Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

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        <div xml:id="echoid-div70" type="section" level="1" n="20">
          <pb o="21" file="0041" n="41" rhead="LIBER PRIMVS."/>
        </div>
        <div xml:id="echoid-div73" type="section" level="1" n="21">
          <head xml:id="echoid-head24" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1472" xml:space="preserve">SOLET à nonnullis, & </s>
            <s xml:id="echoid-s1473" xml:space="preserve">rectè, illa ſuperficies conica, cuius baſim deſcribit centrum Solis, appellari
              <lb/>
              <note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">Superficies co-
                <lb/>
              nica luminis
                <lb/>
              quæ.</note>
            ſuperficies conica luminis, quòd à radio Solis deſcribatur; </s>
            <s xml:id="echoid-s1474" xml:space="preserve">altera verò, cuius baſim punctum centro So-
              <lb/>
            lis oppoſitum deſcribit, ſuperſicies conica vmbræ, quia ab vmbra, quam centrum mundi proijcit, deſcri-
              <lb/>
              <note position="right" xlink:label="note-0041-02" xlink:href="note-0041-02a" xml:space="preserve">Superficies coni
                <lb/>
              ca vmbræ quæ.</note>
            bitur. </s>
            <s xml:id="echoid-s1475" xml:space="preserve">Vt Sole exiſtente in puncto F, ſuperficies luminis eſt E F G, quia tota à Sole illuminatur, ſuper-
              <lb/>
            ficies verò vmbræ E I H, quia ab vmbra centri E, ſecundum rectam E I, proiectam deſcripta eſt. </s>
            <s xml:id="echoid-s1476" xml:space="preserve">Contra
              <lb/>
            autem, Sole punctum I, poſſidente, ſuperficies luminis dicitur E I H, & </s>
            <s xml:id="echoid-s1477" xml:space="preserve">vmbræ E F G. </s>
            <s xml:id="echoid-s1478" xml:space="preserve">Ponimus enim
              <lb/>
            nunc, centrum E, vim habere vmbram proijciendi; </s>
            <s xml:id="echoid-s1479" xml:space="preserve">quia vt in propoſ. </s>
            <s xml:id="echoid-s1480" xml:space="preserve">præcedenti diximus, centrum mun
              <lb/>
            di intelligitur in quolibet borologio eſſe vertex ſtyli, qui vtique corpus opacum cum ſit, vmbram proij-
              <lb/>
              <note position="left" xlink:label="note-0041-03" xlink:href="note-0041-03a" xml:space="preserve">10</note>
            cit, vt manifeſtum eſt.</s>
            <s xml:id="echoid-s1481" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div75" type="section" level="1" n="22">
          <head xml:id="echoid-head25" xml:space="preserve">THEOREMA 3. PROPOSITIO 4.</head>
          <note position="right" xml:space="preserve">Planum horo-
            <lb/>
          logij æquidiftãs
            <lb/>
          baſibus conica-
            <lb/>
          rum ſuperficie-
            <lb/>
          rum facit in al-
            <lb/>
          tera ſuperſicie-
            <lb/>
          rum circulum.</note>
          <p>
            <s xml:id="echoid-s1482" xml:space="preserve">SECTIO communis ſuperficierum conicarum in centro mundi,
              <lb/>
            tanquam vertice communi iunctarum, quarum baſes duo ſunt paralle-
              <lb/>
            li Sphærę oppoſiti, & </s>
            <s xml:id="echoid-s1483" xml:space="preserve">æquales, ad motum diurnum circa mundi polos
              <lb/>
            deſcripti, & </s>
            <s xml:id="echoid-s1484" xml:space="preserve">plani horologij æquidiſtantis circulo maximo, qui baſibus
              <lb/>
              <note position="left" xlink:label="note-0041-05" xlink:href="note-0041-05a" xml:space="preserve">20</note>
            conicarum ſuperficierum æquidiſtat, circulus eſt, centrum habens in
              <lb/>
            axe mundi.</s>
            <s xml:id="echoid-s1485" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1486" xml:space="preserve">IN Sphæra, cuius centrum A, ſint duæ ſuperſicies conicæ A D E, AFG, coniunctæ ad mundi
              <lb/>
            centrum A, tanquam ad verticem communem, quarum baſes paralleli ſint ad motum diurnum
              <lb/>
            deſcripti, oppoſiti & </s>
            <s xml:id="echoid-s1487" xml:space="preserve">æquales D E, F G; </s>
            <s xml:id="echoid-s1488" xml:space="preserve">& </s>
            <s xml:id="echoid-s1489" xml:space="preserve">axis B C. </s>
            <s xml:id="echoid-s1490" xml:space="preserve">Sit quoque HI, circulus maximus in Sphæra
              <lb/>
            ęquidiſtans baſibus D E, F G, di-
