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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          <p>
            <s xml:id="echoid-s1737" xml:space="preserve">
              <pb o="25" file="0045" n="45" rhead="LIBER PRIMVS."/>
            non æquidiſtent inter ſe; </s>
            <s xml:id="echoid-s1738" xml:space="preserve">facietq́ue
              <lb/>
              <figure xlink:label="fig-0045-01" xlink:href="fig-0045-01a" number="23">
                <image file="0045-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0045-01"/>
              </figure>
            communes ſectiones H I, K L, pla-
              <lb/>
            norum parallelorum H I, K L, pa-
              <lb/>
              <note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">16. undec.</note>
            rallelas. </s>
            <s xml:id="echoid-s1739" xml:space="preserve">Faciat quoque idem circu-
              <lb/>
            lus B D C E, triangulum per axem
              <lb/>
            A F G, ſecans rectam K L, & </s>
            <s xml:id="echoid-s1740" xml:space="preserve">ſectio-
              <lb/>
            nem conicam in M. </s>
            <s xml:id="echoid-s1741" xml:space="preserve">Secet etiã pla-
              <lb/>
            num K L, per rectam L M, tranſiens
              <lb/>
            planum circuli F G, (ſecabunt au-
              <lb/>
            tem neceſſario ſe mutuo plana F G,
              <lb/>
              <note position="left" xlink:label="note-0045-02" xlink:href="note-0045-02a" xml:space="preserve">10</note>
            K L, cum non ponantur parallela.)
              <lb/>
            </s>
            <s xml:id="echoid-s1742" xml:space="preserve">vel certè eius planum productum,
              <lb/>
            per rectam N P O, quæ per punctũ
              <lb/>
            P, ducitur. </s>
            <s xml:id="echoid-s1743" xml:space="preserve">Cum enim recta K L,
              <lb/>
            rectam F G, ſecet in P, tranſibit pla
              <lb/>
            num per K L, ductum etiam per P; </s>
            <s xml:id="echoid-s1744" xml:space="preserve">
              <lb/>
            ac proinde communis ſectio pla-
              <lb/>
            norum F G, K L, per punctum P,
              <lb/>
            tranſibit. </s>
            <s xml:id="echoid-s1745" xml:space="preserve">Quoniam igitur plana
              <lb/>
            F G, k L, recta ſuntad planum cir-
              <lb/>
              <note position="left" xlink:label="note-0045-03" xlink:href="note-0045-03a" xml:space="preserve">20</note>
            culi B D C E, propterea quòd hic
              <lb/>
            circulus illa plana ad rectos angu-
              <lb/>
            los ſecat, vt paulo ante oſtendimus;
              <lb/>
            </s>
            <s xml:id="echoid-s1746" xml:space="preserve">
              <note position="right" xlink:label="note-0045-04" xlink:href="note-0045-04a" xml:space="preserve">19. vndec.</note>
            erit quoque eorum communis ſe-
              <lb/>
            ctio N O, ad idẽ recta, atque adeo
              <lb/>
            per defin. </s>
            <s xml:id="echoid-s1747" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1748" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1749" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1750" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1751" xml:space="preserve">& </s>
            <s xml:id="echoid-s1752" xml:space="preserve">ad rectã
              <lb/>
            F G, baſim trianguli per axim, per-
              <lb/>
            pendicularis erit. </s>
            <s xml:id="echoid-s1753" xml:space="preserve">Et quia rectæ
              <lb/>
            H I, k L, oſtenſæ ſunt parallelæ,
              <lb/>
              <note position="right" xlink:label="note-0045-05" xlink:href="note-0045-05a" xml:space="preserve">29. primi.</note>
            erunt anguli H A M, k M A, duo-
              <lb/>
              <note position="left" xlink:label="note-0045-06" xlink:href="note-0045-06a" xml:space="preserve">30</note>
            bus rectis æquales; </s>
            <s xml:id="echoid-s1754" xml:space="preserve">atque adeo an-
              <lb/>
            guli F A M, k M A, duobus rectis
              <lb/>
            minores. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">Conuenient ergo, per
              <lb/>
            pronunciatum 11. </s>
            <s xml:id="echoid-s1756" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1757" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1758" xml:space="preserve">Euclidis,
              <lb/>
            rectæ A F, k L, productæ ad partes
              <lb/>
            F, k, ac proinde planum horologii
              <lb/>
            per k L, ductum latus A F, ſecabit
              <lb/>
            ad eaſdem partes F, k. </s>
            <s xml:id="echoid-s1759" xml:space="preserve">Quam ob
