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-div999" type="section" level="1" n="246">
          <p>
            <s xml:id="echoid-s19540" xml:space="preserve">
              <pb o="289" file="0305" n="305" rhead="LIBER SECVNDVS."/>
            Meridiani, proptereaq́ue circulus horæ 12. </s>
            <s xml:id="echoid-s19541" xml:space="preserve">ab ortu, vel occaſu plano horologii occurret in pun-
              <lb/>
            cto D. </s>
            <s xml:id="echoid-s19542" xml:space="preserve">Quia verò linea horæ 12. </s>
            <s xml:id="echoid-s19543" xml:space="preserve">ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s19544" xml:space="preserve">linea horæ 6. </s>
            <s xml:id="echoid-s19545" xml:space="preserve">à meridie, vel media nocte
              <lb/>
            parallelæ ſunt, per ea, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s19546" xml:space="preserve">22. </s>
            <s xml:id="echoid-s19547" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s19548" xml:space="preserve">ſcripſimus, ſequitur rectam, quæ
              <lb/>
            per D, ducitur parallela lineæ horæ 6. </s>
            <s xml:id="echoid-s19549" xml:space="preserve">à meridie, vel media nocte, lineam eſſe horæ 12. </s>
            <s xml:id="echoid-s19550" xml:space="preserve">ab ortu,
              <lb/>
            vel occaſu. </s>
            <s xml:id="echoid-s19551" xml:space="preserve">Quoniam autem angulus altitudinis poli B A C, æqualis eſt angulo E A D, ad verti-
              <lb/>
              <note position="right" xlink:label="note-0305-01" xlink:href="note-0305-01a" xml:space="preserve">15. primi.</note>
              <note position="right" xlink:label="note-0305-02" xlink:href="note-0305-02a" xml:space="preserve">Aliæ deſcriptio
                <lb/>
              ne@ lineæ horę
                <lb/>
              12. ab or. vel
                <lb/>
              occ. in æquino-
                <lb/>
              ctiali horologio</note>
            cem, efficitur, vt ſi in linea horæ 6. </s>
            <s xml:id="echoid-s19552" xml:space="preserve">à meridie, vel media nocte accipiamus rectam E A, ſtylo æqua
              <lb/>
            lem, & </s>
            <s xml:id="echoid-s19553" xml:space="preserve">in A, conſtituamus angulum E A D, altitudini poli æqualem, reperiamus in meridiana li-
              <lb/>
            nea idem punctum D, per quod linea horæ 12. </s>
            <s xml:id="echoid-s19554" xml:space="preserve">ab ortu, vel occaſu ducenda eſt, etiam ſi circulus
              <lb/>
            B C, non deſcribatur. </s>
            <s xml:id="echoid-s19555" xml:space="preserve">Quinetiam ſi rectę E m, æqualem abſcindamus E D, habebimus idem pun-
              <lb/>
            ctum D. </s>
            <s xml:id="echoid-s19556" xml:space="preserve">Cum enim & </s>
            <s xml:id="echoid-s19557" xml:space="preserve">angulus E A m, æqualis ſit conſtitutus altitudini poli, vt ex propoſ. </s>
            <s xml:id="echoid-s19558" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19559" xml:space="preserve">hu-
              <lb/>
              <note position="left" xlink:label="note-0305-03" xlink:href="note-0305-03a" xml:space="preserve">10</note>
            ius libri conſtat, æquales erunt anguli E A m, E A D, in triangulis E A m, E A D, in triangulis
              <lb/>
            E A m, E A D: </s>
            <s xml:id="echoid-s19560" xml:space="preserve">ſed & </s>
            <s xml:id="echoid-s19561" xml:space="preserve">anguli ad E, æquales ſunt, nemper recti, eſtq́ue latus E A, dictis angulis adia-
              <lb/>
            cens commune. </s>
            <s xml:id="echoid-s19562" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s19563" xml:space="preserve">latera E m, E D, æqualia erunt; </s>
            <s xml:id="echoid-s19564" xml:space="preserve">ac proinde cum per D, tranſeat linea ho
              <lb/>
              <note position="right" xlink:label="note-0305-04" xlink:href="note-0305-04a" xml:space="preserve">26. primi.</note>
            rę 12. </s>
            <s xml:id="echoid-s19565" xml:space="preserve">ab ortu, vel occaſu, vt oſtendimus, liquido conſtat, ſi ipſi E m, æqualis abſcindatur E D, per
              <lb/>
            D, ducendam eſſe lineam horæ 12. </s>
            <s xml:id="echoid-s19566" xml:space="preserve">ab ortu, vel occaſu, quę quidem in D, tangit parallelum ſem-
              <lb/>
            per apparentium maximum, quemadmodum & </s>
            <s xml:id="echoid-s19567" xml:space="preserve">eundem in m, tangit linea horizontalis.</s>
            <s xml:id="echoid-s19568" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19569" xml:space="preserve">SVNT autem ſem per binæ lineę horarum ab occaſu alicui horæ à meridie, vel media nocte
              <lb/>
              <note position="right" xlink:label="note-0305-05" xlink:href="note-0305-05a" xml:space="preserve">Singulis horis
                <lb/>
              à mer. vel med.
