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-div972" type="section" level="1" n="238">
          <p>
            <s xml:id="echoid-s19033" xml:space="preserve">
              <pb o="281" file="0297" n="297" rhead="LIBER SECVNDVS."/>
            tineant ad parallelos Horizontis infra lineam horizontalem, quæ eſt tanquam noua quædã æqui-
              <lb/>
            noctialis linea, deſcribendos, tanquam ſigna auſtralia; </s>
            <s xml:id="echoid-s19034" xml:space="preserve">radij verò emiſſi ad ſiniſtram rectæ A B,
              <lb/>
            referantur ad parallelos Horizontis ſupra lineam horizontalem horologij, nempe in horologio
              <lb/>
            inferiori, deſcribendos, tanquam ſigna borealia. </s>
            <s xml:id="echoid-s19035" xml:space="preserve">Vnde cum portio horologij ſupra lineam hori-
              <lb/>
            zontalem æqualis ſit inferiori horologio, rectè transferuntur in eam radij parallelorum Hori-
              <lb/>
            zontis ex A, educti ad partem ſiniſtram rectæ A B, &</s>
            <s xml:id="echoid-s19036" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19037" xml:space="preserve">quę omnia in figura præcedentis propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s19038" xml:space="preserve">apparent. </s>
            <s xml:id="echoid-s19039" xml:space="preserve">Parallelos ergo Horizontis in eodem æquinoctiali horologio duximus. </s>
            <s xml:id="echoid-s19040" xml:space="preserve">quod erat
              <lb/>
            faciendum.</s>
            <s xml:id="echoid-s19041" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div976" type="section" level="1" n="239">
          <head xml:id="echoid-head246" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s19042" xml:space="preserve">QVONIAM verò Ellipſes, cum integræ ſunt deſcribendæ, cuiuſmodi eſt Ellipſis paralleli Hori-
              <lb/>
              <note position="left" xlink:label="note-0297-01" xlink:href="note-0297-01a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0297-02" xlink:href="note-0297-02a" xml:space="preserve">Quo pacto ex
                <lb/>
              vna medietate
                <lb/>
              Ellipſis reliqua
                <lb/>
              medietas deſc
                <unsure/>
              ri
                <lb/>
              benda ſit.</note>
            zontis grad. </s>
            <s xml:id="echoid-s19043" xml:space="preserve">60. </s>
            <s xml:id="echoid-s19044" xml:space="preserve">in noſtro exemplo difficulter, incommode{q́ue} deſcribuntur per omnia puncta in lineis Ver-
              <lb/>
            ticalibus inuenta; </s>
            <s xml:id="echoid-s19045" xml:space="preserve">vt hic per ea, quæ existunt prope alterum extremum q, diametri Ellipſis P q; </s>
            <s xml:id="echoid-s19046" xml:space="preserve">vte-
              <lb/>
            mur hac induſtria, vt vniformiter eas deſcribamus. </s>
            <s xml:id="echoid-s19047" xml:space="preserve">Inuento in linea meridiana altero extremo diame-
              <lb/>
            tri, vt hic puncto q, (quod quidem reperietur, ſi recta D 90. </s>
            <s xml:id="echoid-s19048" xml:space="preserve">ad dexteram ipſius D F, in proxima figura in-
              <lb/>
            tercepta inter D, & </s>
            <s xml:id="echoid-s19049" xml:space="preserve">radium paralleli grad. </s>
            <s xml:id="echoid-s19050" xml:space="preserve">60. </s>
            <s xml:id="echoid-s19051" xml:space="preserve">transferatur in lineam meridianam horologij ex p, vſque
              <lb/>
            ad q; </s>
            <s xml:id="echoid-s19052" xml:space="preserve">vel certein Analemmate huius propoſ. </s>
            <s xml:id="echoid-s19053" xml:space="preserve">ſumatur diameter Ellipſis par alleli gr. </s>
            <s xml:id="echoid-s19054" xml:space="preserve">60. </s>
