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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              <pb o="33" file="0053" n="53" rhead="LIBER PRIMVS."/>
            ſa axis eſt Hyperbolarum, cum ſecet ordinatim applicatas ad angulos rectos, vt ex propoſ. </s>
            <s xml:id="echoid-s2254" xml:space="preserve">7. </s>
            <s xml:id="echoid-s2255" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2256" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s2257" xml:space="preserve">Apoll. </s>
            <s xml:id="echoid-s2258" xml:space="preserve">liquet.</s>
            <s xml:id="echoid-s2259" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2260" xml:space="preserve">PRO Ellipſi denique duo rurſus lemmata præmittenda ſunt, quæ ſequuntur, quadrant{q́ue} in om-
              <lb/>
            nem conum tam rectum, quàm ſcalenum.</s>
            <s xml:id="echoid-s2261" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div115" type="section" level="1" n="36">
          <head xml:id="echoid-head39" xml:space="preserve">LEMMA PRIMVM.</head>
          <p>
            <s xml:id="echoid-s2262" xml:space="preserve">DATO cono, & </s>
            <s xml:id="echoid-s2263" xml:space="preserve">diametro tranſuerſa Ellipſis, inuenirelatus rectum Ellipſis.</s>
            <s xml:id="echoid-s2264" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Inuentio late-
            <lb/>
          ris recti Ellipſis,
            <lb/>
          cuius tranſuer-
            <lb/>
          ſa diameter in
            <lb/>
          cono data ſit.</note>
          <note position="left" xml:space="preserve">10</note>
          <figure number="36">
            <image file="0053-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053-01"/>
          </figure>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s2265" xml:space="preserve">SIT datus conus A B C, in quo triangulum per axem A B C; </s>
            <s xml:id="echoid-s2266" xml:space="preserve">ſecetur autem conus
              <lb/>
            pla@@ faciente Ellipſim E F, iuxta propoſ. </s>
            <s xml:id="echoid-s2267" xml:space="preserve">13. </s>
            <s xml:id="echoid-s2268" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2269" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2270" xml:space="preserve">Apollonij, ita vtrecta E F, ſit diame-
              <lb/>
            ter tra@ſuerſa Ellipſis. </s>
            <s xml:id="echoid-s2271" xml:space="preserve">Huius igitur latus rectum ita inueniemus. </s>
            <s xml:id="echoid-s2272" xml:space="preserve">Per A, ducatur
              <lb/>
            A G, ipſi E F, parallela ſecans B C, productam in G; </s>
            <s xml:id="echoid-s2273" xml:space="preserve">fiat{q́ue} vt C G, recta inter punctum
              <lb/>
            G, & </s>
            <s xml:id="echoid-s2274" xml:space="preserve">alterum latus trianguli per axem, ad A G, ita A G, ad G H. </s>
            <s xml:id="echoid-s2275" xml:space="preserve">Rurſ{us} fiat, vt G H,
              <lb/>
              <note position="right" xlink:label="note-0053-04" xlink:href="note-0053-04a" xml:space="preserve">11. ſexti.</note>
            ad G B, rectam inter idem punctum G, & </s>
            <s xml:id="echoid-s2276" xml:space="preserve">alterum latus trianguli per axem, ita E F, dia-
              <lb/>
              <note position="right" xlink:label="note-0053-05" xlink:href="note-0053-05a" xml:space="preserve">12. ſexti.</note>
            meter tranſuerſa ad E I. </s>
            <s xml:id="echoid-s2277" xml:space="preserve">Dico E I, eſſe latus rectum Ellipſis, id eſt, eſſe rectam, iuxta quã
              <lb/>
              <note position="left" xlink:label="note-0053-06" xlink:href="note-0053-06a" xml:space="preserve">30</note>
            poſſunt ordinatim applicatæ ad diametrum. </s>
            <s xml:id="echoid-s2278" xml:space="preserve">Sit enim rectangulum B C, contentum ſub
              <lb/>
            B G, G C, rec
              <unsure/>
            tis inter punctum G, & </s>
            <s xml:id="echoid-s2279" xml:space="preserve">later a trianguli per axem interiectis: </s>
            <s xml:id="echoid-s2280" xml:space="preserve">& </s>
            <s xml:id="echoid-s2281" xml:space="preserve">ad G C, ap-
              <lb/>
            plicetur rectangulum C H, ſub G C, G H, contentum; </s>
            <s xml:id="echoid-s2282" xml:space="preserve">quod æquale crit quadrato ex A G;
              <lb/>
            </s>
            <s xml:id="echoid-s2283" xml:space="preserve">
              <note position="right" xlink:label="note-0053-07" xlink:href="note-0053-07a" xml:space="preserve">17. ſexti.</note>
            quòd tresrectæ C G, A G, G H, ſint continuè proportionales ex conſtructione; </s>
            <s xml:id="echoid-s2284" xml:space="preserve">erit{q́ue}
              <lb/>
            B G H, vna linea recta, propter duos angulos rectos ad G. </s>
            <s xml:id="echoid-s2285" xml:space="preserve">Quoniam igitur eſt, vt H G,
              <lb/>