                <lb/>
              noc. parallelæ
                <lb/>
              ſunt binę horæ
                <lb/>
              ab or. vel occ.</note>
            parallelæ, vt ex tabula propoſ. </s>
            <s xml:id="echoid-s19570" xml:space="preserve">19. </s>
            <s xml:id="echoid-s19571" xml:space="preserve">libri ſuperioris liquet, & </s>
            <s xml:id="echoid-s19572" xml:space="preserve">in ſcholio propoſ. </s>
            <s xml:id="echoid-s19573" xml:space="preserve">22. </s>
            <s xml:id="echoid-s19574" xml:space="preserve">eiuſdem libri
              <lb/>
            probatum eſt. </s>
            <s xml:id="echoid-s19575" xml:space="preserve">Vt hora 23. </s>
            <s xml:id="echoid-s19576" xml:space="preserve">& </s>
            <s xml:id="echoid-s19577" xml:space="preserve">11. </s>
            <s xml:id="echoid-s19578" xml:space="preserve">ab occaſu parallelæ ſunt horæ quintæ à meridie, vel media no-
              <lb/>
            cte, &</s>
            <s xml:id="echoid-s19579" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19580" xml:space="preserve">Vnde ſi in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s19581" xml:space="preserve">& </s>
            <s xml:id="echoid-s19582" xml:space="preserve">nocturno horarum 10. </s>
            <s xml:id="echoid-s19583" xml:space="preserve">veì etiam in diurno ho-
              <lb/>
              <note position="left" xlink:label="note-0305-06" xlink:href="note-0305-06a" xml:space="preserve">20</note>
            rarum 24. </s>
            <s xml:id="echoid-s19584" xml:space="preserve">notentur horæ à meridie, vel media nocte reſpondentes horis ab occaſu, prout tabulæ
              <lb/>
            ſcholii propoſ. </s>
            <s xml:id="echoid-s19585" xml:space="preserve">33. </s>
            <s xml:id="echoid-s19586" xml:space="preserve">ſuperioris libri indicant, percommodè eaſdem horas ab occaſu deſcribemus,
              <lb/>
              <note position="right" xlink:label="note-0305-07" xlink:href="note-0305-07a" xml:space="preserve">Alia deſcriptio
                <lb/>
              horarũ ab occ.
                <lb/>
              in borologio ę-
                <lb/>
              quinoctiali.</note>
            ſi per illas horas à meridie, vel media nocte in dictis arcubus notatas ducamus lineas patallelas il-
              <lb/>
            lis horis à meridie, vel media nocte, quas tabula prædicta ſcholii propoſ. </s>
            <s xml:id="echoid-s19587" xml:space="preserve">19. </s>
            <s xml:id="echoid-s19588" xml:space="preserve">eiuſdem libri de-
              <lb/>
            monſtrat. </s>
            <s xml:id="echoid-s19589" xml:space="preserve">Vt quoniam hora 16. </s>
            <s xml:id="echoid-s19590" xml:space="preserve">ab occaſu reſpondet ſecundum tabulam tertiam propoſ. </s>
            <s xml:id="echoid-s19591" xml:space="preserve">33. </s>
            <s xml:id="echoid-s19592" xml:space="preserve">di-
              <lb/>
            cti libri horæ 11. </s>
            <s xml:id="echoid-s19593" xml:space="preserve">à media nocte in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s19594" xml:space="preserve">eſtq́ue parallela horæ 10. </s>
            <s xml:id="echoid-s19595" xml:space="preserve">à meridie
              <lb/>
            vel media nocte, vt vult tabula propoſ. </s>
            <s xml:id="echoid-s19596" xml:space="preserve">19. </s>
            <s xml:id="echoid-s19597" xml:space="preserve">eiuſdem libri, propterea recta ducta per horam 11. </s>
            <s xml:id="echoid-s19598" xml:space="preserve">à
              <lb/>
            media nocte in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s19599" xml:space="preserve">parallela horæ 10. </s>
            <s xml:id="echoid-s19600" xml:space="preserve">à meridie, vel media nocte, erit linea
              <lb/>
            horæ 16. </s>
            <s xml:id="echoid-s19601" xml:space="preserve">ab occaſu, & </s>
            <s xml:id="echoid-s19602" xml:space="preserve">ita de cæteris. </s>
            <s xml:id="echoid-s19603" xml:space="preserve">Horologium igitur Italicum e
              <unsure/>
            quinoctiale conſtruximus.
