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-div970" type="section" level="1" n="237">
          <pb o="279" file="0295" n="295" rhead="LIBER SECVNDVS."/>
        </div>
        <div xml:id="echoid-div972" type="section" level="1" n="238">
          <head xml:id="echoid-head245" xml:space="preserve">PROBLEMA 53. PROPOSITIO 53.</head>
          <p>
            <s xml:id="echoid-s18899" xml:space="preserve">PARALLELOS Horizontis in eodem æquinoctiali horolo-
              <lb/>
            gio ducere.</s>
            <s xml:id="echoid-s18900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18901" xml:space="preserve">SIT Analemma A B C, in quo Horizon B C; </s>
            <s xml:id="echoid-s18902" xml:space="preserve">Verticalis A D; </s>
            <s xml:id="echoid-s18903" xml:space="preserve">axis mundi E F; </s>
            <s xml:id="echoid-s18904" xml:space="preserve">& </s>
            <s xml:id="echoid-s18905" xml:space="preserve">Aequator
              <lb/>
              <note position="right" xlink:label="note-0295-01" xlink:href="note-0295-01a" xml:space="preserve">Paralleli Hori-
                <lb/>
              zontis qua ra-
                <lb/>
              tione in eodem
                <lb/>
              horologio æqui
                <lb/>
              noctiali deſcri-
                <lb/>
              bantur.</note>
            G H. </s>
            <s xml:id="echoid-s18906" xml:space="preserve">Diuiſo autem ſemicirculo B A C, in grad. </s>
            <s xml:id="echoid-s18907" xml:space="preserve">180. </s>
            <s xml:id="echoid-s18908" xml:space="preserve">vel in pauciores partes æquales, prout ho-
              <lb/>
            rologium capax fuerit, (Nos illum diuiſimus in 12. </s>
            <s xml:id="echoid-s18909" xml:space="preserve">vt quælibet complectatur grad. </s>
            <s xml:id="echoid-s18910" xml:space="preserve">15.) </s>
            <s xml:id="echoid-s18911" xml:space="preserve">iungan-
              <lb/>
            tur bina puncta à recta B C, vel à puncto A, æqualiter remota, lineis rectis, quæ communes ſe-
              <lb/>
            ctiones erunt Meridiani, & </s>
            <s xml:id="echoid-s18912" xml:space="preserve">pa-
              <lb/>
              <note position="left" xlink:label="note-0295-02" xlink:href="note-0295-02a" xml:space="preserve">10</note>
              <figure xlink:label="fig-0295-01" xlink:href="fig-0295-01a" number="204">
                <image file="0295-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0295-01"/>
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            rallelorum Horizontis, quos Al-
              <lb/>
            mucantarath dicunt. </s>
            <s xml:id="echoid-s18913" xml:space="preserve">Deinde ex
              <lb/>
            diuiſionum punctis per cẽtrum
              <lb/>
            D, ducantur rectæ lineæ, vt con-
              <lb/>
            ſtituantur triangula per axem in
              <lb/>
            conis, quorum baſes ſunt paral-
              <lb/>
            leli Horizontis tam infra Hori-
              <lb/>
            zontem, quàm ſupra, vertex au-
              <lb/>
            tem communis centrum mundi
              <lb/>
            D. </s>
            <s xml:id="echoid-s18914" xml:space="preserve">Meridianus enim A B C,
              <lb/>
              <note position="left" xlink:label="note-0295-03" xlink:href="note-0295-03a" xml:space="preserve">20</note>
            per axem A D, dictorũ conorũ
              <lb/>
            incedens facit triangula per axẽ,
              <lb/>
            ex propoſ. </s>
            <s xml:id="echoid-s18915" xml:space="preserve">3. </s>
            <s xml:id="echoid-s18916" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s18917" xml:space="preserve">1. </s>
            <s xml:id="echoid-s18918" xml:space="preserve">Apollonij. </s>
            <s xml:id="echoid-s18919" xml:space="preserve">In
              <lb/>
            axe quoque E F, accipiatur vtrin
              <lb/>
            que recta D I, gnomoni æqualis,
              <lb/>
            & </s>
            <s xml:id="echoid-s18920" xml:space="preserve">per I, Aequatori G H, vtrinq;
              <lb/>
            </s>
            <s xml:id="echoid-s18921" xml:space="preserve">parallela agatur K L. </s>
            <s xml:id="echoid-s18922" xml:space="preserve">Erit hæc
              <lb/>
            infra quidem G H, communis
              <lb/>
            ſectio Meridiani, & </s>
            <s xml:id="echoid-s18923" xml:space="preserve">plani ho-
              <lb/>
            rologij ſuperioris, illa verò ſupra
              <lb/>
              <note position="left" xlink:label="note-0295-04" xlink:href="note-0295-04a" xml:space="preserve">30</note>
            G H, communis ſectio Meridia-
              <lb/>
            ni & </s>
            <s xml:id="echoid-s18924" xml:space="preserve">plani horologii inferioris.