              <note position="right" xlink:label="note-0053-08" xlink:href="note-0053-08a" xml:space="preserve">14. primi.</note>
            ad G B, ita E F, ad E I; </s>
            <s xml:id="echoid-s2286" xml:space="preserve">vt autem H G, ad G B, ita eſt H C, rectangulum ad rectangulũ
              <lb/>
              <note position="right" xlink:label="note-0053-09" xlink:href="note-0053-09a" xml:space="preserve">1. ſexti.</note>
            C B, hoc eſt, quadratum ex A G, ad rectangulum ſub B G, G C, contentum. </s>
            <s xml:id="echoid-s2287" xml:space="preserve">Igitur E I,
              <lb/>
            latus rectum eſt Ellipſis E F, ex propoſ. </s>
            <s xml:id="echoid-s2288" xml:space="preserve">13. </s>
            <s xml:id="echoid-s2289" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2290" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2291" xml:space="preserve">Apollonij, id eſt, Recta, iuxta quam poſ-
              <lb/>
              <note position="left" xlink:label="note-0053-10" xlink:href="note-0053-10a" xml:space="preserve">40</note>
              <note position="right" xlink:label="note-0053-11" xlink:href="note-0053-11a" xml:space="preserve">Quomodoquar
                <lb/>
              t
                <unsure/>
              a pars rectan-
                <lb/>
              guli ſub diame-
                <lb/>
              tro tianſuerſa
                <lb/>
              Ellipſis, & latere
                <lb/>
              recto compre-
                <lb/>
              henſi applicetur
                <lb/>
              ad tranſuerſam
                <lb/>
              diametrum ex
                <lb/>
              vtraque parte,
                <lb/>
              ita vt deficiat fi
                <lb/>
              gura quadrata.</note>
            ſunt or dinatim applicatæ &</s>
            <s xml:id="echoid-s2292" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2293" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div117" type="section" level="1" n="37">
          <head xml:id="echoid-head40" xml:space="preserve">LEMMA II.</head>
          <p>
            <s xml:id="echoid-s2294" xml:space="preserve">QVARTAM partem rectanguli ſub diametro tranſuerſa Ellipſis, & </s>
            <s xml:id="echoid-s2295" xml:space="preserve">latere re-
              <lb/>
            cto comprehenſi, ad tranſuerſam diametrum ex,
              <unsure/>
            vtraque parte applicare, ita vt de-
              <lb/>
            ficiat figura quadrata.</s>
            <s xml:id="echoid-s2296" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2297" xml:space="preserve">POSITA eadem figura, reperiatur inter E F, diametrum tranſuerſam, & </s>
            <s xml:id="echoid-s2298" xml:space="preserve">latus re-
              <lb/>
            ctum E I, media proportionalis A B, quæ bifariam ſecetur in C. </s>
            <s xml:id="echoid-s2299" xml:space="preserve">Erit igitur quadratum ex
              <lb/>
              <note position="right" xlink:label="note-0053-12" xlink:href="note-0053-12a" xml:space="preserve">13. ſexti.</note>
            A B, rectangulo ſub E F, E I, æquale, atque adeò quadratum ex A C, quod ex ſc
              <unsure/>
            holio pro-
              <lb/>
              <note position="right" xlink:label="note-0053-13" xlink:href="note-0053-13a" xml:space="preserve">17. ſexti.</note>
            poſ. </s>
            <s xml:id="echoid-s2300" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2301" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2302" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2303" xml:space="preserve">Euclidis, quarta pars eſt quadrati ex
              <lb/>
              <note position="left" xlink:label="note-0053-14" xlink:href="note-0053-14a" xml:space="preserve">50</note>
              <figure xlink:label="fig-0053-02" xlink:href="fig-0053-02a" number="37">
                <image file="0053-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053-02"/>
              </figure>
            A B, quartæ parti rectanguli ſub E F, E I, æquale
              <lb/>
            crit. </s>
            <s xml:id="echoid-s2304" xml:space="preserve">Huic igitur quadrato ex A C, applicabimus
              <lb/>
            ad diametrum tranſuerſam E F, ex vtraque par-
              <lb/>
            te æquale rectangulum, deficiens figura quadrata,
              <lb/>
            hac arte. </s>
            <s xml:id="echoid-s2305" xml:space="preserve">Diuiſa recta E F, bifariam in D; </s>
            <s xml:id="echoid-s2306" xml:space="preserve">quo-
              <lb/>
            niam per ea, quæ ad definitiones ſecundas lib. </s>
            <s xml:id="echoid-s2307" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s2308" xml:space="preserve">Apollonij ab Eutocio ſunt demonſtrata, latus re-
              <lb/>
            ctum E I, minus est diametro tranſuerſa E F, hoc
              <lb/>
            est, diametro maiore Ellipſis, erit quoque A B, media proportionalis inter E F, E I, </s>
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