              <lb/>
              <figure xlink:label="fig-0041-01" xlink:href="fig-0041-01a" number="19">
                <image file="0041-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0041-01"/>
              </figure>
            ctarum ſuperficierum conicarũ:
              <lb/>
            </s>
            <s xml:id="echoid-s1491" xml:space="preserve">Huic autem circulo æquidiſtet
              <lb/>
            horologij planum K L, faciens
              <lb/>
              <note position="left" xlink:label="note-0041-06" xlink:href="note-0041-06a" xml:space="preserve">30</note>
            in conica ſuperficie A F G, ſe-
              <lb/>
            ctionem M N. </s>
            <s xml:id="echoid-s1492" xml:space="preserve">Dico M N, eſſe
              <lb/>
            circulum, qui cẽtrum habeat in
              <lb/>
            axe mundi. </s>
            <s xml:id="echoid-s1493" xml:space="preserve">Cum enim plana
              <lb/>
            F G, K L, plano H I, parallela
              <lb/>
            ponantur, & </s>
            <s xml:id="echoid-s1494" xml:space="preserve">ipſa inter ſe paral-
              <lb/>
            lela erunt, per ea, quę ad propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s1495" xml:space="preserve">16. </s>
            <s xml:id="echoid-s1496" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1497" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1498" xml:space="preserve">Euclidis demonſtra
              <lb/>
            uimus. </s>
            <s xml:id="echoid-s1499" xml:space="preserve">Quamobrem, cùm ſu-
              <lb/>
            perficies conica A F G, ſecetur
              <lb/>
              <note position="left" xlink:label="note-0041-07" xlink:href="note-0041-07a" xml:space="preserve">40</note>
            plano K L, quod baſi F G, æqui-
              <lb/>
            diſtat, ſectio facta M N, per pro-
              <lb/>
            poſitionem 4. </s>
            <s xml:id="echoid-s1500" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1501" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1502" xml:space="preserve">Apollonii,
              <lb/>
            circulus erit centrum habens in
              <lb/>
            axe B C, vbi nimirum planum
              <lb/>
            horologii axi occurrit. </s>
            <s xml:id="echoid-s1503" xml:space="preserve">Eodem
              <lb/>
            modo, ſi planum circulo HI,
              <lb/>
            æquidiſtans ſecet conicam ſu-
              <lb/>
            perficiem A D E, ſectio circulus
              <lb/>
            erit. </s>
            <s xml:id="echoid-s1504" xml:space="preserve">Sectio igitur communis
              <lb/>
              <note position="left" xlink:label="note-0041-08" xlink:href="note-0041-08a" xml:space="preserve">50</note>
            ſuperficierum conicarum, &</s>
            <s xml:id="echoid-s1505" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1506" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1507" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div78" type="section" level="1" n="23">
          <head xml:id="echoid-head26" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s1508" xml:space="preserve">HINC fit, communem ſectionem plani horologij Aequinoctialis, & </s>
            <s xml:id="echoid-s1509" xml:space="preserve">ſuperficierum conicarum, qua-
              <lb/>
              <note position="right" xlink:label="note-0041-09" xlink:href="note-0041-09a" xml:space="preserve">Aequinoctiale
                <lb/>
              horologiũ ſecãs
                <lb/>
              ſuperficiem co-
                <lb/>
              nicam, cuius ba
                <lb/>
              ſis ſit parallelus
                <lb/>
              Aequatoris, fa-
                <lb/>
              cit circulum.</note>
            rum baſes ſunt quicunque paralleli à Sole deſcripti, oppoſiti, & </s>
            <s xml:id="echoid-s1510" xml:space="preserve">æquales, vel alij quicunque his ęquidiſtan
              <lb/>
            tes, quales etiam ſunt maximi parallelorum ſemper apparentium, & </s>
            <s xml:id="echoid-s1511" xml:space="preserve">ſemper deliteſcentium, eſſe circu-
              <lb/>
            lum: </s>
            <s xml:id="echoid-s1512" xml:space="preserve">propterea quòd æquinoctialis circulus, cui planum horologii æquidiſtat, æquidiſtans eſt baſibus
              <lb/>
            ſuperficierum huiuſmodi conicarum.</s>
            <s xml:id="echoid-s1513" xml:space="preserve"/>
          </p>
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