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-div270" type="section" level="1" n="113">
          <pb o="79" file="0099" n="99" rhead="LIBER PRIMVS."/>
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        <div xml:id="echoid-div277" type="section" level="1" n="114">
          <head xml:id="echoid-head117" xml:space="preserve">PROBLEMA 3. PROPOSITIO 23.</head>
          <p>
            <s xml:id="echoid-s4342" xml:space="preserve">DECLINATIONEM cuiuſcunque plani à Verticali circulo,
              <lb/>
            & </s>
            <s xml:id="echoid-s4343" xml:space="preserve">eiuſdem inclinationem ad Horizontem inueſtigare.</s>
            <s xml:id="echoid-s4344" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Inſtrumentum
            <lb/>
          pro declinatio-
            <lb/>
          nibus, inclina-
            <lb/>
          tionibusq́; pla-
            <lb/>
          norum inueſti-
            <lb/>
          gandis.</note>
          <p>
            <s xml:id="echoid-s4345" xml:space="preserve">PARETVR exligno, vel alia materia ſolida, cuius una ſuperficies plana ſit, rectangulum
              <lb/>
            quodcunque A B C D, cuius lateribus A B, D C, diuiſis bifariam in E, & </s>
            <s xml:id="echoid-s4346" xml:space="preserve">F, ducatur recta E F, quæ
              <lb/>
            parallela erit vtriq; </s>
            <s xml:id="echoid-s4347" xml:space="preserve">lateri A D,
              <lb/>
              <figure xlink:label="fig-0099-01" xlink:href="fig-0099-01a" number="62">
                <image file="0099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0099-01"/>
              </figure>
              <note position="left" xlink:label="note-0099-02" xlink:href="note-0099-02a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0099-03" xlink:href="note-0099-03a" xml:space="preserve">33. primi.</note>
              <note position="right" xlink:label="note-0099-04" xlink:href="note-0099-04a" xml:space="preserve">29. primi.</note>
            B C, ac propterea anguli ad
              <lb/>
            E, recti. </s>
            <s xml:id="echoid-s4348" xml:space="preserve">Vel certe in extremo
              <lb/>
            ſuperficiei planæ ſit linea re-
              <lb/>
            cta A B, quam ad rectos an-
              <lb/>
            gulos ſecet recta E F, quid-
              <lb/>
            quid ſit de alijs lineis.</s>
            <s xml:id="echoid-s4349" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4350" xml:space="preserve">HOC inſtrumento, etiãſi
              <lb/>
            non ſit rectangulum, declina-
              <lb/>
            tionẽ cuiuſque plani (Appel-
              <lb/>
            lo autem declinationem angu
              <lb/>
              <note position="left" xlink:label="note-0099-05" xlink:href="note-0099-05a" xml:space="preserve">20</note>
            lum acutum, quem faciunt
              <lb/>
            cõmunes ſectiones Horizon-
              <lb/>
            tis cum plano propoſito, & </s>
            <s xml:id="echoid-s4351" xml:space="preserve">
              <lb/>
            Verticali circulo) inueſtigabi-
              <lb/>
              <note position="right" xlink:label="note-0099-06" xlink:href="note-0099-06a" xml:space="preserve">Declinatie pla-
                <lb/>
              ni p
                <unsure/>
              poſiti quo
                <lb/>
              modo@ inquira-
                <lb/>
              tur.</note>
            mus hoc modo. </s>
            <s xml:id="echoid-s4352" xml:space="preserve">In plano pro-
              <lb/>
            poſito, quod ſit vel rectum ad
              <lb/>
            Horizontem, vt eſt planum
              <lb/>
            cuiuſcunq; </s>
            <s xml:id="echoid-s4353" xml:space="preserve">muri ad perpendi-
              <lb/>
            culum ædificati, vel inclinatũ,
              <lb/>
            vt eſt planum cuiuslibet tecti,
              <lb/>
              <note position="left" xlink:label="note-0099-07" xlink:href="note-0099-07a" xml:space="preserve">30</note>
            deſcribatur beneficio libellæ,
              <lb/>
            & </s>
            <s xml:id="echoid-s4354" xml:space="preserve">perpendiculi, linea A B,
              <lb/>
            Horizonti æquidiſtans, com-
              <lb/>
            munis videlicet ſectio plani
              <lb/>
            propoſiti, & </s>
            <s xml:id="echoid-s4355" xml:space="preserve">Hotizontis. </s>
            <s xml:id="echoid-s4356" xml:space="preserve">Vel
              <lb/>
            certè in plano ad Horizõtem
              <lb/>
            recto, per filum, cui adhæret
              <lb/>
            perpendiculum, libere demiſſum ducatur in muro linea reſpondens filo perpendiculi, quæ ad
              <lb/>
            Horizontẽ perpendicularis erit. </s>
            <s xml:id="echoid-s4357" xml:space="preserve">Deinde hãc ad rectos angulos ſecet alia linea recta AB. </s>
            <s xml:id="echoid-s4358" xml:space="preserve">Hæc enim
              <lb/>
