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-s1939" xml:space="preserve">
              <pb o="28" file="0048" n="48" rhead="GNOMONICES"/>
            non deſcribitur ſemicirculus circa diametrum B C, quia non ſecaret rectã E M. </s>
            <s xml:id="echoid-s1940" xml:space="preserve">Aliquando etiam
              <lb/>
            ſemicirculi ſe interſecant in recta E M, in deſcriptione Ellipſis, vt@emicirculi F P H, R V S, in
              <lb/>
            priori Ellipſi, v@i rectę E P, E V, æquales ſunt, atque perpendiculares k P, T V, ſumptę
              <lb/>
            i
              <unsure/>
            pſis ęquales in tertijs figuris.</s>
            <s xml:id="echoid-s1941" xml:space="preserve"/>
          </p>
          <figure number="28">
            <image file="0048-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0048-01"/>
          </figure>
          <note position="left" xml:space="preserve">10</note>
          <note position="left" xml:space="preserve">In poſteriori
            <lb/>
          harũ media -
            <lb/>
          runi figurar@
            <lb/>
          vbi eſt P, po-
            <lb/>
          ne M, & loco
            <lb/>
          M, repone P.</note>
          <note position="left" xml:space="preserve">20</note>
          <figure number="29">
            <image file="0048-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0048-02"/>
          </figure>
          <note position="left" xml:space="preserve">30</note>
          <figure number="30">
            <image file="0048-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0048-03"/>
          </figure>
          <p>
            <s xml:id="echoid-s1942" xml:space="preserve">SED iam demonſtremus, ſectionem conicam tranſire in plano per puncta Q, P, &</s>
            <s xml:id="echoid-s1943" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1944" xml:space="preserve">circa
              <lb/>
              <note position="left" xlink:label="note-0048-05" xlink:href="note-0048-05a" xml:space="preserve">Demonſtratio
                <lb/>
              ſuperioris de-
                <lb/>
              ſcriptionis.</note>
            diametrum D E, atque adeo lineam per ipſa puncta in plano aptè deſcriptam, eſſe conicam ſectio-
              <lb/>
            nem, vt diximus. </s>
            <s xml:id="echoid-s1945" xml:space="preserve">Ducto in primis figuris per rectam F H, plano, quod baſi coni æquidiſtet, erit
              <lb/>
              <note position="left" xlink:label="note-0048-06" xlink:href="note-0048-06a" xml:space="preserve">40</note>
            ſectio facta F X H, circulus, per propoſ. </s>
            <s xml:id="echoid-s1946" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1947" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1948" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1949" xml:space="preserve">Apollonii, cuius quidem & </s>
            <s xml:id="echoid-s1950" xml:space="preserve">ſectionis communis ſe-
              <lb/>
            ctio ſit recta X Y, quæ per K, tranſibit, vbi ſe ſecant rectæ D E, F H, & </s>
            <s xml:id="echoid-s1951" xml:space="preserve">vbi circulus F X H, per rectã
              <lb/>
            F H, ductus ſectioni conicæ occurrit. </s>
            <s xml:id="echoid-s1952" xml:space="preserve">Et quoniam plana B C, F H, parallela ſecantur plano D E, fa-
              <lb/>
            ciente conicam ſectionem, erunt communes ſectiones Z α X Y, parallelæ: </s>
            <s xml:id="echoid-s1953" xml:space="preserve">Eſt autem Z α, ad re-
              <lb/>
              <note position="left" xlink:label="note-0048-07" xlink:href="note-0048-07a" xml:space="preserve">16. vndec.</note>
            ctam B C, perpendicularis, (vt enim fiat ſectio aliqua conica, neceſſe eſt, vt ſectio communis pla-
              <lb/>
            ni ſecantis, & </s>
            <s xml:id="echoid-s1954" xml:space="preserve">baſis coni, qualis eſt recta Z α, perpendicularis ſit ad baſim trianguli per axem, vt
              <lb/>
