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

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        <div xml:id="echoid-div498" type="section" level="1" n="244">
          <p>
            <s xml:id="echoid-s6649" xml:space="preserve">
              <pb o="178" file="190" n="190" rhead=""/>
            liquo angulo ADC, in triangulo ADC, æqualis. </s>
            <s xml:id="echoid-s6650" xml:space="preserve">Erit igitur, vt AC, ad CD,
              <lb/>
              <note position="left" xlink:label="note-190-01" xlink:href="note-190-01a" xml:space="preserve">4. ſexti.</note>
            ita AB, ad BE. </s>
            <s xml:id="echoid-s6651" xml:space="preserve">Quare rectangulum ſub AC, BE, æquale eſt rectangulo ſub
              <lb/>
              <note position="left" xlink:label="note-190-02" xlink:href="note-190-02a" xml:space="preserve">16. ſexti.</note>
            CD, AB. </s>
            <s xml:id="echoid-s6652" xml:space="preserve">Quoniam igitur rectangulum ſub AC, DE, rectangulo ſub CB,
              <lb/>
              <figure xlink:label="fig-190-01" xlink:href="fig-190-01a" number="140">
                <image file="190-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/190-01"/>
              </figure>
            AD, oſten-
              <lb/>
            ſum eſt æqua
              <lb/>
            le; </s>
            <s xml:id="echoid-s6653" xml:space="preserve">& </s>
            <s xml:id="echoid-s6654" xml:space="preserve">rectãgu
              <lb/>
            lum ſub AC,
              <lb/>
            BE, rectãgu
              <lb/>
            lo ſub CD,
              <lb/>
            AB: </s>
            <s xml:id="echoid-s6655" xml:space="preserve">Suntau
              <lb/>
            tem rectangu
              <lb/>
            la ſub AC,
              <lb/>
            DE, & </s>
            <s xml:id="echoid-s6656" xml:space="preserve">ſub
              <lb/>
            AC, BE, ſimul rectangulo ſub AC, BD, æqualia; </s>
            <s xml:id="echoid-s6657" xml:space="preserve">erit rectangulum ſub AC,
              <lb/>
              <note position="left" xlink:label="note-190-03" xlink:href="note-190-03a" xml:space="preserve">1. ſecundi.</note>
            BD, rectangulis ſub BC, AD, & </s>
            <s xml:id="echoid-s6658" xml:space="preserve">ſub CD, AB, contentis æquale. </s>
            <s xml:id="echoid-s6659" xml:space="preserve">Siergo
              <lb/>
            in circulo quadrilaterum deſcribatur, &</s>
            <s xml:id="echoid-s6660" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6661" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s6662" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div501" type="section" level="1" n="245">
          <head xml:id="echoid-head272" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s6663" xml:space="preserve">_QVANDO_ figura in circulo deſcripta eſt quadratum, vt in prima figura, fa-
              <lb/>
            cilius demonſtrabitur theorema, hoc modo. </s>
            <s xml:id="echoid-s6664" xml:space="preserve">_Q_uoniam rectangulum ſub _AC, BD,_
              <lb/>
              <note position="left" xlink:label="note-190-04" xlink:href="note-190-04a" xml:space="preserve">Schol. 34.