              <lb/>
            rem, cum conus A F G, ſecetur pla-
              <lb/>
            no B D C E, per axem, ſecetur autẽ
              <lb/>
              <note position="left" xlink:label="note-0045-07" xlink:href="note-0045-07a" xml:space="preserve">40</note>
            & </s>
            <s xml:id="echoid-s1760" xml:space="preserve">altero plano k L, conueniente
              <lb/>
            cum utroque latere A F, A G, trian-
              <lb/>
            guli per axem A F G, quod quidem
              <lb/>
            planum k L, neque æquidiſtat baſi
              <lb/>
            F G, neque triangulum ad verticẽ
              <lb/>
            A, aufert ſimile & </s>
            <s xml:id="echoid-s1761" xml:space="preserve">ſubcontrarie po-
              <lb/>
            ſitum triangulo per axem, propte-
              <lb/>
            rea quòd angulus A M P, maior ſit
              <lb/>
              <note position="right" xlink:label="note-0045-08" xlink:href="note-0045-08a" xml:space="preserve">16. primi.</note>
            angulo A G F, externus interno,
              <lb/>
            hoc eſt, angulo A F G, cum hic æqualis ſit angulo A G F; </s>
            <s xml:id="echoid-s1762" xml:space="preserve">eſtq́; </s>
            <s xml:id="echoid-s1763" xml:space="preserve">N O, communis ſectio plani ſecan-
              <lb/>
              <note position="left" xlink:label="note-0045-09" xlink:href="note-0045-09a" xml:space="preserve">50</note>
              <note position="right" xlink:label="note-0045-10" xlink:href="note-0045-10a" xml:space="preserve">5. primi.</note>
            tis k L, & </s>
            <s xml:id="echoid-s1764" xml:space="preserve">baſis coni F G, perpendicularis ad F G, baſim trianguli per axem, vel certè ad eam, quæ
              <lb/>
            in directum ipſi conſtituitur; </s>
            <s xml:id="echoid-s1765" xml:space="preserve">erit communis ſectio M N O, per propoſ. </s>
            <s xml:id="echoid-s1766" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1767" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1768" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1769" xml:space="preserve">Apollonij, El-
              <lb/>
              <note position="right" xlink:label="note-0045-11" xlink:href="note-0045-11a" xml:space="preserve">Planũ horolo-
                <lb/>
              gij Verticalis ad
                <lb/>
              minorẽ latitu-
                <lb/>
              dinẽ, quàm gr.
                <lb/>
              45 facit in alte
                <lb/>
              ra ſuperficierũ
                <lb/>
              conicarũ, quarũ
                <lb/>
              baſes ſunt pa-
                <lb/>
              rallelus ſemper
                <lb/>
              apparentiũ ma-
                <lb/>
              ximus, & maxi-
                <lb/>
              mus ſemper oc-
                <lb/>
              cultorum, Elli-
                <lb/>
              pſim.</note>
            lipſis. </s>
            <s xml:id="echoid-s1770" xml:space="preserve">Sectio ergo communis ſuperficierum earundem, &</s>
            <s xml:id="echoid-s1771" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1772" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s1773" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div95" type="section" level="1" n="30">
          <head xml:id="echoid-head33" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s1774" xml:space="preserve">IGITVR, quia Verticalis circulus minoris latitudinis, quàm grad. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">45. </s>
            <s xml:id="echoid-s1776" xml:space="preserve">neque æquidiſtat parallelis,
              <lb/>
            quorum vnus maximus eſt eorum, qui ſemper apparent, alter verò maximus eorum, qui perpetuo ſub Ho-
              <lb/>
            rizonte latent, neque ipſos tangit, neque ſecat; </s>
            <s xml:id="echoid-s1777" xml:space="preserve">erit communis ſectio plani horologii Verticalis, cuius la-
              <lb/>
            titudo minor eſt, quàm grad. </s>
            <s xml:id="echoid-s1778" xml:space="preserve">45. </s>
            <s xml:id="echoid-s1779" xml:space="preserve">& </s>
            <s xml:id="echoid-s1780" xml:space="preserve">coni, cuius baſis parallelus eſt maximus eorum, qui ſemper occultantur
              <lb/>
            ſub terra, ſi planum horologii ſit ad partes poli occulti, reſpiciatq́; </s>
            <s xml:id="echoid-s1781" xml:space="preserve">polum conſpicuum, vel maximus eorũ,
              <lb/>
            qui perpetuo apparent, ſi horologii planum ad partes poli conſpicui recedat, reſpiciatq́; </s>
            <s xml:id="echoid-s1782" xml:space="preserve">partes poli oc-
              <lb/>
            @ulti, Ellipſis.</s>
            <s xml:id="echoid-s1783" xml:space="preserve"/>
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