </s>
            <s xml:id="echoid-s6702" xml:space="preserve">Quare ſi quadratum rectæ BE, quincupli-
              <lb/>
            cetur, fiet quadratum rectæ DE, 125000000000000. </s>
            <s xml:id="echoid-s6703" xml:space="preserve">cuius radix quadrata
              <lb/>
            dabit rectam DE, partium 11180340. </s>
            <s xml:id="echoid-s6704" xml:space="preserve">ex qua ſi dematur recta BE, partium
              <lb/>
            5000000. </s>
            <s xml:id="echoid-s6705" xml:space="preserve">reliquum erit BD, latus decagoni partium 6180340.</s>
            <s xml:id="echoid-s6706" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6707" xml:space="preserve">POSTREMO, quoniam pentagoni latus poteſt & </s>
            <s xml:id="echoid-s6708" xml:space="preserve">latus hexagoni, & </s>
            <s xml:id="echoid-s6709" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-191-05" xlink:href="note-191-05a" xml:space="preserve">10. tertij-
                <lb/>
              dec.</note>
            latus decagoni; </s>
            <s xml:id="echoid-s6710" xml:space="preserve">ſi quadratum lateris hexagoni 100000000000000. </s>
            <s xml:id="echoid-s6711" xml:space="preserve">& </s>
            <s xml:id="echoid-s6712" xml:space="preserve">quadra-
              <lb/>
            tum lateris decagoni 38196602515600. </s>
            <s xml:id="echoid-s6713" xml:space="preserve">ſimul componantur, fiet quadratum
              <lb/>
            lateris pentagoni 138196602515600. </s>
            <s xml:id="echoid-s6714" xml:space="preserve">cuius radix quadrata dabit latus pen-
              <lb/>
            tagoni partium 11755705. </s>
            <s xml:id="echoid-s6715" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s6716" xml:space="preserve">ita latera trianguli æquilateri, quadrati, pen
              <lb/>
            tagoni, hexagoni, & </s>
            <s xml:id="echoid-s6717" xml:space="preserve">decagoni nota facta ſunt in partibus diametri circuli, in
              <lb/>
            quo deſcribuntur. </s>
            <s xml:id="echoid-s6718" xml:space="preserve">Ex data igitur circuli diametro quotlibet particularum,
              <lb/>
            latera trianguli æquilateri, quadrati, &</s>
            <s xml:id="echoid-s6719" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6720" xml:space="preserve">inueſtigauimus. </s>
            <s xml:id="echoid-s6721" xml:space="preserve">Quod erat fa-
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            ciendum.</s>
            <s xml:id="echoid-s6722" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div508" type="section" level="1" n="247">
          <head xml:id="echoid-head274" xml:space="preserve">PROBL. 5. PROP. 13.</head>
          <note position="right" xml:space="preserve">Qua ratio-
            <lb/>
          ne ex dua-
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          buschordis
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          cognitis in
            <lb/>
          ueſtigetur
            <lb/>
          chorda dif-
            <lb/>
          ferentiæ,
            <lb/>
          qua arcus
            <lb/>
          chordarũ
            <lb/>
          datarũ in-
            <lb/>
          ter ſe diffe
            <lb/>
          runt.</note>
          <p>
            <s xml:id="echoid-s6723" xml:space="preserve">EX datis chordis duorum arcuũ inæqualium
              <lb/>
            chordam arcus, quo maior arcus minorem ſupe-
              <lb/>
            rat, inquirere.</s>
            <s xml:id="echoid-s6724" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6725" xml:space="preserve">IN ſemicirculo ABCD, ſint datæ chordæ AB, AC, & </s>
            <s xml:id="echoid-s6726" xml:space="preserve">BC, ſit chorda
              <lb/>
            arcus BC, quo maior arcus AC, minorem AB, ſuperat: </s>
            <s xml:id="echoid-s6727" xml:space="preserve">oporteatq́; </s>
            <s xml:id="echoid-s6728" xml:space="preserve">inqui-
              <lb/>
            rere chordã BC. </s>
            <s xml:id="echoid-s6729" xml:space="preserve">Ductis rectis BD, CD; </s>
            <s xml:id="echoid-s6730" xml:space="preserve">quoniam
              <lb/>
              <note position="right" xlink:label="note-191-07" xlink:href="note-191-07a" xml:space="preserve">3. huius.</note>
              <figure xlink:label="fig-191-02" xlink:href="fig-191-02a" number="142">
                <image file="191-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/191-02"/>
              </figure>
            chordæ AB, AC, ponuntur notæ, notæ quoque
              <lb/>
            erunt chordæ BD, CD. </s>
            <s xml:id="echoid-s6731" xml:space="preserve">Rectangulum ergo ſub
              <lb/>
            datis rectis AB, CD, comprehenſum, notum erit:
              <lb/>
            </s>
            <s xml:id="echoid-s6732" xml:space="preserve">Itemrectangulum ſub datis rectis AC, BD. </s>
            <s xml:id="echoid-s6733" xml:space="preserve">Eſt
              <lb/>
            autem rectangulum ſub rectis, AC, BD, æquale
              <lb/>
              <note position="right" xlink:label="note-191-08" xlink:href="note-191-08a" xml:space="preserve">11.huius.</note>
            duobus rectangulis ſub AB, CD, & </s>
            <s xml:id="echoid-s6734" xml:space="preserve">ſub BC, AD.
              <lb/>
            </s>
            <s xml:id="echoid-s6735" xml:space="preserve">Ablato ergo rectangulo noto ſub AB, CD, ex
              <lb/>
            rectangulo ſub AC, BD, notum ſiet reliquum rectangulum ſub BC, AD.</s>
            <s xml:id="echoid-s6736" xml:space="preserve"/>
          </p>
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