                <lb/>
              lib. 1.</note>
            hoc eſt, quadratum ex _AC,_ (ſunt enim diametri in quadrato æquales) æquale eſt
              <lb/>
            quadratis ex _AD, DC,_ hoc eſt, rectangulis ſub _AD,
              <emph style="sc">B</emph>
            C,_ & </s>
            <s xml:id="echoid-s6665" xml:space="preserve">ſub _AB, DC,_ conten-
              <lb/>
              <note position="left" xlink:label="note-190-05" xlink:href="note-190-05a" xml:space="preserve">47. primi.</note>
            tis, propter æqualitatem rectarum _AD, BC,_ & </s>
            <s xml:id="echoid-s6666" xml:space="preserve">_AB, DC;_ </s>
            <s xml:id="echoid-s6667" xml:space="preserve">liquido conſtatid, quod
              <lb/>
            proponitur.</s>
            <s xml:id="echoid-s6668" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div503" type="section" level="1" n="246">
          <head xml:id="echoid-head273" xml:space="preserve">PROBL. 4. PROP. 12.</head>
          <note position="left" xml:space="preserve">Ex data dia
            <lb/>
          metro cir-
            <lb/>
          culi quo pa
            <lb/>
          cto latera
            <lb/>
          trianguli ę-
            <lb/>
          quilateri,
            <lb/>
          quadrati,
            <lb/>
          hexagoni,
            <lb/>
          pentagoni,
            <lb/>
          & dccago-
            <lb/>
          ni eiuſdem
            <lb/>
          circuli in-
            <lb/>
          ueſtigent́.</note>
          <p>
            <s xml:id="echoid-s6669" xml:space="preserve">EX data circuli diametro quotlibet particula-
              <lb/>
            rum, latera trianguli æquilateri, quadrati, hexago-
              <lb/>
            ni, pentagoni, & </s>
            <s xml:id="echoid-s6670" xml:space="preserve">decagoni in eodem circulo de-
              <lb/>
            ſcriptorum, in eiſdem partibus inueſtigare.</s>
            <s xml:id="echoid-s6671" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6672" xml:space="preserve">PONATVR diameter partium 20000000. </s>
            <s xml:id="echoid-s6673" xml:space="preserve">Quoniam igitur latus he-
              <lb/>
            xagoni ſemidia metro circuli eſt æquale, ipſum notum fiet partium 10000000.</s>
            <s xml:id="echoid-s6674" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Coroll. 15.
            <lb/>
          quarti.</note>
          <p>
            <s xml:id="echoid-s6675" xml:space="preserve">RVRSVS, quia quadratum à diametro quadrati cuiuſuis deſcriptum,
              <lb/>
            duplum eſt quadrati eiuſdem; </s>
            <s xml:id="echoid-s6676" xml:space="preserve">Eſt autem diameter quadrati in circulo deſcri-
              <lb/>
              <note position="left" xlink:label="note-190-08" xlink:href="note-190-08a" xml:space="preserve">Schol. 47.
                <lb/>
              primi.</note>
            pti eadem, quæ circuli diameter: </s>
            <s xml:id="echoid-s6677" xml:space="preserve">ſi accipiatur quadratum à diametro circuli
              <lb/>
            deſcriptũ, népe 400000000000000. </s>
            <s xml:id="echoid-s6678" xml:space="preserve">erit dimidiũ eius, puta 200000000000000.
              <lb/>
            </s>
            <s xml:id="echoid-s6679" xml:space="preserve">quadratum lateris quadrati, cuius radix quadrata 14142136. </s>
            <s xml:id="echoid-s6680" xml:space="preserve">dabit latus qua-
              <lb/>
            drati. </s>
            <s xml:id="echoid-s6681" xml:space="preserve">Quod hoc etiam modo reperietur. </s>
            <s xml:id="echoid-s6682" xml:space="preserve">Quoniam quadratum in circulo de-
              <lb/>
            ſcriptum duplum eſt quadrati à ſemidiametro deſcriptum, vt patet in trian-
              <lb/>
              <note position="left" xlink:label="note-190-09" xlink:href="note-190-09a" xml:space="preserve">47. ptimi.</note>
            gulo rectangulo ADE, primę figuræ præcedẽtis propoſ. </s>
            <s xml:id="echoid-s6683" xml:space="preserve">ſi 100000000000000.
              <lb/>
            </s>
            <s xml:id="echoid-s6684" xml:space="preserve">quadratum ſemidiametri duplicetur, fiet quadratum in circulo deſcriptum
              <lb/>
            partium 200000000000000. </s>
            <s xml:id="echoid-s6685" xml:space="preserve">cuius radix quadrata 14142136. </s>
            <s xml:id="echoid-s6686" xml:space="preserve">rurſus dabit la-
              <lb/>
            tus quad rati.</s>
            <s xml:id="echoid-s6687" xml:space="preserve"/>
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