Clavius, Christoph, Geometria practica
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          <head xml:id="echoid-head397" xml:space="preserve">PROBL. 17. PROPOS. 26.</head>
          <p>
            <s xml:id="echoid-s16688" xml:space="preserve">SI per idem punctum diametri in rectangulo duæ lineæ ducantur late-
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            ribus parallelæ: </s>
            <s xml:id="echoid-s16689" xml:space="preserve">Erit rectangulum ſub ſegmentis diametri compre-
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            henſum æquale duobus rectangulis ſub ſegmentis duorum laterum
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            comprehenſis.</s>
            <s xml:id="echoid-s16690" xml:space="preserve"/>
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            <s xml:id="echoid-s16691" xml:space="preserve">
              <emph style="sc">In</emph>
            rectangulo BD, per E, punctum diametri AC, ductæ ſint FG, HI, lateri-
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            bus parallelæ. </s>
            <s xml:id="echoid-s16692" xml:space="preserve">Dico rectangulum ſub AE, EC, æquale eſſe rectangulis ſub AF,
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              <note symbol="a" position="right" xlink:label="note-385-01" xlink:href="note-385-01a" xml:space="preserve">4. ſecundi.</note>
            FB, & </s>
            <s xml:id="echoid-s16693" xml:space="preserve">ſub BI, IC. </s>
            <s xml:id="echoid-s16694" xml:space="preserve"> Quoniam enim quadratum ex AC, æquale eſt quadratis
              <note symbol="b" position="right" xlink:label="note-385-02" xlink:href="note-385-02a" xml:space="preserve">47. primi.</note>
            AE, EC, vna cum rectangulo bis ſub AE, EC. </s>
            <s xml:id="echoid-s16695" xml:space="preserve"> Suntautem quadrata ex AB, BC, quadrato ex AC, æqualia; </s>
            <s xml:id="echoid-s16696" xml:space="preserve">erunt quoque duo quadrata ex AE, EC, vna
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            cum rectangulo bis ſub AE, EC, æqualia quadratis ex
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              <figure xlink:label="fig-385-01" xlink:href="fig-385-01a" number="277">
                <image file="385-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/385-01"/>
              </figure>
              <note symbol="c" position="right" xlink:label="note-385-03" xlink:href="note-385-03a" xml:space="preserve">4. ſecundi.</note>
            AB, BC. </s>
            <s xml:id="echoid-s16697" xml:space="preserve"> Sed quadratum ex AB, æquale eſt quadra- tis duobus ex AF, FB, vna cum rectangulo bis ſub AF,
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            FB; </s>
            <s xml:id="echoid-s16698" xml:space="preserve">Et quadratum ex BC, æquale eſt duobus quadra-
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            tis ex BI, IC, vna cum rectangulo bis ſub BI, IC. </s>
            <s xml:id="echoid-s16699" xml:space="preserve">Igi-
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            tur duo quadrata ex AE, EC, vna cum rectangulo bis
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            ſub AE, EC, æqualia erunt quatu or quadratis ex AF,
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            FB, BI, IC, vna cum rectangulis bis ſub AF, FB, & </s>
            <s xml:id="echoid-s16700" xml:space="preserve">ſub BI, IC. </s>
            <s xml:id="echoid-s16701" xml:space="preserve"> Cum ergo
              <note symbol="d" position="right" xlink:label="note-385-04" xlink:href="note-385-04a" xml:space="preserve">47. primi.</note>
            dratum ex AE, quadratis ex AF, FE, hoc eſt, ex AF, BI: </s>
            <s xml:id="echoid-s16702" xml:space="preserve">& </s>
            <s xml:id="echoid-s16703" xml:space="preserve">quadratum ex EC,
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            quadratis ex EI, IC, hoc eſt ex FB, IC: </s>
            <s xml:id="echoid-s16704" xml:space="preserve">æquale ſit; </s>
            <s xml:id="echoid-s16705" xml:space="preserve">Erunt quatuor quadrata
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            ex AF, BI, FB, IC, vna cum rectangulo bis ſub AE, EC, æqualia quatuor qua-
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            dratis ex AF, FB, BI, IC, vna cum rectangulis bis ſub AF, FB, & </s>
            <s xml:id="echoid-s16706" xml:space="preserve">ſub BI, IC; </s>
            <s xml:id="echoid-s16707" xml:space="preserve">Ab-
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            latiſque vtrobique prædictis quatuor quadratis communibus, eritreliquum re-
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            ctangulum bis ſub AE, EC, reliquis rectangulis bis ſub AF, FB, & </s>
            <s xml:id="echoid-s16708" xml:space="preserve">ſub BI, IC, æ-
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            quale. </s>
            <s xml:id="echoid-s16709" xml:space="preserve">Ideo que rectangulum ſemel ſub AE, EC, rectangulis ſemel ſub AF.
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            </s>
            <s xml:id="echoid-s16710" xml:space="preserve">FB, & </s>
            <s xml:id="echoid-s16711" xml:space="preserve">ſub BI, IC, erit æquale. </s>
            <s xml:id="echoid-s16712" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s16713" xml:space="preserve"/>
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          <head xml:id="echoid-head398" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s16714" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            in quadrato, vt in poſteriori figura, rectangulum ſub ſegmentis
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            diametri AE, EC, comprehenſum æquale eſt duobus complementis DE, BE,
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            quippe cum complementa ſub ſegmentis laterum comprehendantur.</s>
            <s xml:id="echoid-s16715" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head399" xml:space="preserve">PROBL. 18. PROPOS. 27.</head>
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            <s xml:id="echoid-s16716" xml:space="preserve">DATO centro Ellipſis in linea in infinitum producta, vna cum duo-
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            bus punctis ad eaſdem partes axis, vel centri, per quæ tranſire dicatur
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            Ellipſis: </s>
            <s xml:id="echoid-s16717" xml:space="preserve">vtrumque axis vtriuſque extremum inuenire.</s>
            <s xml:id="echoid-s16718" xml:space="preserve"/>
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            <s xml:id="echoid-s16719" xml:space="preserve">
              <emph style="sc">Hoc</emph>
            problema conicum eſt, & </s>
            <s xml:id="echoid-s16720" xml:space="preserve">acutum. </s>
            <s xml:id="echoid-s16721" xml:space="preserve">Sit A, centrum, id eſt, punctum me-
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            dium alicuius Ellipſis in linea axis maioris BC, quantacunq;</s>
            <s xml:id="echoid-s16722" xml:space="preserve">: Et duo puncta in
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            eadem Ellipſi D, E, verſus eandem partem, hoc eſt, ſiue ſupra centrum A, ſiue
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            infra; </s>
            <s xml:id="echoid-s16723" xml:space="preserve">è quibus ad BC, perpendiculares ducantur DF, EG: </s>
            <s xml:id="echoid-s16724" xml:space="preserve">Eritque DF, </s>
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