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

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        <div xml:id="echoid-div18" type="section" level="1" n="18">
          <pb o="6" file="018" n="18" rhead=""/>
          <p>
            <s xml:id="echoid-s124" xml:space="preserve">TRANSEAT deinde planum ſecans non per centrum ſphæræ. </s>
            <s xml:id="echoid-s125" xml:space="preserve">Du-
              <lb/>
              <note position="left" xlink:label="note-018-01" xlink:href="note-018-01a" xml:space="preserve">11. vndec.</note>
            catur autem ex D, centro ſphæræ ad planum ſecans perpendicularis D H,
              <lb/>
              <figure xlink:label="fig-018-01" xlink:href="fig-018-01a" number="8">
                <image file="018-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/018-01"/>
              </figure>
            emittãturq; </s>
            <s xml:id="echoid-s126" xml:space="preserve">ex H,
              <lb/>
            rectę vtcunq; </s>
            <s xml:id="echoid-s127" xml:space="preserve">H E,
              <lb/>
            H F, ad lineam B E
              <lb/>
            F C G, & </s>
            <s xml:id="echoid-s128" xml:space="preserve">cõnectan
              <lb/>
            tur rectæ D E, D F.
              <lb/>
            </s>
            <s xml:id="echoid-s129" xml:space="preserve">Quoniã igitur an-
              <lb/>
            guli D H E, D H F,
              <lb/>
            recti ſunt, ex defin. </s>
            <s xml:id="echoid-s130" xml:space="preserve">
              <lb/>
            3. </s>
            <s xml:id="echoid-s131" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s132" xml:space="preserve">11. </s>
            <s xml:id="echoid-s133" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s134" xml:space="preserve">
              <lb/>
            erit tam quadratũ
              <lb/>
            ex D E, quadratis
              <lb/>
            ex D H, H E, quàm
              <lb/>
              <note position="left" xlink:label="note-018-02" xlink:href="note-018-02a" xml:space="preserve">47. primi.</note>
            quadratũ ex D F,
              <lb/>
            quadratis ex D H,
              <lb/>
            H F, æ quale: </s>
            <s xml:id="echoid-s135" xml:space="preserve">Sunt autem quadrata ex D E, D F, inter ſe æqualia, quod & </s>
            <s xml:id="echoid-s136" xml:space="preserve">
              <lb/>
            rectæ D E, D F, ex centro ſphæræ in eius ſuperficiẽ cadentes inter ſe æqua-
              <lb/>
            les ſint. </s>
            <s xml:id="echoid-s137" xml:space="preserve">Quadrata igitur ex D H, H E, ſimul quadratis ex D H, H F, ſi-
              <lb/>
            mul æqualia erunt. </s>
            <s xml:id="echoid-s138" xml:space="preserve">Dempto igitur communi quadrato rectæ D H, reliquæ
              <lb/>
            quadrata rectarum H E, H F, inter ſe æqualia, & </s>
            <s xml:id="echoid-s139" xml:space="preserve">rectæ propterea H E, H F,
              <lb/>
            inter ſe æquales erunt. </s>
            <s xml:id="echoid-s140" xml:space="preserve">Eodem argumento oſtendemus, omnes lineas ex H, ad
              <lb/>
            lineam B E F C G, cadentes eſſe æquales & </s>
            <s xml:id="echoid-s141" xml:space="preserve">inter ſe, & </s>
            <s xml:id="echoid-s142" xml:space="preserve">dictis duabus H E,
              <lb/>
            H F. </s>
            <s xml:id="echoid-s143" xml:space="preserve">Linea ergo B E F C G, circum ſerentia erit circuli, ex defin. </s>
            <s xml:id="echoid-s144" xml:space="preserve">15. </s>
            <s xml:id="echoid-s145" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s146" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s147" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s148" xml:space="preserve">cuius centrum eſt punctum H, in quod perpendicularis D H, cadit. </s>
            <s xml:id="echoid-s149" xml:space="preserve">
              <lb/>
            Quare ſi ſphærica ſuperficies Plano aliquo ſecetur, &</s>
            <s xml:id="echoid-s150" xml:space="preserve">c. </s>
            <s xml:id="echoid-s151" xml:space="preserve">Quod erat demon-
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            ſtrandum.</s>
            <s xml:id="echoid-s152" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div21" type="section" level="1" n="19">
          <head xml:id="echoid-head30" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s153" xml:space="preserve">ITAQVE ſi planum ſecans per centrum ſphæræ tranſierit’, efficietur circulus idem
              <lb/>
            centrum habens, quod ſphæra. </s>
            <s xml:id="echoid-s154" xml:space="preserve">Si verò non per centrum tranſierit, efficientur circulus aliud
              <lb/>
            habens centrum, quàm ſphæra, illud videlicet punctum, in quod cadit perpendicularis ex
              <lb/>
            centro ſphæræ ad planum ſecans deducta. </s>
            <s xml:id="echoid-s155" xml:space="preserve">Nam ſemper demonſtrabuntur lineæ rectæ caden
              <lb/>
            tes ex hoc puncto in circum ferentiam circuli eſſe æquales.</s>
            <s xml:id="echoid-s156" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div22" type="section" level="1" n="20">
          <head xml:id="echoid-head31" xml:space="preserve">HOCEST.</head>
          <p>
            <s xml:id="echoid-s157" xml:space="preserve">IDEM eſt ſphæræ centrum, & </s>
            <s xml:id="echoid-s158" xml:space="preserve">circuli per ſphæræ centrum traiecti. </s>
            <s xml:id="echoid-s159" xml:space="preserve">Et perpendiculatis
              <lb/>
            ducta à centro ſphæræ in planum circuli per centrum ſphæræ non traiecti, cadit in centrum
              <lb/>
            circuli: </s>
            <s xml:id="echoid-s160" xml:space="preserve">quia punctum H, in quod perpendicularis D H, cadit, demonſtratum cſt centrum
              <lb/>
            eſſe circuli.</s>
            <s xml:id="echoid-s161" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div23" type="section" level="1" n="21">
          <head xml:id="echoid-head32" xml:space="preserve">PROBL. 1. PROPOS. 2.</head>
          <note position="left" xml:space="preserve">2.</note>
        </div>
        <div xml:id="echoid-div24" type="section" level="1" n="22">
          <head xml:id="echoid-head33" xml:space="preserve">DATAE Sphæræ centrum inuenire.</head>
          <p>
            <s xml:id="echoid-s162" xml:space="preserve">SIT centrum inueniendum Sphæræ A B C D. </s>
            <s xml:id="echoid-s163" xml:space="preserve">Secetur eius ſuperficies
              <lb/>
              <note position="left" xlink:label="note-018-04" xlink:href="note-018-04a" xml:space="preserve">1. huius.
                <lb/>
              1. tertij.
                <lb/>
              Coroll. 1.
                <lb/>
              huius.</note>
            plano quopiam faciente in ipſa lineam B D E, quæ circuli circumferentia
              <lb/>
            crit. </s>
            <s xml:id="echoid-s164" xml:space="preserve">Sit huius circuli centrum F. </s>
            <s xml:id="echoid-s165" xml:space="preserve">Siigitur circulus B D E, per centrum ſphæ
              <lb/>
            ræ traijcitur, erit punctum F, centrum quoque ſphæræ. </s>
            <s xml:id="echoid-s166" xml:space="preserve">Si verò per centrum
              <lb/>
            ſphæræ non traijcitur, erigatur ex F, ad planum circuli B D E, </s>
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