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-div204" type="section" level="1" n="62">
          <pb o="55" file="0075" n="75" rhead="LIBER PRIMVS."/>
        </div>
        <div xml:id="echoid-div206" type="section" level="1" n="63">
          <head xml:id="echoid-head66" xml:space="preserve">THEOREMA 18. PROPOSITIO 20.</head>
          <p>
            <s xml:id="echoid-s3602" xml:space="preserve">SI ſumantur quæcunque duæ lineæ horariæ ab ortu, vel occaſu, qua-
              <lb/>
              <note position="right" xlink:label="note-0075-01" xlink:href="note-0075-01a" xml:space="preserve">Linea cuiuſcun
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              que horę à mer.
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              vel med. noc. &c
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              duæ lineæ hora
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              rum ab or. vel
                <lb/>
              occ. æqualiter
                <lb/>
              diſtantiũ hinc
                <lb/>
              inde ab illa in
                <lb/>
              maximo paral-
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              lelorũ ſemper
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              apparentium, ſe
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              mutuo interſe-
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              cant in uno eo-
                <lb/>
              dcmq́; puncto
                <lb/>
              cui u@que horo-
                <lb/>
              logii.</note>
            rum circuli ęqualiter diſtent à circulo horæ cuiuſpiam à meridie, vel me-
              <lb/>
            dia nocte in maximo parallelorum ſemper apparentium, interſecabunt
              <lb/>
            ſe ſe mutuo tam duæ illę lineæ horariæ ab ortu, vel occaſu in linea ho-
              <lb/>
            raria illius circuli à meridie, vel media nocte, in vno eodemque puncto,
              <lb/>
              <note position="left" xlink:label="note-0075-02" xlink:href="note-0075-02a" xml:space="preserve">10</note>
            quàm altera illarum ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s3603" xml:space="preserve">linea illa à meridie, vel media
              <lb/>
            nocte, in linea reliqua ab ortu, vel occaſu, in vno quoque & </s>
            <s xml:id="echoid-s3604" xml:space="preserve">eodem
              <lb/>
            puncto.</s>
            <s xml:id="echoid-s3605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3606" xml:space="preserve">SIT parallelorum ſemper apparentium maximus A B C D, quem circulus quiuis horarius
              <lb/>
            à meridie, vel media nocte A C, ſecet in punctis A, C, per rectam A C, quæ diameter erit circuli
              <lb/>
            A B C D, vt in demonſtratione præcedentis propoſ oſtenſum eſt. </s>
            <s xml:id="echoid-s3607" xml:space="preserve">Sumantur autem duo puncta
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            B, D, æqualiter remota ab alterutro punctorum
              <lb/>
            A, C, ita vt tot horas complectatur arcus A B, quot
              <lb/>
              <note position="left" xlink:label="note-0075-03" xlink:href="note-0075-03a" xml:space="preserve">20</note>
              <figure xlink:label="fig-0075-01" xlink:href="fig-0075-01a" number="58">
                <image file="0075-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0075-01"/>
              </figure>
            arcus A D. </s>
            <s xml:id="echoid-s3608" xml:space="preserve">Item tot horas contineat arcus C B,
              <lb/>
            quot arcus C D: </s>
            <s xml:id="echoid-s3609" xml:space="preserve">Et in B, D, tangant parallelum
              <lb/>
            propoſitum A B C D, duo circuli horarii ab ortu,
              <lb/>
            vel occaſu B E, D F, per propoſ. </s>
            <s xml:id="echoid-s3610" xml:space="preserve">10. </s>
            <s xml:id="echoid-s3611" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3612" xml:space="preserve">Di-
              <lb/>
            co lineas horarias ab ortu, vel occaſu circulorum
              <lb/>
            B E, D F, in vno eodemq́ue puncto ſe interſecare in
              <lb/>
            linea horaria à meridie, vel media nocte circuli
              <lb/>
            A C. </s>
            <s xml:id="echoid-s3613" xml:space="preserve">Cum enim circuli horarii B E, D F, parallelũ
              <lb/>
            A B C D, in B, D, tangentes, & </s>
            <s xml:id="echoid-s3614" xml:space="preserve">horarius A C, eun-
              <lb/>
            dem ſecans per rectam A C, habeant per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s3615" xml:space="preserve">
              <note position="left" xlink:label="note-0075-04" xlink:href="note-0075-04a" xml:space="preserve">30</note>
            17. </s>
            <s xml:id="echoid-s3616" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3617" xml:space="preserve">vnam, & </s>
            <s xml:id="echoid-s3618" xml:space="preserve">eandem ſectionem commu
              <lb/>
            nem; </s>
            <s xml:id="echoid-s3619" xml:space="preserve">fit vt ſi planum horologij communi huic ſe-
              <lb/>
            ctioni non æquidiſter, ſed ipſam in aliquo puncto
              <lb/>
            ſecet, in eodem puncto coeant tres horariæ lineæ
              <lb/>
            dictæ, nempe communes ſectiones plani horolo-
              <lb/>
            gii, & </s>
            <s xml:id="echoid-s3620" xml:space="preserve">circulorum A C, B E, D F, per propoſ. </s>
            <s xml:id="echoid-s3621" xml:space="preserve">18.
