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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          <p>
            <s xml:id="echoid-s18658" xml:space="preserve">
              <pb o="275" file="0291" n="291" rhead="LIBER SECVNDVS."/>
            E, in horologio, hoc eſt, in axe mundi, per eandem propoſitionem 4. </s>
            <s xml:id="echoid-s18659" xml:space="preserve">præcedentis lib. </s>
            <s xml:id="echoid-s18660" xml:space="preserve">Quare ſi ex
              <lb/>
            a, ſumantur ſemidiametri vſque ad triangulorum per axem latera, & </s>
            <s xml:id="echoid-s18661" xml:space="preserve">ad earum interualla ex E, cen
              <lb/>
            tro horologii circuli deſcribantur, deſcripti erunt paralleli borealium ſignorum Zodiaci in horo-
              <lb/>
            logio ſuperiori, cum radij ſignorum borealium in prædictam parallelam cadant per centrum E,
              <lb/>
              <figure xlink:label="fig-0291-01" xlink:href="fig-0291-01a" number="202">
                <image file="0291-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0291-01"/>
              </figure>
              <note position="left" xlink:label="note-0291-01" xlink:href="note-0291-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0291-02" xlink:href="note-0291-02a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0291-03" xlink:href="note-0291-03a" xml:space="preserve">30</note>
            producti. </s>
            <s xml:id="echoid-s18662" xml:space="preserve">Quòd ſi ex axe E F, accipiatur rurſum recta E e, ſtylo æqualis, & </s>
            <s xml:id="echoid-s18663" xml:space="preserve">eadem fiant, deſcriben-
              <lb/>
            tur eodem modo in inferiori horologio paralleli ſignorum auſtralium Zodiaci, quòd radii ſigno
              <lb/>
            rum auſtralium in parallelam per e, ductam cadant, ſi per centrum E, extendantur. </s>
            <s xml:id="echoid-s18664" xml:space="preserve">Sed ſatis eſt,
              <lb/>
            ſi eiſdem ſemidiametris ex a, ſumptis circuli deſcribantur in horologio inferiori. </s>
            <s xml:id="echoid-s18665" xml:space="preserve">Nam ſemidia-
              <lb/>
            metri in parallela per a, ducta contentæ, æquales ſunt reſpondentibus ſemidiametris in parallela
              <lb/>
              <note position="left" xlink:label="note-0291-04" xlink:href="note-0291-04a" xml:space="preserve">40</note>
            per e, ducta contentis. </s>
            <s xml:id="echoid-s18666" xml:space="preserve">Quoniam enim, verbi gratia, in triangulis E a b, E e g, anguli ad puncta a, & </s>
            <s xml:id="echoid-s18667" xml:space="preserve">
              <lb/>
            e, recti ſunt, & </s>
            <s xml:id="echoid-s18668" xml:space="preserve">anguli alterni b, & </s>
            <s xml:id="echoid-s18669" xml:space="preserve">g, æquales, propter parallelas lineas per a, & </s>
            <s xml:id="echoid-s18670" xml:space="preserve">e, ductas, ſuntq́ue la-
              <lb/>
              <note position="right" xlink:label="note-0291-05" xlink:href="note-0291-05a" xml:space="preserve">29. primi.</note>
            tera E a, E e, æqualia; </s>
            <s xml:id="echoid-s18671" xml:space="preserve">erunt quoque latera a b, e g, æqualia, nempe ſemidiametri conicarum ſectio-
              <lb/>
              <note position="right" xlink:label="note-0291-06" xlink:href="note-0291-06a" xml:space="preserve">26. primi.</note>
            num: </s>
            <s xml:id="echoid-s18672" xml:space="preserve">eademq̀ue in cæteris eſt demonſtratio.</s>
            <s xml:id="echoid-s18673" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Alia deſcriptio
            <lb/>
          arcuum ſigno-
            <lb/>
          rnm in eodem
            <lb/>
          horologio æqui
            <lb/>
          noctiali.</note>
          <p>
            <s xml:id="echoid-s18674" xml:space="preserve">EOSDEM parallelos deſcribemus ex poſtrema figura propoſ. </s>
            <s xml:id="echoid-s18675" xml:space="preserve">26. </s>
            <s xml:id="echoid-s18676" xml:space="preserve">huius libri, hoc modo.