              <lb/>
            </s>
            <s xml:id="echoid-s19604" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s19605" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
        </div>
        <div xml:id="echoid-div1007" type="section" level="1" n="247">
          <head xml:id="echoid-head254" xml:space="preserve">PROBLEMA 59. PROPOSITIO 59.</head>
          <head xml:id="echoid-head255" xml:space="preserve">HOROLOGIVM Babylonicum ęquinoctiale componere.</head>
          <note position="right" xml:space="preserve">Horologii Ba-
            <lb/>
          bylonici æqui-
            <lb/>
          noctialis com-
            <lb/>
          poſitio.</note>
          <p>
            <s xml:id="echoid-s19606" xml:space="preserve">EISDEM vijs, ac rationibus, quibus Italicũ conſtruximus, horologiũ Babylonicum conficie-
              <lb/>
            mus, ſi tamen in primo modo diuiſio circulorum ex E, deſcriptorum initium ſumat à parte dextra
              <lb/>
            ſuperioris horologii, quæ nimirum vmbram ſtyli ſub ortum Solis excipere ſolet; </s>
            <s xml:id="echoid-s19607" xml:space="preserve">in inferiori verò
              <lb/>
            à parte ſiniſtra, accipiendo horologium inferius, vt in primo modo antecedentis propoſ. </s>
            <s xml:id="echoid-s19608" xml:space="preserve">diximus.
              <lb/>
            </s>
            <s xml:id="echoid-s19609" xml:space="preserve">Item horariæ lineæ ita ducantur, vt primum per proxima puncta diuiſionum ſupra, vel infra ho-
              <lb/>
            rizontalem lineam, à qua diuiſio initium habuit, vna ducatur; </s>
            <s xml:id="echoid-s19610" xml:space="preserve">Deinde per ſequentia puncta ince-
              <lb/>
              <note position="left" xlink:label="note-0305-10" xlink:href="note-0305-10a" xml:space="preserve">40</note>
            dat alia, & </s>
            <s xml:id="echoid-s19611" xml:space="preserve">ita deinceps. </s>
            <s xml:id="echoid-s19612" xml:space="preserve">Ordo horarum hic eſt. </s>
            <s xml:id="echoid-s19613" xml:space="preserve">Prima linea infra horizontalem lineam ex parte
              <lb/>
              <note position="right" xlink:label="note-0305-11" xlink:href="note-0305-11a" xml:space="preserve">Ordo horarum
                <lb/>
              ab or. in horo-
                <lb/>
              gio æquinoctia
                <lb/>
              li.</note>
            dextra dat in ſuperiori horologio horam 1. </s>
            <s xml:id="echoid-s19614" xml:space="preserve">ab ortu, ſequens 2. </s>
            <s xml:id="echoid-s19615" xml:space="preserve">&</s>
            <s xml:id="echoid-s19616" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19617" xml:space="preserve">In horologio autem inferiori
              <lb/>
            proxima linea infra horizontalem lineam ad ſiniſtram monſtrabit horam 1. </s>
            <s xml:id="echoid-s19618" xml:space="preserve">ab ortu, & </s>
            <s xml:id="echoid-s19619" xml:space="preserve">inſequens
              <lb/>
            ſecundam, &</s>
            <s xml:id="echoid-s19620" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19621" xml:space="preserve">ita vt ſint horarum ab ortu in ſuperiori horologio complementa vſque ad 24.
