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">
          <head xml:id="echoid-head23" xml:space="preserve">THEOREMA 2. PROPOSITIO 3.</head>
          <p>
            <s xml:id="echoid-s1422" xml:space="preserve">RADIVS Solis in Aequatore quidem exiſtentis, motu diurno cir-
              <lb/>
              <note position="left" xlink:label="note-0040-01" xlink:href="note-0040-01a" xml:space="preserve">Sol in Aequa-
                <lb/>
              tore exiſtens de
                <lb/>
              ſcribit ſuo ra-
                <lb/>
              dio æquinoctia
                <lb/>
              lem circulum.
                <lb/>
              extra vero Ae-
                <lb/>
              quatorem duas
                <lb/>
              conicas ſuperfi-
                <lb/>
              cies.</note>
            ca centrum mundi deſcribit circulum, nem pe ipſummet Aequatorem:
              <lb/>
            </s>
            <s xml:id="echoid-s1423" xml:space="preserve">extra verò Aequatorem conſtituti, duas conicas ſuperficies ad centrum
              <lb/>
            mundi, tanquam ad communem verticem, coniunctas, quarum vnius
              <lb/>
            baſis eſt parallelus à centro Solis deſcriptus, alterius autem, parallelus pa-
              <lb/>
              <note position="left" xlink:label="note-0040-02" xlink:href="note-0040-02a" xml:space="preserve">10</note>
            rallelo huic oppoſitus; </s>
            <s xml:id="echoid-s1424" xml:space="preserve">& </s>
            <s xml:id="echoid-s1425" xml:space="preserve">vtriuſque axis idem, qui mundi.</s>
            <s xml:id="echoid-s1426" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1427" xml:space="preserve">IN Analemmate A B C D, cuius centrum E, axis mundi ſit D B; </s>
            <s xml:id="echoid-s1428" xml:space="preserve">communis ſectio Aequatoris,
              <lb/>
            & </s>
            <s xml:id="echoid-s1429" xml:space="preserve">Meridiani recta A C; </s>
            <s xml:id="echoid-s1430" xml:space="preserve">duorum parallelorum oppoſitorum, & </s>
            <s xml:id="echoid-s1431" xml:space="preserve">eiuſdem Meridiani communes
              <lb/>
            ſectiones rectæ F G, H I, ſecantes axem in Q, R, punctis, quæ centra erunt ipſorum parallelorũ,
              <lb/>
            ex propoſ. </s>
            <s xml:id="echoid-s1432" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1433" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1434" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1435" xml:space="preserve">Theodoſii, quandoquidem axis per ipſorum polos ducitur, atque adeo ex di-
              <lb/>
            cta propoſ. </s>
            <s xml:id="echoid-s1436" xml:space="preserve">per centra eorundem tranſit. </s>
            <s xml:id="echoid-s1437" xml:space="preserve">In telligantur quoque circa diametros A C, F G, H I, de-
              <lb/>
              <figure xlink:label="fig-0040-01" xlink:href="fig-0040-01a" number="18">
                <image file="0040-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0040-01"/>
              </figure>
            ſcripti circuli, nempe Aequator
              <lb/>
            A K C L, & </s>
            <s xml:id="echoid-s1438" xml:space="preserve">duo paralleli F M
              <lb/>
            G N, H O I P, ad Meridianum
              <lb/>
              <note position="left" xlink:label="note-0040-03" xlink:href="note-0040-03a" xml:space="preserve">20</note>
            recti. </s>
            <s xml:id="echoid-s1439" xml:space="preserve">In Sphæra enim Aequator,
              <lb/>
            & </s>
            <s xml:id="echoid-s1440" xml:space="preserve">ei
              <emph style="sub">9</emph>
            paralleli ad Meridiani pla-
              <lb/>
            num, ex propoſ. </s>
            <s xml:id="echoid-s1441" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1442" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1443" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1444" xml:space="preserve">Theo
              <lb/>
            doſii, recti ſunt, cum eos Meri-
              <lb/>
            dianus circulus per ipſorum po-
              <lb/>
            los ſecet. </s>
            <s xml:id="echoid-s1445" xml:space="preserve">Quoniam igitur, Sole
              <lb/>
            in Aequatore exiſtente, nimirũ
              <lb/>
            in puncto A, centrum eius à cir-
              <lb/>
            cunferẽtia Aequatoris A K C L,
              <lb/>
            & </s>
            <s xml:id="echoid-s1446" xml:space="preserve">radius A E, ad centrum mun-
              <lb/>