              <lb/>
            </s>
            <s xml:id="echoid-s3622" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3623" xml:space="preserve">Quare in quocunque puncto vna illarum alteram reliquarum ſecet, in eodem & </s>
            <s xml:id="echoid-s3624" xml:space="preserve">reliqua
              <lb/>
            eandem ſecabit. </s>
            <s xml:id="echoid-s3625" xml:space="preserve">Hoc eſt, ſi linea horaria ab ortu, vel occaſu circuli B E, horariam lineam à me-
              <lb/>
            tidie, vel media nocte circuli A C, ſecuerit in aliquo puncto, ſecabit in eodem & </s>
            <s xml:id="echoid-s3626" xml:space="preserve">horaria linea ab
              <lb/>
            ortu, vel occaſu circuli D F, eandem horariam lineam à meridie, vel media nocte circuli A C. </s>
            <s xml:id="echoid-s3627" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0075-05" xlink:href="note-0075-05a" xml:space="preserve">40</note>
            Item ſi linea circuli B E, lineam circuli D F, in aliquo puncto ſecuerit, ſecabit in eodem & </s>
            <s xml:id="echoid-s3628" xml:space="preserve">linea
              <lb/>
            circuli A C, eandem lineam circuli D E. </s>
            <s xml:id="echoid-s3629" xml:space="preserve">Et ſi linea circuli A C, ſecuerit lineam circuli B E, in
              <lb/>
            aliquo puncto, ſecabit in eodem, & </s>
            <s xml:id="echoid-s3630" xml:space="preserve">linea circuli D F, eandem lineam circuli B E, &</s>
            <s xml:id="echoid-s3631" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3632" xml:space="preserve">Quocir-
              <lb/>
            ca, ſi ſumantur quęcunque duæ lineę horarię ab ortu, vel occaſu in linea horaria illius circuli à me
              <lb/>
            ridie, vel media nocte, in vno eodemq́ue puncto, quàm altera illarum ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s3633" xml:space="preserve">linea
              <lb/>
            illa à meridie, vel media nocte, in linea reliqua ab ortu, vel occaſu, in vno quoque & </s>
            <s xml:id="echoid-s3634" xml:space="preserve">eodem pun-
              <lb/>
            cto. </s>
            <s xml:id="echoid-s3635" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s3636" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div209" type="section" level="1" n="64">
          <head xml:id="echoid-head67" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">50</note>
          <note position="right" xml:space="preserve">Cõpoſitio qua-
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          tuor tabularũ,
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          in qua cõtineã-
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          tur horæ à mer.
            <lb/>
          vel med. noc. &
            <lb/>
          ab or. uel occ. ſe
            <lb/>
          mutuo ſecantes
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          in uno eodem-
            <lb/>
          q́ue puncto li-
            <lb/>
          neæ horę 24. ab
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          or. vel occ. & li-
            <lb/>
          neæ horæ 12. ab
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          or uel occ Item
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          lineæ horę 6. à
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          mer. vel med.
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          noc & lineæ ho
            <lb/>
          ræ 12. à mer. vel
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          med. noc. cuiuſ
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          cunque horolo-
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          gii.</note>
          <p style="it">
            <s xml:id="echoid-s3637" xml:space="preserve">EX hac propoſitione confectæ ſunt ſequentes quatuor tabulę, quarum tituli ſunt.</s>
            <s xml:id="echoid-s3638" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3639" xml:space="preserve">LINEA HORAE XXIIII, AB ORTV, VEL OCCASV.</s>
            <s xml:id="echoid-s3640" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3641" xml:space="preserve">LINEA HORAE XII. </s>
            <s xml:id="echoid-s3642" xml:space="preserve">AB ORTV, VEL OCCASV.</s>
            <s xml:id="echoid-s3643" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3644" xml:space="preserve">LINEA HORAE VI. </s>
            <s xml:id="echoid-s3645" xml:space="preserve">AMERIDIE, VEL MEDIA NOCTE.</s>
            <s xml:id="echoid-s3646" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3647" xml:space="preserve">LINEA HORAE XII. </s>
            <s xml:id="echoid-s3648" xml:space="preserve">AMERIDIE, VEL MEDIA NOCTE.</s>
            <s xml:id="echoid-s3649" xml:space="preserve"/>
          </p>
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