Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1112" type="section" level="1" n="403">
          <p>
            <s xml:id="echoid-s17672" xml:space="preserve">
              <pb o="374" file="402" n="402" rhead="GEOMETR. PRACT."/>
            planum ducatur baſibus parallelum. </s>
            <s xml:id="echoid-s17673" xml:space="preserve">Hoc enim ſecabit tam priſma, quam
              <note symbol="a" position="left" xlink:label="note-402-01" xlink:href="note-402-01a" xml:space="preserve">ſchol. 14.
                <lb/>
              duodec.</note>
            lindrum in datam proportionem.
              <lb/>
            </s>
            <s xml:id="echoid-s17674" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-402-02" xlink:href="note-402-02a" xml:space="preserve">14. duodec.</note>
            </s>
          </p>
        </div>
        <div xml:id="echoid-div1114" type="section" level="1" n="404">
          <head xml:id="echoid-head431" xml:space="preserve">PROBL. 33. PROPOS. 47.</head>
          <p>
            <s xml:id="echoid-s17675" xml:space="preserve">FIGVRAM Ellipſi ſimilem, quam ouatam dicunt, circino deſcri-
              <lb/>
            bere.</s>
            <s xml:id="echoid-s17676" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17677" xml:space="preserve">
              <emph style="sc">Libet</emph>
            miſcellaneorum hunc librum peruulgato illo problemate conclu-
              <lb/>
            dere, quo artifices ope circini deſcribere ſolent ſiguram ouatam Ellipſi ſimilem,
              <lb/>
            ita vt nulli anguli appareant: </s>
            <s xml:id="echoid-s17678" xml:space="preserve">cum non rarò eiuſmo di figura à Geometris in ſuis
              <lb/>
            delineationibus adhibeatur. </s>
            <s xml:id="echoid-s17679" xml:space="preserve">Docui quidem in lib. </s>
            <s xml:id="echoid-s17680" xml:space="preserve">1 noſtræ Gnomonicę in ſcho-
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s17681" xml:space="preserve">8. </s>
            <s xml:id="echoid-s17682" xml:space="preserve">qua ratione vera Ellipſis, quę coni-
              <lb/>
              <figure xlink:label="fig-402-01" xlink:href="fig-402-01a" number="291">
                <image file="402-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/402-01"/>
              </figure>
            ca ſectio eſt, deſcribenda ſit: </s>
            <s xml:id="echoid-s17683" xml:space="preserve">Sed hic ſimilem figu-
              <lb/>
              <note symbol="c" position="left" xlink:label="note-402-03" xlink:href="note-402-03a" xml:space="preserve">15. primi.</note>
            ram ex ſegmentis circulorum conſtantem deſcri-
              <lb/>
            bendam proponimus. </s>
            <s xml:id="echoid-s17684" xml:space="preserve">Ita ergo, vt ex variis ſcri-
              <lb/>
            ptoribus colligitur, agemus. </s>
            <s xml:id="echoid-s17685" xml:space="preserve">Conſtruantur duo
              <lb/>
            triangula æquilatera, vel Iſoſcelia ſupra ba-
              <lb/>
            ſem communem A C, in diuerſas partes A B C,
              <lb/>
            ADC. </s>
            <s xml:id="echoid-s17686" xml:space="preserve">(Æquilatera venuſtiorem faciunt figuram,
              <lb/>
            vt experientia te docebit) productiſque lateribus,
              <lb/>
            deſcribantur ex A, C, duo arcus EFG, HIK, vſque
              <lb/>
            ad latera producta. </s>
            <s xml:id="echoid-s17687" xml:space="preserve">Si namque ex B, D, per E, K,
              <lb/>
            G, H, alij arcus deſcribantur, tangent
              <note symbol="d" position="left" xlink:label="note-402-04" xlink:href="note-402-04a" xml:space="preserve">ſchol. 13.
                <lb/>
              tertii.</note>
            arcus in punctis E, K, G, H: </s>
            <s xml:id="echoid-s17688" xml:space="preserve">ac proinde illos non
              <lb/>
            ſecabunt, conſtituta que erit figura ouata.</s>
            <s xml:id="echoid-s17689" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17690" xml:space="preserve">
              <emph style="sc">Bene</emph>
            autem vides, ex eiſdem centris A, C, B, D, deſcribi poſſe varias figuras,
              <lb/>
            prout arcus EFG, HIK, maiores fuerint, autminores, vt in figura apparet.</s>
            <s xml:id="echoid-s17691" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17692" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi triangula conſtituta ſint Iſoſcelia, poterunt latera AB, CB, &</s>
            <s xml:id="echoid-s17693" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17694" xml:space="preserve">vel
              <lb/>
            maiora fieri baſe AC, vel minora. </s>
            <s xml:id="echoid-s17695" xml:space="preserve">In figura noſtra ſunt minora.</s>
            <s xml:id="echoid-s17696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17697" xml:space="preserve">
              <emph style="sc">Potes</emph>
            etiam, ſi placet, primo loco ex centris B, D, deſcribere arcus EMK,
              <lb/>
            GLH, ad quodcunque interuallum, pro latitudine figuræ deſcribendę: </s>
            <s xml:id="echoid-s17698" xml:space="preserve">deinde
              <lb/>
            ex centris A, C, minores arcus delineare EFG, HIK.</s>
            <s xml:id="echoid-s17699" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17700" xml:space="preserve">
              <emph style="sc">Qvin</emph>
            etiam ſine conſtructione triangulorum idem effi ciemus hoc modo.
              <lb/>
            </s>
            <s xml:id="echoid-s17701" xml:space="preserve">Ductis duabus rectis AC, BD, ad angulos rectos ſe ſecantibus in N; </s>
            <s xml:id="echoid-s17702" xml:space="preserve">ſumptiſque
              <lb/>
            æqualibus NA, NC, quantiſcunque pro longitudine figurę, deſcribantur ex A,
              <lb/>
            C, arcus circulorum EFG, HIK, parui, aut magni, prout deſideras extremitates
              <lb/>
            figurę ſecundum longitudinem habere anguſtiores, latioreſue. </s>
            <s xml:id="echoid-s17703" xml:space="preserve">Deinde acce-
              <lb/>
            ptis aliis duabus rectis æqualibus NB, ND, quantiſcunque, (quo autem puncta
              <lb/>
            B, D, remotiora fuerint ab N, eo anguſtior figura euadet: </s>
            <s xml:id="echoid-s17704" xml:space="preserve">& </s>
            <s xml:id="echoid-s17705" xml:space="preserve">quo minus remota,
              <lb/>
            eo latior. </s>
            <s xml:id="echoid-s17706" xml:space="preserve">Sed vſus magiſter optimus facilè docebit, quantæ debeant eſſe re-
              <lb/>
            ctæ NB, ND,) ducantur ex B, D, per centra A, C, rectæ ſecantes priores arcus in
              <lb/>
            E, K, &</s>
            <s xml:id="echoid-s17707" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17708" xml:space="preserve">Nam ſi ex B, D, per puncta E, K, &</s>
            <s xml:id="echoid-s17709" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17710" xml:space="preserve">alij duo arcus deſcribantur, per-
              <lb/>
            fecta erit figura Ellipſi ſimilis.</s>
            <s xml:id="echoid-s17711" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17712" xml:space="preserve">
              <emph style="sc">Vt</emph>
            autem videas, venuſtiores figuras deſcribi, ſi triangula ABC, ADC, </s>
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