            conſtat
              <unsure/>
            ex propoſ. </s>
            <s xml:id="echoid-s1955" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1956" xml:space="preserve">12. </s>
            <s xml:id="echoid-s1957" xml:space="preserve">& </s>
            <s xml:id="echoid-s1958" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1959" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1960" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1961" xml:space="preserve">Apollonii) & </s>
            <s xml:id="echoid-s1962" xml:space="preserve">anguli B E Z, F K X, æquales ſunt, propte-
              <lb/>
              <note position="left" xlink:label="note-0048-08" xlink:href="note-0048-08a" xml:space="preserve">10. vndec.</note>
            rea quòd rectæ B E, E Z, rectis F K, k X, ſunt parallelæ. </s>
            <s xml:id="echoid-s1963" xml:space="preserve">Igitur erit & </s>
            <s xml:id="echoid-s1964" xml:space="preserve">angulus F K X, rectus, at-
              <lb/>
            que adeo X K, ad F H, perpendicularis, ac proinde X K, in ſemicirculo F X H, media erit propor-
              <lb/>
            tionalis inter F K, K H, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s1965" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1966" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1967" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1968" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1969" xml:space="preserve">Atqui & </s>
            <s xml:id="echoid-s1970" xml:space="preserve">in ſecundis figuris E P, eadem
              <lb/>
              <note position="left" xlink:label="note-0048-09" xlink:href="note-0048-09a" xml:space="preserve">50</note>
            ratione media eſt proportionalis inter F E, E H, hoc eſt, inter eaſdẽ F k, K H, in primis figuris, at-
              <lb/>
            que adeo ipſi X K, in primis figuris æqualis: </s>
            <s xml:id="echoid-s1971" xml:space="preserve">(ſumptæ enim ſunt E F, E H, in ſecundis figuris, ip-
              <lb/>
            ſis K.</s>
            <s xml:id="echoid-s1972" xml:space="preserve">F, K H, in primis æquales) Eſt autem eadem E P, in ſecundis figuris, ipſi k P, in tertiis æqua-
              <lb/>
            lis. </s>
            <s xml:id="echoid-s1973" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s1974" xml:space="preserve">k P, in tertiis figuris, ipſi K X, in primis, ęqualis eſt. </s>
            <s xml:id="echoid-s1975" xml:space="preserve">Quare cum in primis figuris
              <lb/>
            per X, in conica ſuperficie tranſeat ſectio conica, tranſibit eadem in plano per punctum P; </s>
            <s xml:id="echoid-s1976" xml:space="preserve">quo-
              <lb/>
            niam hac ratione, poſito puncto K, tertiarum figurarum in puncto k, primarum, ita vt diameter
              <lb/>
            k D, tertiarum congruat diametro k D, primarum, congruet perpendicularis k P, in tertiis figu-
              <lb/>
            ris, perpendiculari k X, in primis; </s>
            <s xml:id="echoid-s1977" xml:space="preserve">atque adeo punctum P, in punctum X, cader, (ob æqualitatem
              <lb/>
            rectarũ k P, k X,) & </s>
            <s xml:id="echoid-s1978" xml:space="preserve">ſectio conica per punctum P, quod à puncto X, non differt, tranſibit. </s>
            <s xml:id="echoid-s1979" xml:space="preserve">Ea-
              <lb/>
            demq́ue ratione oſtendemus, ſectionem eandem tranſire per punctum Q, & </s>
            <s xml:id="echoid-s1980" xml:space="preserve">per reliqua, ſi qua
              <lb/>
            ſunt. </s>
            <s xml:id="echoid-s1981" xml:space="preserve">Dato ergo cono, & </s>
            <s xml:id="echoid-s1982" xml:space="preserve">diametro conicæ ſectionis, &</s>
            <s xml:id="echoid-s1983" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1984" xml:space="preserve">quod faciendum erat.</s>
            <s xml:id="echoid-s1985" xml:space="preserve"/>
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