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-div86" type="section" level="1" n="26">
          <pb o="24" file="0044" n="44" rhead="GNOMONICES"/>
          <figure number="22">
            <image file="0044-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0044-01"/>
          </figure>
          <note position="left" xml:space="preserve">10</note>
        </div>
        <div xml:id="echoid-div88" type="section" level="1" n="27">
          <head xml:id="echoid-head30" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s1673" xml:space="preserve">QVOD ſi quando planum K L, cir culo maximo H I, æquidiſtans tantum à centro A, abſit, vt in fi-
              <lb/>
            gura B D C E, non ſecet vtramque ſuperficiem conicam, ſed vnam tantum, vel neutram, augenda erit
              <lb/>
            vtraque ſuperficies, donec à plano K L, ſecetur, vt in duabus appoſitis figuris vides.</s>
            <s xml:id="echoid-s1674" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Planũ horolo-
            <lb/>
          gii Meridiani,
            <lb/>
          atque æquidi-
            <lb/>
          ſtantis cuilibet
            <lb/>
          circulo horarũ
            <lb/>
          à meridie uel
            <lb/>
          media noctc, im
            <lb/>
          mo & Vertica-
            <lb/>
          lis ad maiorẽ la
            <lb/>
          citudinẽ quàm
            <lb/>
          gr. 45 facit in co
            <lb/>
          nicis ſuperficie-
            <lb/>
          bus, quarũ ba-
            <lb/>
          ſes ſunt paralle
            <lb/>
          lus ſemper ap-
            <lb/>
          parentium ma-
            <lb/>
          ximus, & maxi-
            <lb/>
          mus ſemper la-
            <lb/>
          tentium, duas
            <lb/>
          hyperbolas op-
            <lb/>
          poſitas, & æqua
            <lb/>
          les.</note>
        </div>
        <div xml:id="echoid-div89" type="section" level="1" n="28">
          <head xml:id="echoid-head31" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s1675" xml:space="preserve">CVM ergo & </s>
            <s xml:id="echoid-s1676" xml:space="preserve">Meridianus, & </s>
            <s xml:id="echoid-s1677" xml:space="preserve">circulus cuiuslibet horæ à meridie, vel media nocte, vt propoſ. </s>
            <s xml:id="echoid-s1678" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1679" xml:space="preserve">dice-
              <lb/>
            mus, ſiue Horizon rectus, immo & </s>
            <s xml:id="echoid-s1680" xml:space="preserve">Verticalis circulus maioris latitudinis, quàm grad. </s>
            <s xml:id="echoid-s1681" xml:space="preserve">45. </s>
            <s xml:id="echoid-s1682" xml:space="preserve">ſecet vtrum que
              <lb/>
            parallelum, quorum alter maximus eſt eorum, qui ſemper apparent, alter maximus eorum, qui ſemper oc-
              <lb/>
            cultantur; </s>
            <s xml:id="echoid-s1683" xml:space="preserve">erunt communes ſectiones ſuperficierum conicarum baſes habentium dictos parallelos, quas
              <lb/>
              <note position="left" xlink:label="note-0044-04" xlink:href="note-0044-04a" xml:space="preserve">30</note>
            faciunt plana horologiorum dictis circulis maximis æquidiſtantia, hyperbolæ oppoſitæ, & </s>
            <s xml:id="echoid-s1684" xml:space="preserve">æquales.</s>
            <s xml:id="echoid-s1685" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1686" xml:space="preserve">ITA quoque communes ſectiones cuiuſque horologij, & </s>
            <s xml:id="echoid-s1687" xml:space="preserve">conorum, quorum baſes paralleli ſunt Solis
              <lb/>
            minorem declinationem habentes, quàm quantum eſt cõplementum altitudinis poli ſupra circulum ma-
              <lb/>
            ximum, cui planum horologii æquidiſtat, hyperbolæ erunt oppoſitæ, & </s>
            <s xml:id="echoid-s1688" xml:space="preserve">æquales. </s>
            <s xml:id="echoid-s1689" xml:space="preserve">Tales erunt ſectiones
              <lb/>
            conorum, quorum baſes ſunt paralleli ♋ & </s>
            <s xml:id="echoid-s1690" xml:space="preserve">♑, ac proinde omnium aliorum inter hos, (cum alii om
              <lb/>
            nes minorem habeant declinationem, quàm illi) & </s>
            <s xml:id="echoid-s1691" xml:space="preserve">horologii Horizontalis ad latitudinem minorẽ quàm
              <lb/>
            grad. </s>
            <s xml:id="echoid-s1692" xml:space="preserve">66. </s>
            <s xml:id="echoid-s1693" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1694" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1695" xml:space="preserve">quia hac ratione complementum altitudinis poli maius erit, quàm grad. </s>
            <s xml:id="echoid-s1696" xml:space="preserve">23. </s>
            <s xml:id="echoid-s1697" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1698" xml:space="preserve">30.