              <lb/>
            </s>
            <s xml:id="echoid-s18677" xml:space="preserve">Ex axe D G, vtrinque abſcindantur rectæ D h, D q, ſtylo æquales, & </s>
            <s xml:id="echoid-s18678" xml:space="preserve">per h, q, agantur h l, q n, pa-
              <lb/>
            rallelæ radio Æquatoris D C. </s>
            <s xml:id="echoid-s18679" xml:space="preserve">Nam rectæ inter puncta h, q, & </s>
            <s xml:id="echoid-s18680" xml:space="preserve">radios ſignorum comprehenſæ ſunt
              <lb/>
            æquales ſemidiametris conicarum ſectionum prius inuentis. </s>
            <s xml:id="echoid-s18681" xml:space="preserve">Quoniam enim v. </s>
            <s xml:id="echoid-s18682" xml:space="preserve">g. </s>
            <s xml:id="echoid-s18683" xml:space="preserve">in triangulis
              <lb/>
              <note position="right" xlink:label="note-0291-08" xlink:href="note-0291-08a" xml:space="preserve">Demonſtratio
                <lb/>
              poſterioris hu-
                <lb/>
              r
                <unsure/>
              uſce deſcriptio
                <lb/>
              nis parallelor@
                <lb/>
              solis.</note>
            E a b, D h m, D q o, quorum illud in priori figura, hæc autem in poſteriori cõtinentur, anguli ad
              <lb/>
            puncta a, h, q, recti ſunt, & </s>
            <s xml:id="echoid-s18684" xml:space="preserve">anguli a E b, h D m, q D o, ęquales, quòd quilibet eorũ ſit cõplemento
              <lb/>
              <note position="left" xlink:label="note-0291-09" xlink:href="note-0291-09a" xml:space="preserve">50</note>
            declinationis accepti paralleli æqualis, vt conſtat; </s>
            <s xml:id="echoid-s18685" xml:space="preserve">ſuntq́ue latera E a, D h, D q, æqualia, ex con-
              <lb/>
              <note position="right" xlink:label="note-0291-10" xlink:href="note-0291-10a" xml:space="preserve">26. primi.</note>
            ſtructione; </s>
            <s xml:id="echoid-s18686" xml:space="preserve">erunt quoque latera a b, h m, q o, æqualia. </s>
            <s xml:id="echoid-s18687" xml:space="preserve">Ex quo patet, ſatis etiam eſſe, ſi vna tantũ
              <lb/>
              <note position="right" xlink:label="note-0291-11" xlink:href="note-0291-11a" xml:space="preserve">Satis eſt, ſ
                <unsure/>
              i
                <unsure/>
                <lb/>
              in poſteriori
                <lb/>
              modo ducatur
                <lb/>
              vel ſola paralle
                <lb/>
              la h l, vel q n.</note>
            parallela ducatur, nempe vel h l, vel q n, vt inueniantur ſemidia metri circulorum, vel ſectionum
              <lb/>
            conicarum in vtroque horologio. </s>
            <s xml:id="echoid-s18688" xml:space="preserve">Cum enim oſtenſum ſit, ſemidiametros vtriuſque parallelæ
              <lb/>
            æquales eſſe ſemidiametris parallelę per a, ductę in priori figura; </s>
            <s xml:id="echoid-s18689" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s18690" xml:space="preserve">ipſæ inter ſe æquales.
              <lb/>
            </s>
            <s xml:id="echoid-s18691" xml:space="preserve">
              <note position="right" xlink:label="note-0291-12" xlink:href="note-0291-12a" xml:space="preserve">Linea ęquino-
                <lb/>
              ctialis deſcribi
                <lb/>
              nõ poteſt in ho
                <lb/>
              rologio æquino
                <lb/>
              cti
                <unsure/>
              ali.</note>
            Manifeſtum autem eſt, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s18692" xml:space="preserve">11. </s>
            <s xml:id="echoid-s18693" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18694" xml:space="preserve">lineam æquinoctialem in horologio
              <lb/>
            æquinoctiali deſcribi non poſſe, ſed totam euaneſcere; </s>
            <s xml:id="echoid-s18695" xml:space="preserve">propterea quòd Aequator plano vtriuſq;
              <lb/>
            </s>
            <s xml:id="echoid-s18696" xml:space="preserve">horologii ęquinoctialis æquidiſtat. </s>
            <s xml:id="echoid-s18697" xml:space="preserve">Quòd ſi horas obſeruare libuerit prope tempus ęquinoctio-
              <lb/>
              <note position="right" xlink:label="note-0291-13" xlink:href="note-0291-13a" xml:space="preserve">Quid agend@,
                <lb/>
              vt vmbra horas
                <lb/>
              indicet prope
                <unsure/>
                <lb/>
              tempus æquino
                <lb/>
              ctiorum.</note>
            rum, nempe ante, vel poſt ęquinoctia, producendæ erunt lineę horarię vltra extremum circulum,
              <lb/>
            qui in ſuperiori horologio ſignis ♉, & </s>
            <s xml:id="echoid-s18698" xml:space="preserve">♍, in inferiori verò ſignis ♏, & </s>
            <s xml:id="echoid-s18699" xml:space="preserve">♓, deputatur; </s>
            <s xml:id="echoid-s18700" xml:space="preserve">producen-
              <lb/>
            dę, inquam, erunt, quantum magnitudo plani, in quo deſcribitur horologium, patietur: </s>
            <s xml:id="echoid-s18701" xml:space="preserve">vel </s>
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