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-s9261" xml:space="preserve">CONSTRVCTIONIS autẽ huius hęc erit demonſtratio. </s>
            <s xml:id="echoid-s9262" xml:space="preserve">Intelligatur portio Analem-
              <lb/>
              <note position="left" xlink:label="note-0164-01" xlink:href="note-0164-01a" xml:space="preserve">Demonſtratio
                <lb/>
              conſtructionis
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              horologij hori-
                <lb/>
              zontalis.</note>
            matis horologio ſuperpoſita, ita vt punctũ H, puncto H, & </s>
            <s xml:id="echoid-s9263" xml:space="preserve">punctũ I, puncto I, atq; </s>
            <s xml:id="echoid-s9264" xml:space="preserve">recta H I, re-
              <lb/>
            ctę H I, congruat, (congruet autem ei propter æqualitatem rectarum HI, HI,) ipſaq́; </s>
            <s xml:id="echoid-s9265" xml:space="preserve">porti@
              <lb/>
              <figure xlink:label="fig-0164-01" xlink:href="fig-0164-01a" number="121">
                <image file="0164-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0164-01"/>
              </figure>
              <note position="left" xlink:label="note-0164-02" xlink:href="note-0164-02a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0164-03" xlink:href="note-0164-03a" xml:space="preserve">20</note>
            Analemmatis animo concipiatur recta ad planum horologii, & </s>
            <s xml:id="echoid-s9266" xml:space="preserve">meridiana linea H E, habeat pro-
              <lb/>
            prium ſitum, ita vt ſit communis ſectio Meridiani, & </s>
            <s xml:id="echoid-s9267" xml:space="preserve">plani horologij, punctumq́; </s>
            <s xml:id="echoid-s9268" xml:space="preserve">H, ad auſtrum,
              <lb/>
              <note position="left" xlink:label="note-0164-04" xlink:href="note-0164-04a" xml:space="preserve">30</note>
            & </s>
            <s xml:id="echoid-s9269" xml:space="preserve">E, ad boream vergat; </s>
            <s xml:id="echoid-s9270" xml:space="preserve">& </s>
            <s xml:id="echoid-s9271" xml:space="preserve">denique recta B C, plano horologij æquidiſtet, ita vt ſit communis ſe-
              <lb/>
            ctio Meridiani & </s>
            <s xml:id="echoid-s9272" xml:space="preserve">Horizontis, cum D, vertex ſtyli ſit centrum mundi, vt propoſ. </s>
            <s xml:id="echoid-s9273" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9274" xml:space="preserve">præcedentis lib.
              <lb/>
            </s>
            <s xml:id="echoid-s9275" xml:space="preserve">oſtendimus. </s>
            <s xml:id="echoid-s9276" xml:space="preserve">Vel potius loco portionis Analemmatis intelligatur duntaxat triangulum D H I, ea
              <lb/>
            ratione, vt diximus, ſuperpoſitum eſſe horologio, ita vt D H, referat axem mundi, & </s>
            <s xml:id="echoid-s9277" xml:space="preserve">D I, commu-
              <lb/>
            nem ſectionem Meridiani & </s>
            <s xml:id="echoid-s9278" xml:space="preserve">Aequatoris, & </s>
            <s xml:id="echoid-s9279" xml:space="preserve">tandem D G, ſtylus communem ſectionem Meridia-
              <lb/>
            ni, ac Verticalis circuli per D, centrum mundi ducti. </s>
            <s xml:id="echoid-s9280" xml:space="preserve">quod quidem triangulum D H I, vna cum
              <lb/>
            ſtylo D G, in horologio deſcriptum eſt. </s>
            <s xml:id="echoid-s9281" xml:space="preserve">His ita poſitis, occurret axis D H, plano horologij in H, & </s>
            <s xml:id="echoid-s9282" xml:space="preserve">
              <lb/>
            Aequatoris diameter D I, in I; </s>
            <s xml:id="echoid-s9283" xml:space="preserve">Verticalis autem diameter D G, in G. </s>
            <s xml:id="echoid-s9284" xml:space="preserve">Quoniam igitur tam planum
              <lb/>
            Aequatoris, quàm planũ horologij Horizonti æquidiſtãs rectũ eſt ad Meridiani planũ, erit & </s>
            <s xml:id="echoid-s9285" xml:space="preserve">cõ
              <lb/>
            munis ſectio Aequatoris; </s>
            <s xml:id="echoid-s9286" xml:space="preserve">ac plani horologij ad idẽ planum Meridiani, ideoq́; </s>
            <s xml:id="echoid-s9287" xml:space="preserve">per defin. </s>
            <s xml:id="echoid-s9288" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9289" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9290" xml:space="preserve">11. </s>
