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-div201" type="section" level="1" n="61">
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              <pb o="54" file="0074" n="74" rhead="GNOMONICES"/>
            muni huic ſectioni non æquidiſtet, ſed ipſam in terſecet in aliquo puncto, ſeeabunt eandem com-
              <lb/>
            munes ſectiones dictorum circulorum, & </s>
            <s xml:id="echoid-s3552" xml:space="preserve">plani horologii, hoc eſt, linea ęquinoctialis, lineę duę
              <lb/>
            horarię ab ortn, vel occaſu circulorum B E, D F, & </s>
            <s xml:id="echoid-s3553" xml:space="preserve">linea horaria à meridie, vel media nocte circu-
              <lb/>
            li A C, in eodem puncto, per propoſ. </s>
            <s xml:id="echoid-s3554" xml:space="preserve">pręcedentem. </s>
            <s xml:id="echoid-s3555" xml:space="preserve">Ac propterea, in quo puncto linea horaria à
              <lb/>
            meridie, vel media nocte circuli A C, ſecat lineam ęquinoctialem in aliquo horologio, in illo pun
              <lb/>
            cto occurret plano horologii communis ſectio dictorum circulorum, ac proinde in eodem ſeca-
              <lb/>
            bunt eandem lineam æquinoctialem duæ lineæ horarie ab ortu, vel occaſu circulorum B E, D F.
              <lb/>
            </s>
            <s xml:id="echoid-s3556" xml:space="preserve">Eademq́ue eſt ratio de ceteris. </s>
            <s xml:id="echoid-s3557" xml:space="preserve">In quocunque ergo puncto linea quæuis horaria à meridie, &</s>
            <s xml:id="echoid-s3558" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3559" xml:space="preserve">
              <lb/>
            Quod erat oſtendendum.</s>
            <s xml:id="echoid-s3560" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div204" type="section" level="1" n="62">
          <head xml:id="echoid-head65" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">10</note>
          <p style="it">
            <s xml:id="echoid-s3561" xml:space="preserve">EX hac propoſitione conſtruximus ſequentem tabulam, cuius titulus eſt, AE QVINOCTI A.
              <lb/>
            </s>
            <s xml:id="echoid-s3562" xml:space="preserve">
              <note position="left" xlink:label="note-0074-02" xlink:href="note-0074-02a" xml:space="preserve">Compoſitio ta-
                <lb/>
              bulæ, in qua cõ
                <lb/>
              tineantur horę
                <lb/>
              à mer. vel med.
                <lb/>
              noc. & ab or. uel
                <lb/>
              occ. ſe mutuo
                <lb/>
              interſecantes in
                <lb/>
              uno eodemq́ue
                <lb/>
              puncto lineæ
                <lb/>
              æquinoctialis
                <lb/>
              cuiuſuis horolo
                <lb/>
              gii.</note>
            LIS LINE A. </s>
            <s xml:id="echoid-s3563" xml:space="preserve">Indicat enim, quænam lineæ horariæ ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s3564" xml:space="preserve">à meridie, vel media
              <lb/>
            nocte æquinoctialem lineam cuiuſcunque horologij in vno eodemq́; </s>
            <s xml:id="echoid-s3565" xml:space="preserve">puncto interſecent, vt facile colligi po-
              <lb/>
            teſt ex hac propoſitione. </s>
            <s xml:id="echoid-s3566" xml:space="preserve">Vt ſi ſumatur in tabula ſequenti quæcunque hora, vel pars, partesve horæ à
              <lb/>
            meridie, vel media nocte, & </s>
            <s xml:id="echoid-s3567" xml:space="preserve">duæ horę, vel partes horarum ab ortu, vel occaſu illi collaterales; </s>
            <s xml:id="echoid-s3568" xml:space="preserve">ſecabunt
              <lb/>
            lineę illarum trium hor arum, vel etiam partium horarum, lineam ęquinoctialem in uno eodemq, puncto.
              <lb/>
            </s>
            <s xml:id="echoid-s3569" xml:space="preserve">Exempli gratia, linea horæ ſeptimæ à meridie, vel media nocte, linea horæ 1. </s>
            <s xml:id="echoid-s3570" xml:space="preserve">& </s>
            <s xml:id="echoid-s3571" xml:space="preserve">linea horæ 13. </s>
            <s xml:id="echoid-s3572" xml:space="preserve">ab ortu,
              <lb/>
            vel occaſu, in vno eodem{q́ue} puncto lineam æquinoctialem interſecant. </s>
            <s xml:id="echoid-s3573" xml:space="preserve">Eodem modo linea horę 7 {1/4}. </s>
            <s xml:id="echoid-s3574" xml:space="preserve">à
              <lb/>
            meridie, vel media nocte, linea horæ 1 {1/4}. </s>
            <s xml:id="echoid-s3575" xml:space="preserve">& </s>
            <s xml:id="echoid-s3576" xml:space="preserve">linea horæ 13 {1/4}. </s>
            <s xml:id="echoid-s3577" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s3578" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s3579" xml:space="preserve">in vno eodemq́, puncto li-
              <lb/>
              <note position="left" xlink:label="note-0074-03" xlink:href="note-0074-03a" xml:space="preserve">20</note>
            neam æquinoctialem ſecant, & </s>
            <s xml:id="echoid-s3580" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s3581" xml:space="preserve">Si enim rectè conſideretur hæc tabula, & </s>
            <s xml:id="echoid-s3582" xml:space="preserve">figura propoſ. </s>
            <s xml:id="echoid-s3583" xml:space="preserve">9.