            <s xml:id="echoid-s19055" xml:space="preserve">inter P, & </s>
            <s xml:id="echoid-s19056" xml:space="preserve">aliud
              <lb/>
            latus trianguli per axem in cono, cuius baſes ſunt paralleli gr. </s>
            <s xml:id="echoid-s19057" xml:space="preserve">60. </s>
            <s xml:id="echoid-s19058" xml:space="preserve">intercepta, transferatur q; </s>
            <s xml:id="echoid-s19059" xml:space="preserve">ex P, uſque
              <lb/>
            ad q.) </s>
            <s xml:id="echoid-s19060" xml:space="preserve">ſecabimus totam diametrum P q, bifariam in r, vt r, ſit centrum Ellipſis, vt conſtat ex definitio-
              <lb/>
            nibus ſecundis Apollonij, ducemus{q́ue} per r, perpendicularem ad P q, nempe diametrum ſecundam El-
              <lb/>
            lipſis. </s>
            <s xml:id="echoid-s19061" xml:space="preserve">Deinde quia per propoſ. </s>
            <s xml:id="echoid-s19062" xml:space="preserve">30. </s>
            <s xml:id="echoid-s19063" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s19064" xml:space="preserve">1. </s>
            <s xml:id="echoid-s19065" xml:space="preserve">Apollonij, recta linea quæcunq; </s>
            <s xml:id="echoid-s19066" xml:space="preserve">per centrum Ellipſis ducta in
              <lb/>
              <note position="left" xlink:label="note-0297-03" xlink:href="note-0297-03a" xml:space="preserve">20</note>
            centro bifariam diuiditur, ducemus ex punctis verticalium linearum, per quæ medietas ſuperior Ellipſis
              <lb/>
            tranſit, (quæ quidem medietas commodius deſcribi poteſt, quam inferior, vt patet) per centrum r, lineas
              <lb/>
            occultas, & </s>
            <s xml:id="echoid-s19067" xml:space="preserve">earum partibus inter dicta puncta, & </s>
            <s xml:id="echoid-s19068" xml:space="preserve">centrum r, abſcind cmus infra centrum æquales rectas
              <lb/>
            lineas, imprimendo puncta in lineis illis occultis. </s>
            <s xml:id="echoid-s19069" xml:space="preserve">Per hæc enim puncta ducenda erit inferior medietas
              <lb/>
            Ellipſis. </s>
            <s xml:id="echoid-s19070" xml:space="preserve">Facile autem ex propoſitione 75. </s>
            <s xml:id="echoid-s19071" xml:space="preserve">ſuperioris libri, & </s>
            <s xml:id="echoid-s19072" xml:space="preserve">priori figura huius propoſ. </s>
            <s xml:id="echoid-s19073" xml:space="preserve">cognoſcemus,
              <lb/>
            quinã parallelus Horizontis Ellipſim faciat in horologio. </s>
            <s xml:id="echoid-s19074" xml:space="preserve">Hac arte vtemur quoque in Ellipſibus aliorum
              <lb/>
            horologiorum, vbi hæ deſcribendæ erunt.</s>
            <s xml:id="echoid-s19075" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s19076" xml:space="preserve">EODEM modo in horologio inferiori deſcribemus parallelos Horizontis ſupra lineam horizonta-
              <lb/>
              <note position="right" xlink:label="note-0297-04" xlink:href="note-0297-04a" xml:space="preserve">Qua tatione pa
                <lb/>
              ralleli ſupra li-
                <lb/>
              neam horizon-
                <lb/>
              talem ex eorũ
                <unsure/>
                <lb/>
              oppoſitis infra
                <lb/>
              horizontalem
                <lb/>
              lineam deſcri-
                <lb/>
              ptis deſcriban-
                <lb/>
              tur.</note>
            lem, ex eorum oppoſitis in horologio ſuperiori deſcriptis, & </s>
            <s xml:id="echoid-s19077" xml:space="preserve">accur atius multo, ſi ſecundum doctrinam in
              <lb/>
            fine propoſ. </s>
            <s xml:id="echoid-s19078" xml:space="preserve">2. </s>