              <lb/>
            </s>
            <s xml:id="echoid-s18925" xml:space="preserve">Secabit autem vtraque recta KL,
              <lb/>
            latera triangulorum per axem in
              <lb/>
            punctis M, N, O, P, Q, R, eruntq́ue diametri ſectionum conicarum M L, N L, O L, P L, Q R. </s>
            <s xml:id="echoid-s18926" xml:space="preserve">
              <lb/>
            Si igitur puncta M, N, O, P, (omittimus hic punctum Q, quoniam conica ſectio per ipſum du-
              <lb/>
            cta extra tropicos cadit) transferantur in lineam meridianam infra horizontalem lineam in horo
              <lb/>
            logio ſuperiori, incipiendo in hac figura ab S, puncto Horizontis, in horologio verò ab m, puncto
              <lb/>
            horizontalis lineæ & </s>
            <s xml:id="echoid-s18927" xml:space="preserve">per propoſitionem 8. </s>
            <s xml:id="echoid-s18928" xml:space="preserve">ſupetioris lib. </s>
            <s xml:id="echoid-s18929" xml:space="preserve">circa lineam meridianam dictæ coni-
              <lb/>
            cæ ſectiones deſcribantur tranſeuntes per puncta M, N, O, P, (quæ ſectiones conicę partim erunt
              <lb/>
              <note position="left" xlink:label="note-0295-05" xlink:href="note-0295-05a" xml:space="preserve">40</note>
            hyperbolæ, partim ellipſes, vt ex propoſ. </s>
            <s xml:id="echoid-s18930" xml:space="preserve">6. </s>
            <s xml:id="echoid-s18931" xml:space="preserve">& </s>
            <s xml:id="echoid-s18932" xml:space="preserve">7. </s>
            <s xml:id="echoid-s18933" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18934" xml:space="preserve">conſtat: </s>
            <s xml:id="echoid-s18935" xml:space="preserve">Parallelus autem Horizon
              <lb/>
            tis grad. </s>
            <s xml:id="echoid-s18936" xml:space="preserve">48. </s>
            <s xml:id="echoid-s18937" xml:space="preserve">erit parabola, ex propoſ. </s>
            <s xml:id="echoid-s18938" xml:space="preserve">5. </s>
            <s xml:id="echoid-s18939" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s18940" xml:space="preserve">ſuperioris, quòd illum Aequator in puncto
              <lb/>
            G, contingat) & </s>
            <s xml:id="echoid-s18941" xml:space="preserve">à linea horizontali eò magis ſemper recedentes, quò longius ex vtraque parte li-
              <lb/>
            neæ meridianę fuerint productæ, deſcripti erunt paralleli Horizontis. </s>
            <s xml:id="echoid-s18942" xml:space="preserve">In horologio inferiori
              <lb/>
            transferendæ ſunt rectæ S T, S V, in lineam meridianam à puncto m, infra lineam horizon-
              <lb/>
            talem, &</s>
            <s xml:id="echoid-s18943" xml:space="preserve">c. </s>
            <s xml:id="echoid-s18944" xml:space="preserve">Nam T L, eſt diameter conicæ ſectionis paralleli Horizontis grad. </s>
            <s xml:id="echoid-s18945" xml:space="preserve">15. </s>
            <s xml:id="echoid-s18946" xml:space="preserve">ſupra Hori-
              <lb/>
            zontem, & </s>
            <s xml:id="echoid-s18947" xml:space="preserve">V L, diameter conicæ ſectionis paralleli Horizontis grad. </s>
            <s xml:id="echoid-s18948" xml:space="preserve">30. </s>
            <s xml:id="echoid-s18949" xml:space="preserve">&</s>
            <s xml:id="echoid-s18950" xml:space="preserve">c. </s>
            <s xml:id="echoid-s18951" xml:space="preserve">Eſt igitur G H,
              <lb/>
            tanquam Horizon, & </s>