              <lb/>
            </s>
            <s xml:id="echoid-s3584" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3585" xml:space="preserve">reperientur quælibet huiuſmodi duæ horæ ab ortu, vel occaſu, ab intermedia hora à meridie,
              <lb/>
            vel media nocte diſtare quadrante integro, ſeu ſex horis. </s>
            <s xml:id="echoid-s3586" xml:space="preserve">Quare lineæ ipſarum in eodem puncto lineam
              <lb/>
            æquinoctialem interſecant, in quo linea horæ à meridie, vel media nocte eandem lineam æquinoctialem
              <lb/>
            ſecat, vt in hac propoſ. </s>
            <s xml:id="echoid-s3587" xml:space="preserve">demonſtrauimus. </s>
            <s xml:id="echoid-s3588" xml:space="preserve">Itaque ſinotum fuerit punctum in æquinoctialiv linea cuiuſcun-
              <lb/>
            que horologij, per quod tranſit vna ex tribus horis, ſciemus per idem illud punctum tranſire debere reli-
              <lb/>
            quas duas horas. </s>
            <s xml:id="echoid-s3589" xml:space="preserve">Pariratione, ſi perſpectum fuerit punctum, in quo duæ ex tribus horis quæcumque ſe
              <lb/>
            mutuo ſecent, cognoſcemus etiam, per illud idem punctum duci debere lineam æquinoctialem, &</s>
            <s xml:id="echoid-s3590" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3591" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          ########### AE QVINOCTIALIS LINEA.
            <lb/>
          Horæ ab ortu \\ vel occaſu. # Horæ à meridic \\ vel media noct. # Horæ ab ortu \\ vel occaſu. # # Horæ ab ortu \\ vel occaſu. # Horę à meridic \\ vel media noct. # Horę ab ortu \\ vel occaſu. # # Horę ab ortu \\ vel occaſu. # Horę à meridic \\ vel media noct. # Horę ab ortu \\ vel occaſu.
            <lb/>
          {1/4} # 6 {1/4} # 12 {1/4} # # 4 {1/4} # 10 {1/4} # 16 {1/4} # # 8 {1/4} # 2 {1/4} # 20 {1/4} {1/2} # 6 {1/2} # 12 {1/2} # # 4 {1/2} # 10 {1/2} # 16 {1/2} # # 8 {1/2} # 2 {1/2} # 20 {1/2} {3/4} # 6 {3/4} # 12 {3/4} # # 4 {3/4} # 10 {3/4} # 16 {3/4} # # 8 {3/4} # 2 {3/4} # 20 {3/4} 1 # VII # 13 # # 5 # XI # 17 # # 9 # III # 21 1 {1/4} # 7 {1/4} # 13 {1/4} # # 5 {1/4} # 11 {1/4} # 17 {1/4} # # 9 {1/4} # 3 {1/4} # 21 {1/4} 1 {1/2} # 7 {1/2} # 13 {1/2} # # 5 {1/2} # 11 {1/2} # 17 {1/2} # # 9 {1/2} # 3 {1/2} # 21 {1/2} 1 {3/4} # 7 {3/4} # 13 {3/4} # # 5 {3/4} # 11 {3/4} # 17 {3/4} # # 9 {3/4} # 3 {3/4} # 21 {3/4} 2 # VIII # 14 # # 6 # XII # 18 # # 10 # IIII # 22 2 {1/4} # 8 {1/4} # 14 {1/4} # # 6 {1/4} # {1/4} # 18 {1/4} # # 10 {1/4} # 4 {1/4} # 22 {1/4} 2 {1/2} # 8 {1/2} # 14 {1/2} # # 6 {1/2} # {1/2} # 18 {1/2} # # 10 {1/2} # 4 {1/2} # 22 {1/2} 2 {3/4} # 8 {3/4} # 14 {3/4} # # 6 {3/4} # {3/4} # 18 {3/4} # # 10 {3/4} # 4 {3/4} # 22 {3/4} 3 # IX # 15 # # 7 # I # 19 # # 11 # V # 23 3 {1/4} # 9 {1/4} # 15 {1/4} # # 7 {1/4} # 1 {1/4} # 19 {1/4} # # 11 {1/4} # 5 {1/4} # 23 {1/4} 3 {1/2} # 9 {1/2} # 15 {1/2} # # 7 {1/2} # 1 {1/2} # 19 {1/2} # # 11 {1/2} # 5 {1/2} # 23 {1/2} 3 {3/4} # 9 {3/4} # 15 {3/4} # # 7 {3/4} # 1 {3/4} # 19 {3/4} # # 11 {3/4} # 5 {3/4} # 23 {3/4} 4 # X # 16 # # 8 # II # 20 # # 12 # VI # 24</note>
          <p style="it">
            <s xml:id="echoid-s3592" xml:space="preserve">In horologio Aequinoctiali lineę quarumlibet trium horarum huius tabulę parallelę ſunt (vt ex ſcho
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s3593" xml:space="preserve">22. </s>
            <s xml:id="echoid-s3594" xml:space="preserve">huius libri perſpicuum eſt) Similiter & </s>
            <s xml:id="echoid-s3595" xml:space="preserve">in quibuſdam alijs horologiis parallelę ſunt li-
              <lb/>
            neę iſtarum horarum, nimirum 12. </s>
            <s xml:id="echoid-s3596" xml:space="preserve">& </s>
            <s xml:id="echoid-s3597" xml:space="preserve">24. </s>
            <s xml:id="echoid-s3598" xml:space="preserve">ab ortu vel occaſu, & </s>
            <s xml:id="echoid-s3599" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3600" xml:space="preserve">à meridie vel media nocte, vt in e
              <unsure/>
            o-
              <lb/>
            dem ſcholio docetur.</s>
            <s xml:id="echoid-s3601" xml:space="preserve"/>
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