              <lb/>
            </s>
            <s xml:id="echoid-s1699" xml:space="preserve">quæ eſt declinatio ♋, & </s>
            <s xml:id="echoid-s1700" xml:space="preserve">♑. </s>
            <s xml:id="echoid-s1701" xml:space="preserve">Idem dic de ſectionibus eorundem conorum, & </s>
            <s xml:id="echoid-s1702" xml:space="preserve">horologii cuiusuis ęqui-
              <lb/>
            diſtantis circulo maximo, ſupra quem polus mundi extollitur paucioribus gradibus, quam 66. </s>
            <s xml:id="echoid-s1703" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1704" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1705" xml:space="preserve">
              <lb/>
            Ex quibus facile cognoſces, quænam plana horologiorum hyperbolas faciant, Sole quemcunque paralle-
              <lb/>
              <note position="left" xlink:label="note-0044-05" xlink:href="note-0044-05a" xml:space="preserve">Quæ horologia
                <lb/>
              in ſuperficiebus
                <lb/>
              eonicis, quarũ
                <lb/>
              baſes sũt cũq;
                <lb/>
              paralleli Aequa
                <lb/>
              toris, facianthy
                <lb/>
              perbolas oppoſi
                <lb/>
              tas & æquales.</note>
            lum percurrente. </s>
            <s xml:id="echoid-s1706" xml:space="preserve">Si enim Sol exiſtat in parallelo, quem circulus maximus plano horologii ęquidiſtans,
              <lb/>
              <note position="left" xlink:label="note-0044-06" xlink:href="note-0044-06a" xml:space="preserve">40</note>
            atque adeo & </s>
            <s xml:id="echoid-s1707" xml:space="preserve">eius oppoſitum ſecat, erunt communes ſectiones horologii, & </s>
            <s xml:id="echoid-s1708" xml:space="preserve">conorum baſes habentium
              <lb/>
            parallelum illum, eiusq́; </s>
            <s xml:id="echoid-s1709" xml:space="preserve">oppoſitum, Hyperbolæ. </s>
            <s xml:id="echoid-s1710" xml:space="preserve">Quæ quidem omnia ex figura ſuperiore facile intelligi
              <lb/>
            poſſunt. </s>
            <s xml:id="echoid-s1711" xml:space="preserve">In vniuerſum autem circulus quilibet maximus illum parallelum ſecat, cuius declinatio minor
              <lb/>
            eſt complemento altitudinis poli ſupra circulum illum maximum, vel cuius declinationis complementũ
              <lb/>
            maius eſt altitudine poli ſupra circulum maximum, vt figura indicat.</s>
            <s xml:id="echoid-s1712" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div92" type="section" level="1" n="29">
          <head xml:id="echoid-head32" xml:space="preserve">THEOREMA 6. PROPOSITIO 7.</head>
          <p>
            <s xml:id="echoid-s1713" xml:space="preserve">SECTIO communis ſuperficierum earundem conicarum, & </s>
            <s xml:id="echoid-s1714" xml:space="preserve">pla-
              <lb/>
              <note position="left" xlink:label="note-0044-07" xlink:href="note-0044-07a" xml:space="preserve">Planum horo-
                <lb/>
              logii æquidiſtãs
                <lb/>
              circulo maxi-
                <lb/>
              mo baſibus co-
                <lb/>
              nicarum ſuper-
                <lb/>
              ficierum neque
                <lb/>
              æquidiſtanti,
                <lb/>
              neque eas tan-
                <lb/>
              genti, aut ſecan
                <lb/>
              ti, facit in altera
                <lb/>
              ſuperficierum
                <lb/>
              Ellipſim.</note>
            ni horologii æquidiſtantis circulo maximo, qui neque baſibus conica-
              <lb/>
              <note position="left" xlink:label="note-0044-08" xlink:href="note-0044-08a" xml:space="preserve">50</note>
            rum ſuperficierum ęquidiſtat, neque eas tangit, neque ſecat, Ellipſis eſt.</s>
            <s xml:id="echoid-s1715" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1716" xml:space="preserve">SINT in eadem Sphæra duæ conicæ ſuperficies, quæ prius; </s>
            <s xml:id="echoid-s1717" xml:space="preserve">& </s>
            <s xml:id="echoid-s1718" xml:space="preserve">circulus maximus H I, neque
              <lb/>
            æquidiſtet baſibus D E, F G, neque eas tangat, neque ſecet, etiamſi in infinitum augeantur ipſæ
              <lb/>
            ſuperficies: </s>
            <s xml:id="echoid-s1719" xml:space="preserve">Cui circulo æquidiſtet planum horologii K L, faciens in conica ſuperficie A F G,
              <lb/>
            fectionem M N O. </s>
            <s xml:id="echoid-s1720" xml:space="preserve">Dico M N O, Ellipſim eſſe. </s>
            <s xml:id="echoid-s1721" xml:space="preserve">Ducatur enim per polos circulorum F G, H I, at-
              <lb/>
            que adeo & </s>
            <s xml:id="echoid-s1722" xml:space="preserve">per polos circuli K L, quem planum horologii in Sphæra efficit, ex propoſ. </s>
            <s xml:id="echoid-s1723" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1724" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1725" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s1726" xml:space="preserve">Theodoſii. </s>
            <s xml:id="echoid-s1727" xml:space="preserve">(cum huius poli ſint iidem, qui circuli H I, per propoſ. </s>
            <s xml:id="echoid-s1728" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1729" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1730" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1731" xml:space="preserve">Theod.) </s>
            <s xml:id="echoid-s1732" xml:space="preserve">circulus ma-
              <lb/>
            ximus B D C E, qui ſecabit, per propoſ. </s>
            <s xml:id="echoid-s1733" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1734" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1735" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1736" xml:space="preserve">Theodoſii, circulos F G, K L, bifariam, & </s>
            <s xml:id="echoid-s1737" xml:space="preserve">ad angu
              <lb/>
            los rectos per rectas F G, K L, quæ ſe mutuo interſecabunt, nempe in puncto P, propterea </s>
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