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-div1046" type="section" level="1" n="255">
          <p style="it">
            <s xml:id="echoid-s20992" xml:space="preserve">
              <pb o="312" file="0328" n="328" rhead="GNOMONICES"/>
            bit boreale ſpectans quoque ad occaſum. </s>
            <s xml:id="echoid-s20993" xml:space="preserve">Vnde ſi quis deſideret horologium boreale declinans in or-
              <lb/>
            tum, deſcribendum crit auſtrale horologium ſpectans ad ortum. </s>
            <s xml:id="echoid-s20994" xml:space="preserve">Hocenim inuerſum, it a vt ſuperiora
              <lb/>
            cuadant inferiora, dabit opt at um horologium boreale in ortum v@rgens, ſi numeri horarum vertantur in
              <lb/>
            carum complementa vſq; </s>
            <s xml:id="echoid-s20995" xml:space="preserve">ad 12. </s>
            <s xml:id="echoid-s20996" xml:space="preserve">Similiter ſi quis optet horologium boreale, quod in occaſum deſlectat,
              <lb/>
            deſcribendum erit horologium auſtrale in occaſum declinans. </s>
            <s xml:id="echoid-s20997" xml:space="preserve">Nam ſi huius pars ſuperior fiat infe-
              <lb/>
            rior, habebitur boreale horologium ſpectans in occaſum, ſi numeri mutentur, vt dictum eſt. </s>
            <s xml:id="echoid-s20998" xml:space="preserve">Quę om-
              <lb/>
            nia ex ijs, quę dicta ſunt, colliguntur, ac perſpicua ſunt, ſirecte conſiderentur plana horologiorum in
              <lb/>
            proprijs poſitionib{us}.</s>
            <s xml:id="echoid-s20999" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s21000" xml:space="preserve">QVIN immo vna opera, & </s>
            <s xml:id="echoid-s21001" xml:space="preserve">vno labore quatuor diuerſa horologia, ſeruata ſemper eadem quantita
              <lb/>
              <note position="left" xlink:label="note-0328-01" xlink:href="note-0328-01a" xml:space="preserve">Qua ratione ex
                <lb/>
              horologio, qd
                <lb/>
              a meridie decli
                <lb/>
              mat in ortum,
                <lb/>
              cõficiatur aliud
                <lb/>
              declinans à bo
                <lb/>
              rea in ortum, a
                <lb/>
              meridie in oc-
                <lb/>
              caſum, & à bo-
                <lb/>
              rea in occasũ.</note>
            te declinationis, deſcribere commodiſſimè poterim{us}. </s>
            <s xml:id="echoid-s21002" xml:space="preserve">Nam ſi exempli gratia deſcribam{us} horologium
              <lb/>
              <note position="left" xlink:label="note-0328-02" xlink:href="note-0328-02a" xml:space="preserve">10</note>
            declinans à meridie in ortum grad. </s>
            <s xml:id="echoid-s21003" xml:space="preserve">30. </s>
            <s xml:id="echoid-s21004" xml:space="preserve">& </s>
            <s xml:id="echoid-s21005" xml:space="preserve">partem eius ſuperiorem mutem{us} in inferiorem, deſcriptum
              <lb/>
            quoque iam erit horologium declinans grad. </s>
            <s xml:id="echoid-s21006" xml:space="preserve">30. </s>
            <s xml:id="echoid-s21007" xml:space="preserve">à Septentrione in ortum: </s>
            <s xml:id="echoid-s21008" xml:space="preserve">Si verò eiuſdem illi{us} dextrã
              <lb/>
            partem eſſiciam{us} ſiniſtram, non mutata parte ſuperiore in inferiorem, habebim{us} horologium declinans
              <lb/>
            à meridie in occaſum grad. </s>
            <s xml:id="echoid-s21009" xml:space="preserve">30. </s>
            <s xml:id="echoid-s21010" xml:space="preserve">Si denique non ſolum dextram partem in ſinistram conuertam{us}, ſed
              <lb/>
            etiam partem, quę nobis poſt hanc mutationem ſuperior est, efficiam{us} inferiorem, conſtructum erit ho
              <lb/>
            rologium à borea deſlectens in occaſum grad. </s>
            <s xml:id="echoid-s21011" xml:space="preserve">30. </s>
            <s xml:id="echoid-s21012" xml:space="preserve">Eadem ratione, ſi deſcribatur horologium declinans à
              <lb/>
            meridie in occaſum grad. </s>
            <s xml:id="echoid-s21013" xml:space="preserve">30. </s>
            <s xml:id="echoid-s21014" xml:space="preserve">efficiemus ex eo horologium declinans à borea in occaſum declinans grad.