            <s xml:id="echoid-s9291" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0164-05" xlink:href="note-0164-05a" xml:space="preserve">19. vndec.</note>
              <note position="left" xlink:label="note-0164-06" xlink:href="note-0164-06a" xml:space="preserve">40</note>
            Euclidis, & </s>
            <s xml:id="echoid-s9292" xml:space="preserve">ad lineã meridianã H E, in plano Meridiani exiſtentẽ perpendicularis in puncto I, in
              <lb/>
            quo Aequator per rectam D I, ductus lineæ meridianę in horologio occurrit, vt dictum eſt. </s>
            <s xml:id="echoid-s9293" xml:space="preserve">Re-
              <lb/>
            cta igitur F K, quæ in horologio per I, ad meridianam lineam H I, perpendicularis educta eſt,
              <lb/>
            communis ſectio eſt Aequatoris, & </s>
            <s xml:id="echoid-s9294" xml:space="preserve">plani horologij, nempe linea æquinoctialis: </s>
            <s xml:id="echoid-s9295" xml:space="preserve">Circa quam ſi mo
              <lb/>
            ueri intelligatur planum circuli ex centro E, deſcripti, donec cum mundi centro D, in triangulo
              <lb/>
            D H I, (quod rectum eſſe diximus, vna cum tota portione Analemmatis, ad planum horologij,
              <lb/>
            quamuis ſolum triangulum deſcriptum ſit in horologio, & </s>
            <s xml:id="echoid-s9296" xml:space="preserve">in plano Meridiani exiſtere) con-
              <lb/>
            iungatur E, centrum circuli, propterea quòd rectæ D I, I E, ęquales ſunt ex conſtructione, & </s>
            <s xml:id="echoid-s9297" xml:space="preserve">in
              <lb/>
            illo motu circuli ex E, deſcripti recta I E, ſemper maneat in plano Meridiani, in quo exiſtit recta
              <lb/>
            D I; </s>
            <s xml:id="echoid-s9298" xml:space="preserve">erit ipſe circulus circa centrum mũdi D, ſeu Aequatoris deſcriptus, & </s>
            <s xml:id="echoid-s9299" xml:space="preserve">in plano eiuſdẽ Aequa-
              <lb/>
              <note position="left" xlink:label="note-0164-07" xlink:href="note-0164-07a" xml:space="preserve">50</note>
            toris exiſtens, cum Aequatoris planum per rectas D I, I k, ducatur, quemadmodum & </s>
            <s xml:id="echoid-s9300" xml:space="preserve">circulus di-
              <lb/>
            crus in tali poſitione per eaſdem eſt ductus; </s>
            <s xml:id="echoid-s9301" xml:space="preserve">ita vt circulus hic, & </s>
            <s xml:id="echoid-s9302" xml:space="preserve">Aequator in eodem exiſtant pla-
              <lb/>
            no, idemq́; </s>
            <s xml:id="echoid-s9303" xml:space="preserve">habeant centrum, nimirum D, centrum mundi. </s>
            <s xml:id="echoid-s9304" xml:space="preserve">Intelligatur quoque I E, protracta in
              <lb/>
            vtramque partem in eadem poſitione, quippe quę ſimul cum circulo moueatur, tanquam commu-
              <lb/>
            nis ſectio Meridiani, & </s>
            <s xml:id="echoid-s9305" xml:space="preserve">Aequatoris, cum tam Meridianus, quàm Aequator, in huiuſmodi poſitio-
              <lb/>
            ne per réctam D I, vel I E, (quæ eadem eſt in eo ſitu, que D I) tranſeat. </s>
            <s xml:id="echoid-s9306" xml:space="preserve">Quoniam verò ex ijs, quæ
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            in commentarijs in ſphęram ad finem capitis 1. </s>
            <s xml:id="echoid-s9307" xml:space="preserve">ſcripſimus, circuli in eodem plano, & </s>
            <s xml:id="echoid-s9308" xml:space="preserve">circa idem
              <lb/>
            centrum deſcripti ſecantur in partes ſimiles à lineis è centro egredientibus, ſit vt rectę illę occultę
              <lb/>
            per centrum E, quod iam cum puncto D, hoc eſt, cum centro mundi eſt coniunctum, ductę, quę
              <lb/>
            quidem circumferentiam circuli ſecant in partes 24. </s>
            <s xml:id="echoid-s9309" xml:space="preserve">æquales, occurruntq́; </s>
            <s xml:id="echoid-s9310" xml:space="preserve">rectæ F K, communi
              <lb/>
            ſectioni Aequatoris, & </s>
            <s xml:id="echoid-s9311" xml:space="preserve">plani horologii, in punctis I, A, B, &</s>
            <s xml:id="echoid-s9312" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9313" xml:space="preserve">ſecent quoque, ſi producantur, cir-</s>
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