            erit Horizonti æquidiſtans, vel ſi mauis, cõmunis ſectio Horizontis & </s>
            <s xml:id="echoid-s4359" xml:space="preserve">muri. </s>
            <s xml:id="echoid-s4360" xml:space="preserve">Quoniã enim murus
              <lb/>
              <note position="left" xlink:label="note-0099-08" xlink:href="note-0099-08a" xml:space="preserve">40</note>
            ad Horizontem rectus ponitur, & </s>
            <s xml:id="echoid-s4361" xml:space="preserve">in muro per filum perpendiculi ducta eſt ad Horizontem linea
              <lb/>
            perpendicularis, erit hæc eadem, per defin. </s>
            <s xml:id="echoid-s4362" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4363" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4364" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4365" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4366" xml:space="preserve">ad communem ſectionem Horizontis
              <lb/>
            atq; </s>
            <s xml:id="echoid-s4367" xml:space="preserve">muri perpendicularis. </s>
            <s xml:id="echoid-s4368" xml:space="preserve">Recta ergo A B, ad hãc ducta perpendicularis, cõmunis erit ſectio muri
              <lb/>
            atq; </s>
            <s xml:id="echoid-s4369" xml:space="preserve">Horizontis. </s>
            <s xml:id="echoid-s4370" xml:space="preserve">Huic lineæ A B, latus inſtrumẽti A B, applicetur, ipſumq́; </s>
            <s xml:id="echoid-s4371" xml:space="preserve">inſtrumentũ Horizonti
              <lb/>
            æquidiſtãs beneficio libellæ, & </s>
            <s xml:id="echoid-s4372" xml:space="preserve">perpendiculi ſtatuatur. </s>
            <s xml:id="echoid-s4373" xml:space="preserve">Deinde in inſtrumẽto inueniatur beneficio
              <lb/>
            acus Magnete illitæ, vel ea ratione, quam in cõmentariis in ſphæram, cũ de Meridiano circulo age
              <lb/>
            remus, tradidimus, vel quod magis probo, ex ſcholio ſequẽti, linea meridiana G H. </s>
            <s xml:id="echoid-s4374" xml:space="preserve">Ex hac enim
              <lb/>
            id, quod proponitur, abſoluemus hac ratione. </s>
            <s xml:id="echoid-s4375" xml:space="preserve">Si linea meridiana G H, æquidiſter rectæ E F, oc-
              <lb/>
            curratq́ muro, vel lineæ A B, quæ Horizonti æquidiſtat, ad angulos rectos, carebit murus decli-
              <lb/>
            natione, ſpectabitq́; </s>
            <s xml:id="echoid-s4376" xml:space="preserve">rectà ad meridiem, vel Septentrionem, ita vt, ſi rectus fuerit ad Horizontem,
              <lb/>
              <note position="left" xlink:label="note-0099-09" xlink:href="note-0099-09a" xml:space="preserve">50</note>
            Verticali circulo proprie dicto æquidiſter; </s>
            <s xml:id="echoid-s4377" xml:space="preserve">Si vero ad Horizontem fuerit inclinatus, rectus ſitad
              <lb/>
            Meridianum, æquidiſtetq́; </s>
            <s xml:id="echoid-s4378" xml:space="preserve">circulo maximo per puncta ortus & </s>
            <s xml:id="echoid-s4379" xml:space="preserve">occaſus æquinoctialis tranſeunti;
              <lb/>
            </s>
            <s xml:id="echoid-s4380" xml:space="preserve">quale eſt planum æquinoctialis circuli, circuli horæ ſextæ aſtronomicæ, circuli horæ 12. </s>
            <s xml:id="echoid-s4381" xml:space="preserve">ab ortu,
              <lb/>
            vel occaſu, & </s>
            <s xml:id="echoid-s4382" xml:space="preserve">denique plana circulorum hectemoriorum, de quibus Prolemæus in Analemmate. </s>
            <s xml:id="echoid-s4383" xml:space="preserve">
              <lb/>
            At ſi meridiana linea G H, rectam E F, ſecet in I, ad angulos rectos, planum muri rectà in ortum,
              <lb/>
            vel occaſum verget, ita vt, ſi rectum ad Horizontem fuerit, parallelum ſit Meridiano circulo. </s>
            <s xml:id="echoid-s4384" xml:space="preserve">Si
              <lb/>
            verò inclinatum fuerit ad Horizontem, rectum ſit ad Verticalem circulum proprie dictum, æqui
              <lb/>
            diſtetq́; </s>
            <s xml:id="echoid-s4385" xml:space="preserve">maximo circulo per puncta, vbi circunferentia Meridiani circuli Horizontis circunferen
              <lb/>
            tiam interſecat, ducto; </s>
            <s xml:id="echoid-s4386" xml:space="preserve">qualia ſunt plana circulorum horariorum, de quibus Ptolemæus in A-
              <lb/>
            nalemmate. </s>
            <s xml:id="echoid-s4387" xml:space="preserve">Si denique linea meridiana G H, rectam E F, ſecet ad angulos inæquales in I, decli-
              <lb/>
            nabit planum & </s>
            <s xml:id="echoid-s4388" xml:space="preserve">à Verticali circulo, & </s>
            <s xml:id="echoid-s4389" xml:space="preserve">à Meridiano, ita vt neque rectà ad meridiem, Septentrio-
              <lb/>
            nemve, neque ad ortum, vel occaſum ſpectet. </s>
            <s xml:id="echoid-s4390" xml:space="preserve">Angulus autem E I G, ſemper erit angulus </s>
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