              <lb/>
            </s>
            <s xml:id="echoid-s21015" xml:space="preserve">30. </s>
            <s xml:id="echoid-s21016" xml:space="preserve">& </s>
            <s xml:id="echoid-s21017" xml:space="preserve">declinans à meridie in ortum totidem gradib{us}, nec non à borea in ortum grad. </s>
            <s xml:id="echoid-s21018" xml:space="preserve">30. </s>
            <s xml:id="echoid-s21019" xml:space="preserve">deflectens, ſi
              <lb/>
            prædictę partium inuer ſiones fiant, vt ex dictis perſpicuum eſt. </s>
            <s xml:id="echoid-s21020" xml:space="preserve">Sed in omnibus numeri horarum lineis
              <lb/>
            aſcribendi ſunt, vt in priore deſcriptione horologij declinantis docuim{us} in hac pro poſitione.</s>
            <s xml:id="echoid-s21021" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
        </div>
        <div xml:id="echoid-div1073" type="section" level="1" n="256">
          <head xml:id="echoid-head265" xml:space="preserve">PROBLEMA 2. PROPOSITIO 2.</head>
          <p>
            <s xml:id="echoid-s21022" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in horologio,
              <lb/>
            quod à Verticali circulo declinat, deſcribere.</s>
            <s xml:id="echoid-s21023" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21024" xml:space="preserve">INVENTA altitudine poli ſupra planum declinans ex propoſ. </s>
            <s xml:id="echoid-s21025" xml:space="preserve">29. </s>
            <s xml:id="echoid-s21026" xml:space="preserve">primi libri, quam qui-
              <lb/>
              <note position="left" xlink:label="note-0328-04" xlink:href="note-0328-04a" xml:space="preserve">Arcus ſignorũ
                <lb/>
              Zodiaci in ho-
                <lb/>
              rologio declinã
                <lb/>
              se à Verticali
                <lb/>
              quomodo de-
                <lb/>
              ſcribantur ex
                <lb/>
              Analem mate.</note>
            dem, vt diximus, indicat etiam ſecundum priorem deſcriptionem horologii declinantis in præ-
              <lb/>
            cedenti propoſ. </s>
            <s xml:id="echoid-s21027" xml:space="preserve">vel etiam in deſcriptione, quam in ſcholio eiuſdem propoſ. </s>
            <s xml:id="echoid-s21028" xml:space="preserve">tradidimus ad datam
              <lb/>
              <note position="left" xlink:label="note-0328-05" xlink:href="note-0328-05a" xml:space="preserve">30</note>
            ſtyli longitudinem, cuius quoque locus datus ſit, angulus G C I, comprehenſus â linea ſtyli, & </s>
            <s xml:id="echoid-s21029" xml:space="preserve">
              <lb/>
            axe mundi; </s>
            <s xml:id="echoid-s21030" xml:space="preserve">conſtituatur ad eam Analemma, vt in propoſ. </s>
            <s xml:id="echoid-s21031" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21032" xml:space="preserve">præcedentis libri, ita vt arcus C E, in
              <lb/>
            Analemmate illius propoſ. </s>
            <s xml:id="echoid-s21033" xml:space="preserve">metiatur altitudinem poli ſupra planum declinans, hoc eſt, in propo-
              <lb/>
            ſito exemplo, contineat grad. </s>
            <s xml:id="echoid-s21034" xml:space="preserve">40. </s>
            <s xml:id="echoid-s21035" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s21036" xml:space="preserve">3. </s>
            <s xml:id="echoid-s21037" xml:space="preserve">vel certè angulus C D E, illius Analemmatis æqualis ſit
              <lb/>
            angulo G C I, in horologio declinante præcedentis propoſ. </s>
            <s xml:id="echoid-s21038" xml:space="preserve">Si enim ſumatur in eodem Analem-
              <lb/>
            mate recta D G, æqualis ſtylo I K, quem horologium priori via deſcriptum offert, vel quem in
              <lb/>
            poſteriore deſcriptione aſſumpſimus in portione Analemmatis deſcripta in antecedenti propof.
