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 style="it">
            <s xml:id="echoid-s28418" xml:space="preserve">
              <pb o="433" file="0449" n="449" rhead="LIBER QVARTVS."/>
            maior eſt ſtylo, abſcindi recta B I, ſtylo æqualis, vt ſi quando stylus amittatur, aut frangatur, ei-
              <lb/>
            æqualem poſſimus exhibere.</s>
            <s xml:id="echoid-s28419" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1467" type="section" level="1" n="356">
          <head xml:id="echoid-head369" xml:space="preserve">PROBLEMA 13. PROPOSITIO 13.</head>
          <p>
            <s xml:id="echoid-s28420" xml:space="preserve">DATO horologio, vna cum ſtylo, eiuſq́; </s>
            <s xml:id="echoid-s28421" xml:space="preserve">loco, ad quam poli al-
              <lb/>
            titudinem fabricatum ſit, & </s>
            <s xml:id="echoid-s28422" xml:space="preserve">quam declinationem habeat à Verticali,
              <lb/>
            & </s>
            <s xml:id="echoid-s28423" xml:space="preserve">inclinationem ad Horizontem, ſi declinans eſt, aut inclinatum, nec
              <lb/>
              <note position="left" xlink:label="note-0449-01" xlink:href="note-0449-01a" xml:space="preserve">10</note>
            non quanta ſit altitudo poli ſupra ipſum planum declinans, aut inclina-
              <lb/>
            tum, cognoſcere. </s>
            <s xml:id="echoid-s28424" xml:space="preserve">Et contra, dato horologio, vna cum altitudine
              <lb/>
            poli, ad quam conſtructum eſt, nec non inclinatione eius ad Horizon
              <lb/>
            tem, ſi inclinatum eſt, longitudinem ſtyli, eiusq; </s>
            <s xml:id="echoid-s28425" xml:space="preserve">locum, vna cum de-
              <lb/>
            clinatione à Verticali, ſi horologium declinans eſt, atque altitudinem
              <lb/>
            poli ſupra ipſum planum declinans, inclinatumve, inueſtigare.</s>
            <s xml:id="echoid-s28426" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s28427" xml:space="preserve">FREQVENTER accidit, vt ignoretur, ad quam eleuationem poli horologium aliquod
              <lb/>
            oblatum ſit conſtructum, aut quantus debeat eſſe eius ſtylus, (ſi fortè is aut amiſſus fuerit, aut con
              <lb/>
              <note position="left" xlink:label="note-0449-02" xlink:href="note-0449-02a" xml:space="preserve">20</note>
            fractus) & </s>
            <s xml:id="echoid-s28428" xml:space="preserve">in quo ſtatuendus loco, vt horas indicet. </s>
            <s xml:id="echoid-s28429" xml:space="preserve">Vtrumque igitur hac ratione cognoſcemus.</s>
            <s xml:id="echoid-s28430" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s28431" xml:space="preserve">SIT primum horologium horizontale A, in quo æquinoctialis linea B C, & </s>
            <s xml:id="echoid-s28432" xml:space="preserve">meridiana D E,
              <lb/>
              <note position="right" xlink:label="note-0449-03" xlink:href="note-0449-03a" xml:space="preserve">Qua ratione in
                <lb/>
              horologio hori
                <lb/>
              zontali ex da@o
                <lb/>
              ſtylo, eiu@q́ue
                <lb/>
              loc
                <unsure/>
              o, ad quam
                <lb/>
              poli altitudinẽ
                <lb/>
              fabricatum ſit,
                <lb/>
              inueſtigetur.</note>
            ſtylus autem F G, in puncto F, collocandus. </s>
            <s xml:id="echoid-s28433" xml:space="preserve">Excitetur ex F, loco ſtyli ad meridianam lineam per-
              <lb/>
            pendicularis F H, ſtylo F G, æqualis. </s>
            <s xml:id="echoid-s28434" xml:space="preserve">Ducta autem recta I H, ex puncto I, vbi meridiana linea, & </s>
            <s xml:id="echoid-s28435" xml:space="preserve">
              <lb/>
            æquinoctialis ſe interſecant, ad H, erigatur ex H, ad I H, perpendicularis H D, ſecans lineam meri
              <lb/>
            dianam in D. </s>
            <s xml:id="echoid-s28436" xml:space="preserve">Dico I D H, eſſe angulum altitudinis poli, ad quam horologium eſt fabricatum.