              <note position="left" xlink:label="note-0040-04" xlink:href="note-0040-04a" xml:space="preserve">30</note>
            di pertinens à plano eiuſdem
              <lb/>
            Aequatoris, quod per centrum
              <lb/>
            etiam mundi ducitur, non rece-
              <lb/>
            dit, ſed motu diurno in eo ſem-
              <lb/>
            per circunfertur, (Negligimus
              <lb/>
            enim nũc declinationem, quam
              <lb/>
            proprio motu Sol acqui@it.) </s>
            <s xml:id="echoid-s1447" xml:space="preserve">per-
              <lb/>
            ſpicuum eſt, ex definitione circu
              <lb/>
            li, à Solis radio circulum, nem-
              <lb/>
            pe ipſummet Aequa@orem A K-
              <lb/>
              <note position="left" xlink:label="note-0040-05" xlink:href="note-0040-05a" xml:space="preserve">40</note>
            C L, deſcribi, cuius circunferen-
              <lb/>
            tiam centrum eiuſdẽ deſcribit.</s>
            <s xml:id="echoid-s1448" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1449" xml:space="preserve">AT vero Sole extra Aequatorem conſtituto, vt in puncto F, radius eius F E, ad mundi centrũ
              <lb/>
            pertinens, & </s>
            <s xml:id="echoid-s1450" xml:space="preserve">in rectum, continuumq́; </s>
            <s xml:id="echoid-s1451" xml:space="preserve">productus, conuertitur (manente puncto E, ſixo) circa cir-
              <lb/>
            cunferentiam circuli F M G N, (cũ ad motum diurnum cẽtrum Solis ab ea non recedat) & </s>
            <s xml:id="echoid-s1452" xml:space="preserve">altera
              <lb/>
            ex parte circa circunferentiam circuli H O I P, qui illi æqualis eſt, & </s>
            <s xml:id="echoid-s1453" xml:space="preserve">oppoſitus. </s>
            <s xml:id="echoid-s1454" xml:space="preserve">Igitur radius So-
              <lb/>
            lis F E, productus ad I, deſcribit conicas ſuperficies E F G, E I H, ad centrum E, aptatas, quarum
              <lb/>
            baſes ſunt paralleli oppoſiti F M G N, H O I P; </s>
            <s xml:id="echoid-s1455" xml:space="preserve">vertex communis E, centrum mundi; </s>
            <s xml:id="echoid-s1456" xml:space="preserve">axis verò
              <lb/>
            vtriuſque E Q, E R, idem, qui axis mundi, quandoquidem, Q, R, centra ſunt, vt oſtendimus, cir-
              <lb/>
            culorum F M G N, H O I P. </s>
            <s xml:id="echoid-s1457" xml:space="preserve">Quæ omnia perſpicua ſunt ex definitionibus Apollonij Pergæi.</s>
            <s xml:id="echoid-s1458" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <p>
            <s xml:id="echoid-s1459" xml:space="preserve">EAEDEM ſuperficies conicæ deſcribentur, dum Sol in puncto I, oppoſito fuerit conſtitutus,
              <lb/>
            vt patet.</s>
            <s xml:id="echoid-s1460" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1461" xml:space="preserve">DENIQVE, ſi à quouis puncto cęli per centrum mundi recta linea ducatur, deſcribet
              <lb/>
            ipſa motu diurno circumlata duas ſuperficies conicas ad centrum mundi connexas, quarum baſes
              <lb/>
            deſcribuntur à puncto illo, eiusq́; </s>
            <s xml:id="echoid-s1462" xml:space="preserve">oppoſito, axesq́; </s>
            <s xml:id="echoid-s1463" xml:space="preserve">habent partes axis mundi. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">Vt ſi a puncto S,
              <lb/>
            paralleli ſemper apparentium maximi recta S E, per centrum mundi extendatur, deſcribentur mo-
              <lb/>
            tu diurno conicæ ſuperficies E S V, E α Y, ad centrum E, tanquam verticem communem aptatas,
              <lb/>
            quarum baſes ſunt paralleli à puncto S, eiusq́; </s>
            <s xml:id="echoid-s1465" xml:space="preserve">oppoſito α, deſcripti, quorum S T V X, maximus
              <lb/>
            eſt eorum, qui ſemper apparent, at Y Z α β, maximus eorum, qui nunquam apparent ſupra Ho-
              <lb/>
            rizontem Y V. </s>
            <s xml:id="echoid-s1466" xml:space="preserve">Eademq́; </s>
            <s xml:id="echoid-s1467" xml:space="preserve">eſt ratio de cæteris celi punctis. </s>
            <s xml:id="echoid-s1468" xml:space="preserve">Radius ergo Solis in Aequatore quidem
              <lb/>
            exiſtentis, motu diurno, &</s>
            <s xml:id="echoid-s1469" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1470" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1471" xml:space="preserve"/>
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