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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            <s xml:id="echoid-s14037" xml:space="preserve">
              <pb o="204" file="0224" n="224" rhead="GNOMONICES"/>
            que ad meridiem. </s>
            <s xml:id="echoid-s14038" xml:space="preserve">Igitur eadem hora. </s>
            <s xml:id="echoid-s14039" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14040" xml:space="preserve">inæqualis incidet in horam 7. </s>
            <s xml:id="echoid-s14041" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s14042" xml:space="preserve">40. </s>
            <s xml:id="echoid-s14043" xml:space="preserve">à proxima media nocte.
              <lb/>
            </s>
            <s xml:id="echoid-s14044" xml:space="preserve">Hoc artificio horam temporalem, ſiue inæqualẽ deprehendemus quocunque tempore propoſito, ad quam-
              <lb/>
            cunque latitudinem.</s>
            <s xml:id="echoid-s14045" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div711" type="section" level="1" n="177">
          <head xml:id="echoid-head180" xml:space="preserve">DE HOROLOGIIS VERTICALIBVS.
            <lb/>
          PROBLEMA 13. PROPOSITIO 13.</head>
          <p>
            <s xml:id="echoid-s14046" xml:space="preserve">HOROLOGIVM Aſtronomicum Verticale conſtituere.
              <lb/>
            </s>
            <s xml:id="echoid-s14047" xml:space="preserve">
              <note position="left" xlink:label="note-0224-01" xlink:href="note-0224-01a" xml:space="preserve">10</note>
            Hoc eſt, lineas horarum à meridie, vel media nocte in plano, quod
              <lb/>
            Verticali circulo ęquidiſtat, deſcribere.</s>
            <s xml:id="echoid-s14048" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14049" xml:space="preserve">SIT rurſus, vt in propoſ. </s>
            <s xml:id="echoid-s14050" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14051" xml:space="preserve">huius libri, portio Analemmatis A B C, hoc eſt, Meridiani ſemi-
              <lb/>
              <note position="left" xlink:label="note-0224-02" xlink:href="note-0224-02a" xml:space="preserve">Deſcriptio ho-
                <lb/>
              rologii Aſtrono
                <lb/>
              mi@i Verticalis.</note>
            circulus ſit A B C, cuius centrum D; </s>
            <s xml:id="echoid-s14052" xml:space="preserve">communis ſectio ipſius & </s>
            <s xml:id="echoid-s14053" xml:space="preserve">Horizontis, B C; </s>
            <s xml:id="echoid-s14054" xml:space="preserve">communis ſe-
              <lb/>
              <figure xlink:label="fig-0224-01" xlink:href="fig-0224-01a" number="155">
                <image file="0224-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0224-01"/>
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            ctio eiuſdem & </s>
            <s xml:id="echoid-s14055" xml:space="preserve">Verticalis, A D; </s>
            <s xml:id="echoid-s14056" xml:space="preserve">com-
              <lb/>
            munis ſectio eiuſdem & </s>
            <s xml:id="echoid-s14057" xml:space="preserve">Aequatoris,
              <lb/>
            F D; </s>
            <s xml:id="echoid-s14058" xml:space="preserve">axis mundi E D. </s>
            <s xml:id="echoid-s14059" xml:space="preserve">Productis autẽ
              <lb/>
            rectis F D, E D, ad partes D, ſumatur
              <lb/>
              <note position="left" xlink:label="note-0224-03" xlink:href="note-0224-03a" xml:space="preserve">20</note>
            in recta B C, ſtylo horologij futuri,
              <lb/>
            cuiuſcunque magnitudinis datus fue-
              <lb/>
            rit, æqualis recta D G, ex vtraque par-
              <lb/>
            te. </s>
            <s xml:id="echoid-s14060" xml:space="preserve">Et per G, agatur ipſi A D, parallela
              <lb/>
            H I, ſecans E D, & </s>
            <s xml:id="echoid-s14061" xml:space="preserve">F D, in H, I. </s>
            <s xml:id="echoid-s14062" xml:space="preserve">Si igi-
              <lb/>
            tur per A D, duci intelligatur Vertica
              <lb/>
            lis circulus propriè dictus, & </s>
            <s xml:id="echoid-s14063" xml:space="preserve">per H I,
              <lb/>
            planũ horologii illi Verticali æquidi-
              <lb/>
            ſtans; </s>
            <s xml:id="echoid-s14064" xml:space="preserve">cum & </s>
            <s xml:id="echoid-s14065" xml:space="preserve">Meridianus, & </s>
            <s xml:id="echoid-s14066" xml:space="preserve">Horizon
              <lb/>
            ad dictum Verticalẽ rectus ſit, erit ad
              <lb/>
              <note position="left" xlink:label="note-0224-04" xlink:href="note-0224-04a" xml:space="preserve">30</note>
            eundem communis illorẽ ſectio BC,
              <lb/>
              <note position="left" xlink:label="note-0224-05" xlink:href="note-0224-05a" xml:space="preserve">19. vndec.</note>
            perpendicularis, atque adeo & </s>
            <s xml:id="echoid-s14067" xml:space="preserve">ad pla-
              <lb/>
            num horologii per H I, ductum Ver-
              <lb/>
            ticali parallelum, ex demonſtratis à
              <lb/>
            nobis ad propoſ. </s>
            <s xml:id="echoid-s14068" xml:space="preserve">14. </s>