            <s xml:id="echoid-s19079" xml:space="preserve">huius libri traditam inueniamus prius diametros tranſuerſas oppoſitarum ſectionum, ea-
              <lb/>
              <note position="left" xlink:label="note-0297-05" xlink:href="note-0297-05a" xml:space="preserve">30</note>
            rumq; </s>
            <s xml:id="echoid-s19080" xml:space="preserve">centra, &</s>
            <s xml:id="echoid-s19081" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19082" xml:space="preserve">In poſteriori quidem figura huius propoſ. </s>
            <s xml:id="echoid-s19083" xml:space="preserve">diametri tranſuerſæ ſunt portiones rectæ
              <lb/>
            D E, poſitæ inter radios parallelorum horizontis oppoſitorum ex A, egredientes, æqualiter q; </s>
            <s xml:id="echoid-s19084" xml:space="preserve">diſtantes
              <lb/>
            à recta A B.</s>
            <s xml:id="echoid-s19085" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div979" type="section" level="1" n="240">
          <head xml:id="echoid-head247" xml:space="preserve">PROBLEMA 54. PROPOSITIO 54.</head>
          <p>
            <s xml:id="echoid-s19086" xml:space="preserve">MERIDIANOS, id eſt, circulos longitudinum ciuitatum, in eo-
              <lb/>
            dem horologio æquinoctiali deſcribere.</s>
            <s xml:id="echoid-s19087" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19088" xml:space="preserve">CIRCVLI Meri-
              <lb/>
              <figure xlink:label="fig-0297-01" xlink:href="fig-0297-01a" number="206">
                <image file="0297-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0297-01"/>
              </figure>
              <note position="right" xlink:label="note-0297-06" xlink:href="note-0297-06a" xml:space="preserve">Meridianorum
                <lb/>
              deſcriptio in eo
                <lb/>
              dem horologio
                <lb/>
              @quinoctiali.</note>
            diani deſcribentur, vt
              <lb/>
              <note position="left" xlink:label="note-0297-07" xlink:href="note-0297-07a" xml:space="preserve">40</note>
            horæ à meridie, vel me-
              <lb/>
            dia nocte, quemadmo-
              <lb/>
            dum docuimus propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s19089" xml:space="preserve">6. </s>
            <s xml:id="echoid-s19090" xml:space="preserve">huius libri, ſi tamen
              <lb/>
            circulus A C B D, be-
              <lb/>
            neficio cuiuspropoſ. </s>
            <s xml:id="echoid-s19091" xml:space="preserve">49. </s>
            <s xml:id="echoid-s19092" xml:space="preserve">
              <lb/>
            huius libri lineas hora-
              <lb/>
            rias duximus, principiũ
              <lb/>
            diuiſionis in 360. </s>
            <s xml:id="echoid-s19093" xml:space="preserve">gra-
              <lb/>
            dus ſumat à Meridiano
              <lb/>
              <note position="left" xlink:label="note-0297-08" xlink:href="note-0297-08a" xml:space="preserve">50</note>
            circulo inſularum For-
              <lb/>
            tunatarum, qui habetur
              <lb/>
            in horologio ſuperiori,
              <lb/>
            ſi loci longitudo nume-
              <lb/>
            retur à Meridiano loci,
              <lb/>
            nempe à puncto A, uer-
              <lb/>
            ſus D, partes occidenta-
              <lb/>
            les, vſq; </s>
            <s xml:id="echoid-s19094" xml:space="preserve">ad punctum G;
              <lb/>
            </s>
            <s xml:id="echoid-s19095" xml:space="preserve">vt perſpicuum eſt, ſi ho-
              <lb/>
            rologium in proprio ſi-
              <lb/>
            tu intelligatur eſſe </s>
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