              <lb/>
            </s>
            <s xml:id="echoid-s28437" xml:space="preserve">Quoniam enim, vt ex de-
              <lb/>
              <figure xlink:label="fig-0449-01" xlink:href="fig-0449-01a" number="298">
                <image file="0449-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0449-01"/>
              </figure>
            monſtratis in propoſ. </s>
            <s xml:id="echoid-s28438" xml:space="preserve">1. </s>
            <s xml:id="echoid-s28439" xml:space="preserve">li-
              <lb/>
            bri ſuperioris conſtat, re-
              <lb/>
            cta H I, communis ſectio
              <lb/>
              <note position="left" xlink:label="note-0449-04" xlink:href="note-0449-04a" xml:space="preserve">30</note>
            eſt (ſi triangulum D H I,
              <lb/>
            ſtatuatur rectum ad planũ
              <lb/>
            horologii, hoc eſt, in Me-
              <lb/>
            ridiani plano) Aequato-
              <lb/>
            ris, & </s>
            <s xml:id="echoid-s28440" xml:space="preserve">Meridiani, axisq́ue
              <lb/>
            mundi per verticem ſtyli
              <lb/>
            H, tranſiens rectus eſt ad
              <lb/>
            planum Aequatoris, atque
              <lb/>
            adeò per defin. </s>
            <s xml:id="echoid-s28441" xml:space="preserve">3. </s>
            <s xml:id="echoid-s28442" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s28443" xml:space="preserve">11.
              <lb/>
            </s>
            <s xml:id="echoid-s28444" xml:space="preserve">Euclidis, ad H I, perpendi
              <lb/>
              <note position="left" xlink:label="note-0449-05" xlink:href="note-0449-05a" xml:space="preserve">40</note>
            cularis, erit H D, quæ per-
              <lb/>
            pendicularis ducta eſt ad
              <lb/>
            H I, axis mundi occurrens
              <lb/>
            meridianæ lineæ, & </s>
            <s xml:id="echoid-s28445" xml:space="preserve">plano
              <lb/>
            horologii in D. </s>
            <s xml:id="echoid-s28446" xml:space="preserve">Eſt igitur
              <lb/>
            H D I, angulus altitudinis
              <lb/>
            poli ſupra Horizontem,
              <lb/>
            quem nimirum axis mun
              <lb/>
            di cum meridiana linea ſa
              <lb/>
            cit in plano horizontalis
              <lb/>
            horologii.</s>
            <s xml:id="echoid-s28447" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <p>
            <s xml:id="echoid-s28448" xml:space="preserve">QVOD ſi in linea meridiana datum fuerit D, centrum horologii, in quo omnes lineæ hora-
              <lb/>
            rum à meridie & </s>
            <s xml:id="echoid-s28449" xml:space="preserve">media nocte coeunt, facilius inueniemus eandem altitudinem poli, ſi ex D, ad
              <lb/>
            H, rectam ducamus D H. </s>
            <s xml:id="echoid-s28450" xml:space="preserve">Erit enim rurſus D H, axis mundi (cum per centrum mundi H, & </s>
            <s xml:id="echoid-s28451" xml:space="preserve">per
              <lb/>
            D, centrum horologii ducatur) & </s>
            <s xml:id="echoid-s28452" xml:space="preserve">H D I, angulus altitudinis poli.</s>
            <s xml:id="echoid-s28453" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Qua uia ſtylus
            <lb/>
          eiusque locus
            <lb/>
          in horizont
            <unsure/>
          ali
            <lb/>
          horologio in-
            <lb/>
          quiratur ex da
            <lb/>
          ta altitudine
            <lb/>
          poli, ad quam
            <lb/>
          fabricatum eſt
            <lb/>
          horologium.</note>
          <p>
            <s xml:id="echoid-s28454" xml:space="preserve">IAM verò ſit nota altitudo poli, ad quam fabricatum eſt horologium, ſed ſtylus ignotus, nec
              <lb/>
            non & </s>
            <s xml:id="echoid-s28455" xml:space="preserve">locus eiuſdem, quem ita inquiremus. </s>
            <s xml:id="echoid-s28456" xml:space="preserve">Circa rectam D I, inter centrum horologii, & </s>
            <s xml:id="echoid-s28457" xml:space="preserve">æqui
              <lb/>
            noctialem lineam interiectam deſcribemus ſemicirculum D H I, & </s>
            <s xml:id="echoid-s28458" xml:space="preserve">ex D, centro horologii axem
              <lb/>
            mundi educemus D H, facientem cum meridiana linea angulum altitudinis poli H D I, qui cir-
              <lb/>
            culum ſecet in H. </s>
            <s xml:id="echoid-s28459" xml:space="preserve">Nam ex H, ad lineam meridianam demiſſa perpendicularis H F, erit longitu-
              <lb/>
            do ſtyli, eiuſq́ue ſedes in puncto F. </s>
            <s xml:id="echoid-s28460" xml:space="preserve">Ducta enim recta H I, erit angulus D H I, rectus in ſemicircu-
              <lb/>
              <note position="right" xlink:label="note-0449-08" xlink:href="note-0449-08a" xml:space="preserve">31. tertij.</note>
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