              <lb/>
            </s>
            <s xml:id="echoid-s19622" xml:space="preserve">Quæ enim in ſuperiori dabat horam 23. </s>
            <s xml:id="echoid-s19623" xml:space="preserve">in inferiori exhibet primam, &</s>
            <s xml:id="echoid-s19624" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19625" xml:space="preserve">vt de Italico diximus
              <lb/>
            in præcedenti propoſ. </s>
            <s xml:id="echoid-s19626" xml:space="preserve">quamuis nullum exemplum inferioris horologii ſecundum hanc viam po-
              <lb/>
            ſuerimus. </s>
            <s xml:id="echoid-s19627" xml:space="preserve">Demonſtratio eadem hic erit, quæ in præcedenti propoſ. </s>
            <s xml:id="echoid-s19628" xml:space="preserve">ſumendo pro horis ab occa. </s>
            <s xml:id="echoid-s19629" xml:space="preserve">
              <lb/>
            ſu horas ab ortu in parallelis Solis.</s>
            <s xml:id="echoid-s19630" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19631" xml:space="preserve">IN reliquis modis nulla eſt difficultas, ſi ea, quæ ſupra dicta ſunt de horis ab occaſu, hic de ho
              <lb/>
              <note position="right" xlink:label="note-0305-12" xlink:href="note-0305-12a" xml:space="preserve">Aliæ deſcriptio
                <lb/>
              nes horologii
                <lb/>
              Babylonici æ-
                <lb/>
              ꝗnoctialis quo-
                <lb/>
              modo fiant.</note>
            ris ab ortu, & </s>
            <s xml:id="echoid-s19632" xml:space="preserve">contra, quæ ibi de horis ab or. </s>
            <s xml:id="echoid-s19633" xml:space="preserve">hic de horis ab occ. </s>
            <s xml:id="echoid-s19634" xml:space="preserve">intelligantur. </s>
            <s xml:id="echoid-s19635" xml:space="preserve">Exemplum horolo-
              <lb/>
              <note position="left" xlink:label="note-0305-13" xlink:href="note-0305-13a" xml:space="preserve">50</note>
            gii Babylonici extat in figura præcedentis propoſ. </s>
            <s xml:id="echoid-s19636" xml:space="preserve">vbi etiam continentur horæ à meridie, vel me-
              <lb/>
            dia nocte, & </s>
            <s xml:id="echoid-s19637" xml:space="preserve">ab occaſu, quæ ita inter ſe diſtinguuntur. </s>
            <s xml:id="echoid-s19638" xml:space="preserve">Horis à meridie, vel media nocte aſcripſi-
              <lb/>
            mus numeros prope arcum diurnum horarum 14. </s>
            <s xml:id="echoid-s19639" xml:space="preserve">& </s>
            <s xml:id="echoid-s19640" xml:space="preserve">nocturnum horarum 10. </s>
            <s xml:id="echoid-s19641" xml:space="preserve">earumq́ue lineæ
              <lb/>
            punctis duntaxat notatæ vſque ad arcum horarum 24. </s>
            <s xml:id="echoid-s19642" xml:space="preserve">excurrunt. </s>
            <s xml:id="echoid-s19643" xml:space="preserve">Horæ ab occaſu habent chara
              <lb/>
            cteres numerorum communes hoc modo 24. </s>
            <s xml:id="echoid-s19644" xml:space="preserve">23. </s>
            <s xml:id="echoid-s19645" xml:space="preserve">22. </s>
            <s xml:id="echoid-s19646" xml:space="preserve">&</s>
            <s xml:id="echoid-s19647" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19648" xml:space="preserve">Horæ denique ab ortu notis numerorũ
              <lb/>
            antiquis ab alijs ſecernuntur hoc modo I. </s>
            <s xml:id="echoid-s19649" xml:space="preserve">II. </s>
            <s xml:id="echoid-s19650" xml:space="preserve">III. </s>
            <s xml:id="echoid-s19651" xml:space="preserve">&</s>
            <s xml:id="echoid-s19652" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19653" xml:space="preserve">Itaque horologium Babylonicum æquino
              <lb/>
            ctiale compoſuimus. </s>
            <s xml:id="echoid-s19654" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s19655" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1010" type="section" level="1" n="248">
          <head xml:id="echoid-head256" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="right" xml:space="preserve">Quomodo In-
            <lb/>
          ferius horolo-
            <lb/>
          gium Babyloni
            <lb/>
          cum ex ſupetio
            <lb/>
          ri colligatur.</note>
          <p style="it">
            <s xml:id="echoid-s19656" xml:space="preserve">LINEAE horarum ab ortu in ſuperiori horologio vltra lineam horizontalem protractæ </s>
          </p>
        </div>
      </text>
    </echo>
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