            <s xml:id="echoid-s18952" xml:space="preserve">E F, veluti Verticalis; </s>
            <s xml:id="echoid-s18953" xml:space="preserve">B C, quaſi Aequator quidam, & </s>
            <s xml:id="echoid-s18954" xml:space="preserve">paralleli Horizontis
              <lb/>
            inſtar parallelorum noui Aequatoris B C. </s>
            <s xml:id="echoid-s18955" xml:space="preserve">Quibus poſitis, erunt Verticales circuli inſtar horario-
              <lb/>
            rum circulorum, qui omnes meridianam lineam horologij ſecant in puncto X, vbi eandem ſecat
              <lb/>
              <note position="left" xlink:label="note-0295-06" xlink:href="note-0295-06a" xml:space="preserve">50</note>
            A D, axis Horizontis, quem nunc munere Æquatoris cuiuſdam noui fungi diximus: </s>
            <s xml:id="echoid-s18956" xml:space="preserve">Ita vt ſi per-
              <lb/>
            mutatio hæc circulorum benè conſideretur, deſcriptio hæc parallelorum Horizontis à deſcriptio-
              <lb/>
            ne parallelorum Aequatoris in horizontali horologio non differat.</s>
            <s xml:id="echoid-s18957" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18958" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s18959" xml:space="preserve">Deſcripto quadrante A B C, cuiuslibet magnitudinis, eoq́ue diuiſo in grad. </s>
            <s xml:id="echoid-s18960" xml:space="preserve">90.
              <lb/>
            </s>
            <s xml:id="echoid-s18961" xml:space="preserve">
              <note position="right" xlink:label="note-0295-07" xlink:href="note-0295-07a" xml:space="preserve">Alia deſcriptio
                <lb/>
              parallelorũ Ho
                <lb/>
              rizontis in eo-
                <lb/>
              dem æquino-
                <lb/>
              ctiali horolo
                <unsure/>
              -
                <lb/>
              gio.</note>
            vel in partes pauciores, pro capacitate horologii, ducantur ex A, centro per puncta diuiſionum li-
              <lb/>
            neæ rectæ, quæ reſpondebunt radijs parallelorum Horizontis in quadrante D C 90. </s>
            <s xml:id="echoid-s18962" xml:space="preserve">figuræ ante-
              <lb/>
            cedentis comprehenſis, initio facto à recta A B, vt figura indicat. </s>
            <s xml:id="echoid-s18963" xml:space="preserve">Deinde ex figura præcedentis
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s18964" xml:space="preserve">rectæ F p, in linea A C, huius figuræ ſumatur æqualis A D; </s>
            <s xml:id="echoid-s18965" xml:space="preserve">Et rectæ m F, vel m e, acci-
              <lb/>
            piatur in linea A B, æqualis AE, ducaturq́; </s>
            <s xml:id="echoid-s18966" xml:space="preserve">recta D E. </s>
            <s xml:id="echoid-s18967" xml:space="preserve">Erit triangulũ hoc A D E, omnino æquale triã
              <lb/>
              <note position="right" xlink:label="note-0295-08" xlink:href="note-0295-08a" xml:space="preserve">4. primi.</note>
            gulo F p m, figuræ præcedentis propoſ. </s>
            <s xml:id="echoid-s18968" xml:space="preserve">cum anguli ad puncta A, & </s>
            <s xml:id="echoid-s18969" xml:space="preserve">F, recti ſint, contineanturq́ue
              <lb/>
            æqualibus lateribus, ex conſtructione. </s>
            <s xml:id="echoid-s18970" xml:space="preserve">Itaque linea D E, meridianæ lineæ p m, æqualis erit. </s>
            <s xml:id="echoid-s18971" xml:space="preserve"/>
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