            <s xml:id="echoid-s14069" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14070" xml:space="preserve">11. </s>
            <s xml:id="echoid-s14071" xml:space="preserve">Euclidis,
              <lb/>
            perpendicularis erit. </s>
            <s xml:id="echoid-s14072" xml:space="preserve">Erit ergo H I, in
              <lb/>
            plano horologii linea meridiana, vel
              <lb/>
            horæ 12. </s>
            <s xml:id="echoid-s14073" xml:space="preserve">nempe cõmunis ſectio Me-
              <lb/>
            ridiani, & </s>
            <s xml:id="echoid-s14074" xml:space="preserve">plani horologii. </s>
            <s xml:id="echoid-s14075" xml:space="preserve">Eſt enim
              <lb/>
            recta H I, in plano rectarum H D, I D, hoc eſt, in plano Meridiani. </s>
            <s xml:id="echoid-s14076" xml:space="preserve">D G, gnomon erit ad horologii
              <lb/>
              <note position="left" xlink:label="note-0224-06" xlink:href="note-0224-06a" xml:space="preserve">2. v
                <unsure/>
              ndec
                <unsure/>
              .</note>
              <note position="left" xlink:label="note-0224-07" xlink:href="note-0224-07a" xml:space="preserve">40</note>
            planum rectus, ac proinde & </s>
            <s xml:id="echoid-s14077" xml:space="preserve">ad H I, lineam Meridianam, per definitionem 3. </s>
            <s xml:id="echoid-s14078" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14079" xml:space="preserve">11. </s>
            <s xml:id="echoid-s14080" xml:space="preserve">Euclidis, per-
              <lb/>
            pendicularis, cuius vertex D, idem eſt, quod centrum mundi, ex propoſ. </s>
            <s xml:id="echoid-s14081" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14082" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s14083" xml:space="preserve">Locus
              <lb/>
            gnomonis punctum G, in linea meridiana diſtans à puncto H, in quo axis mundi plano horolo-
              <lb/>
            gii occurrit, & </s>
            <s xml:id="echoid-s14084" xml:space="preserve">quod centrum horologii dicitur, interuallo G H, vel à puncto I, in quo planum
              <lb/>
            Aequatoris lineam meridianam ſecat, interuallo G I. </s>
            <s xml:id="echoid-s14085" xml:space="preserve">Quæ omnia perſpicua ſunt, ſi Meridianus
              <lb/>
            proprium ſitum habere concipiatur, vt videlicet punctum E, in boream vergat, & </s>
            <s xml:id="echoid-s14086" xml:space="preserve">F, in auſtrum.
              <lb/>
            </s>
            <s xml:id="echoid-s14087" xml:space="preserve">Figuram autem ita cõſtructam appellabimus, doctrinæ cauſa, portionem Analemmatis, quemad-
              <lb/>
            modum & </s>
            <s xml:id="echoid-s14088" xml:space="preserve">illam, quam ad initium propoſ. </s>
            <s xml:id="echoid-s14089" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14090" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14091" xml:space="preserve">deſcripſimus, portionem Analemma-
              <lb/>
            tis vocauimus.</s>
            <s xml:id="echoid-s14092" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14093" xml:space="preserve">IAM verò beneficio trianguli D H I, conficiemus horologium Verticale Aſtronomicum hoc
              <lb/>
              <note position="left" xlink:label="note-0224-08" xlink:href="note-0224-08a" xml:space="preserve">50</note>
            modo. </s>
            <s xml:id="echoid-s14094" xml:space="preserve">In lineam rectam H E, ductam vtcunque in plano, in quo horologium deſcribendum eſt,
              <lb/>
            transferatur recta H I, linea meridiana portionis Analemmatis, deorſum quidem à puncto H, ſi
              <lb/>
            horologium ad meridiem ſpectans ſit deſcribendum, ſurſum autem, ſi ſeptentrionale delinean-
              <lb/>
            dum ſit, vt ex portione Analemmatis patet. </s>
            <s xml:id="echoid-s14095" xml:space="preserve">Nam planum horologii ad meridiem ſpectans, rece
              <lb/>
            dens nimirum à D, centro mundi ad partes poli Borealis E, ſecat Aequatorem F D, infra punctũ
              <lb/>
            H, in puncto I; </s>
            <s xml:id="echoid-s14096" xml:space="preserve">planum verò horologii reſpiciens Septentrionem, recedens videlicet à D, centro
              <lb/>
            mundi ad partes auſtrales, ſecat eundem Aequatorem ſupra punctum H, in puncto I, &</s>
            <s xml:id="echoid-s14097" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14098" xml:space="preserve">Deinde
              <lb/>
            ex recta H E, abſcindatur I E, rectæ D I, portionis Analemmatis æqualis: </s>
            <s xml:id="echoid-s14099" xml:space="preserve">Et per I, educatur ad
              <lb/>
            H E, in plano horologii perpendicularis F K. </s>
            <s xml:id="echoid-s14100" xml:space="preserve">Ex E, verò deſcribatur circulus cuiuſuis magnitu-
              <lb/>
            dinis, quo diuiſo in partes 24. </s>
            <s xml:id="echoid-s14101" xml:space="preserve">æquales, initio facto à linea meridiana H E, producta, ducantur per
              <lb/>
            puncta diuiſionum, & </s>
            <s xml:id="echoid-s14102" xml:space="preserve">centrum E, rectæ lineæ occultæ ſecantes rectam F K, in punctis, per </s>
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