              <lb/>
            </s>
            <s xml:id="echoid-s21039" xml:space="preserve">quæ priori figuræ propoſ. </s>
            <s xml:id="echoid-s21040" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21041" xml:space="preserve">ſuperioris libri reſpondet, vel cerre quem aſſumpſimus in ea deſcri-
              <lb/>
            ptione, in qua longitudo ſtyli vnà cum eius loco data fuit; </s>
            <s xml:id="echoid-s21042" xml:space="preserve">& </s>
            <s xml:id="echoid-s21043" xml:space="preserve">per G, recta O R, parallela agatur ipſi
              <lb/>
            B C, habebimus in recta O R, diametros conicarum ſectionum, quemadmodum earundem dia-
              <lb/>
              <note position="left" xlink:label="note-0328-06" xlink:href="note-0328-06a" xml:space="preserve">40</note>
            metros K R, L R, M R, N O, P O, Q O, habuimus in horizontali horologio propoſ. </s>
            <s xml:id="echoid-s21044" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21045" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21046" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s21047" xml:space="preserve">Quamobrem parallelos, ſiuearcus ſignorum hic deſcribemus, vt ibi docuimus, nempe conicas
              <lb/>
            ſectiones circa diametros inuentas, quarum illæ, quæ inter centrum C, & </s>
            <s xml:id="echoid-s21048" xml:space="preserve">lineam æquinoctialẽ
              <lb/>
            continentur, cornua inflectent verſus centrum, reliquæ verò in oppoſitam partem, non ſecus at-
              <lb/>
            que in horizontali horologio. </s>
            <s xml:id="echoid-s21049" xml:space="preserve">Nam ſicut in horologio horizontali circulus Analemmatis A B C,
              <lb/>
            reſert Meridianum Horizontis, & </s>
            <s xml:id="echoid-s21050" xml:space="preserve">recta O R, communem ſectionem plani horologij horizonta-
              <lb/>
            lis, & </s>
            <s xml:id="echoid-s21051" xml:space="preserve">Meridiani, ſeu lineam meridianam; </s>
            <s xml:id="echoid-s21052" xml:space="preserve">ita in horologio declinante circulus idem ſumitur pro
              <lb/>
            Meridiano proprio plani declinantis, hoc eſt, pro circulo per polos mundi, & </s>
            <s xml:id="echoid-s21053" xml:space="preserve">per polos plani de-
              <lb/>
            clinantis ducto, recta autem O R, pro communi ſectione dicti Meridiani, & </s>
            <s xml:id="echoid-s21054" xml:space="preserve">plani horologii de-
              <lb/>
            clinantis, nempe pro linea ſtyli. </s>
            <s xml:id="echoid-s21055" xml:space="preserve">Non conſtituimus autem ad inuentam altitudinem poli ſupra
              <lb/>
              <note position="left" xlink:label="note-0328-07" xlink:href="note-0328-07a" xml:space="preserve">50</note>
            planum declinans proprium Analemma, quia & </s>
            <s xml:id="echoid-s21056" xml:space="preserve">tota hæc res facile intelligi poteſt ex Analemma
              <lb/>
            re propoſ. </s>
            <s xml:id="echoid-s21057" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21058" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s21059" xml:space="preserve">& </s>
            <s xml:id="echoid-s21060" xml:space="preserve">nos in hac propoſ. </s>
            <s xml:id="echoid-s21061" xml:space="preserve">arcus ſignorum deſcribemus alia ratione, quam
              <lb/>
              <note position="left" xlink:label="note-0328-08" xlink:href="note-0328-08a" xml:space="preserve">Qua ratione
                <lb/>
              maius aut mi-
                <lb/>
              nus horologiũ
                <lb/>
              ſecundum idẽ
                <lb/>
              Analemma de-
                <lb/>
              ſcribatur.</note>
            mox explicabimus.</s>
            <s xml:id="echoid-s21062" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21063" xml:space="preserve">QVOD ſi maius horologium quis optet, aut minus, ſumendus erit in Analemmate longior,
              <lb/>
            aut breuior ſtylus D M, & </s>
            <s xml:id="echoid-s21064" xml:space="preserve">per M, linea ducenda parallela ipſi B C, &</s>
            <s xml:id="echoid-s21065" xml:space="preserve">c. </s>
            <s xml:id="echoid-s21066" xml:space="preserve">vt de horizontali horolo-
              <lb/>
            gio diximus propoſ. </s>
            <s xml:id="echoid-s21067" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21068" xml:space="preserve">ſuperioris lib.</s>
            <s xml:id="echoid-s21069" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21070" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s21071" xml:space="preserve">Ducta recta C I, quæ axem mundi referat, excitetur in I, ad C I, perpendicularis
              <lb/>
              <note position="left" xlink:label="note-0328-09" xlink:href="note-0328-09a" xml:space="preserve">Alia deſcriptio
                <lb/>
              atcuum ſigno-
                <lb/>
              rum in eodem
                <lb/>
              horologio de-
                <lb/>
              clinante à Ver
                <lb/>
              t
                <unsure/>
              icali.</note>
            I G, pro radio Aequatoris, ex cuius vtraque parte radij aliorum ſignorum educãtur, vt in ſuperio-
              <lb/>
            ribus non ſemel factum eſt: </s>
            <s xml:id="echoid-s21072" xml:space="preserve">ſumaturq́ue C I, æqualis rectæ C I, in axe horologij præcedentis pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s21073" xml:space="preserve">vel in horologio, quod in ſcholio eiuſdem propoſ. </s>
            <s xml:id="echoid-s21074" xml:space="preserve">conſtruximus ad datum ſtylum in dato lo-
              <lb/>
            co; </s>
            <s xml:id="echoid-s21075" xml:space="preserve">& </s>
            <s xml:id="echoid-s21076" xml:space="preserve">recta I G, æqualis rectæ I G, vel L G, in eodem horologio; </s>
            <s xml:id="echoid-s21077" xml:space="preserve">& </s>
            <s xml:id="echoid-s21078" xml:space="preserve">ex C, per G, recta </s>
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