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-s21589" xml:space="preserve">
              <pb o="322" file="0338" n="338" rhead="GNOMONICES"/>
            tro mundi. </s>
            <s xml:id="echoid-s21590" xml:space="preserve">Et quia communes ſectiones Horizontis & </s>
            <s xml:id="echoid-s21591" xml:space="preserve">circulorum Verticalium, inter quos eſt
              <lb/>
            eriam Meridianus, per polos Horizontis ductorum, diuidunt Horizõtem, ac proinde & </s>
            <s xml:id="echoid-s21592" xml:space="preserve">circulum
              <lb/>
            ex A, centro Horizontis deſcriptum, in dicta poſitione, in partes æquales; </s>
            <s xml:id="echoid-s21593" xml:space="preserve">occurrit autem Meri-
              <lb/>
            dianus per A, centrum mundi ductus plano horologii in B, faciens cum eo communem ſectio-
              <lb/>
            nem, ipſam lineam meridianam B C, & </s>
            <s xml:id="echoid-s21594" xml:space="preserve">Verticalis propriè dictus per centrum quoque mundi
              <lb/>
            incedens idem planum ſecat in D, quòd vmbra ſtyli, Sole exiſtente in communi ſectione Horizon
              <lb/>
            tis, Aequatoris, circuli horæ 6. </s>
            <s xml:id="echoid-s21595" xml:space="preserve">& </s>
            <s xml:id="echoid-s21596" xml:space="preserve">Verticalis propriè dicti, cadat in punctum D, nempe in com-
              <lb/>
            munem ſectionem plani horologii & </s>
            <s xml:id="echoid-s21597" xml:space="preserve">Aequatoris, & </s>
            <s xml:id="echoid-s21598" xml:space="preserve">communem ſectionem eiuſdem horologii
              <lb/>
            atque Horizontis, vt ex propoſ. </s>
            <s xml:id="echoid-s21599" xml:space="preserve">11. </s>
            <s xml:id="echoid-s21600" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21601" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21602" xml:space="preserve">conſtat; </s>
            <s xml:id="echoid-s21603" xml:space="preserve">erit A B, communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s21604" xml:space="preserve">Meri-
              <lb/>
            diani; </s>
            <s xml:id="echoid-s21605" xml:space="preserve">A D, communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s21606" xml:space="preserve">Verticalis proprie dicti; </s>
            <s xml:id="echoid-s21607" xml:space="preserve">ac proinde reliquæ occultæ
              <lb/>
              <note position="left" xlink:label="note-0338-01" xlink:href="note-0338-01a" xml:space="preserve">10</note>
            lineæ per centrum A, & </s>
            <s xml:id="echoid-s21608" xml:space="preserve">puncta diuiſionum circuli ex A, deſcripti ductæ, cõmunes ſectiones erunt
              <lb/>
            Horizontis & </s>
            <s xml:id="echoid-s21609" xml:space="preserve">reliquorum circulorum Verticalium. </s>
            <s xml:id="echoid-s21610" xml:space="preserve">Quocirca Verticales circuli planum horolo-
              <lb/>
            gii ſecant in punctis lineæ horizontalis, in quæ cadunt dictæ ſectiones communes. </s>
            <s xml:id="echoid-s21611" xml:space="preserve">Cum ergo per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s21612" xml:space="preserve">18. </s>
            <s xml:id="echoid-s21613" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21614" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21615" xml:space="preserve">ſectiones communes circulorum Verticalium, & </s>
            <s xml:id="echoid-s21616" xml:space="preserve">plani horologii ſint parallelæ,
              <lb/>
            quòd planum horologij æquidiſtet communi illorum ſectioni, nempe axi Horizontis per verticẽ
              <lb/>
            loci, eiusq́ue oppoſitum ducto; </s>
            <s xml:id="echoid-s21617" xml:space="preserve">perſpicuum relinquitur, dictas illas lineas meridianę lineæ paral-
              <lb/>
            lelas, communes eſſe ſectiones plani horologii, & </s>
            <s xml:id="echoid-s21618" xml:space="preserve">circulorum Verticalium. </s>
            <s xml:id="echoid-s21619" xml:space="preserve">Quamobrem Vertica
              <lb/>
            les circulos in eodem declinante horologio deſcripſimus. </s>
            <s xml:id="echoid-s21620" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s21621" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1102" type="section" level="1" n="261">
          <head xml:id="echoid-head270" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s21622" xml:space="preserve">LINEA horizontalis aufert hic quoque portionem, quæ in facie eiuſdem plani collocanda eſt, ita
              <lb/>
            vt horizontalis linea in ſuperiori loco ſtatuatur, & </s>
            <s xml:id="echoid-s21623" xml:space="preserve">pars, quę in eo ſitu nobis dextra eſt, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s21624" xml:space="preserve">
              <lb/>
            contra, vt conſtat ex demonſtratis in ſcholio propoſ. </s>
            <s xml:id="echoid-s21625" xml:space="preserve">14. </s>
            <s xml:id="echoid-s21626" xml:space="preserve">ſuperioris libri. </s>
            <s xml:id="echoid-s21627" xml:space="preserve">In vtroque porrò horologio
              <lb/>
              <note position="left" xlink:label="note-0338-03" xlink:href="note-0338-03a" xml:space="preserve">Ordo Vertica
                <lb/>
              lium circulorũ
                <lb/>
              in horologio.</note>
            tam australi, quàm boreali, numeri graduum incipiunt à parallela per punctum D, ducta, quæ communis
              <lb/>
            ſectio eſt Verticalis propriè dicti, & </s>
            <s xml:id="echoid-s21628" xml:space="preserve">plani horologii, ita vt in exemplo noſtro proximæ lineæ hinc inde à
              <lb/>
            puncto D, habeant numeros grad. </s>
            <s xml:id="echoid-s21629" xml:space="preserve">15. </s>
            <s xml:id="echoid-s21630" xml:space="preserve">&</s>
            <s xml:id="echoid-s21631" xml:space="preserve">c.</s>
            <s xml:id="echoid-s21632" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s21633" xml:space="preserve">QVONIAM verò oſtenſum eſt, Verticalem propriè dictum tranſire per A D, & </s>
            <s xml:id="echoid-s21634" xml:space="preserve">Meridianũ
              <lb/>
            per A B, ſi circulus ex A, deſcriptus propriam poſitionem habeat; </s>
            <s xml:id="echoid-s21635" xml:space="preserve">fit vt A D B, ſi erratum non eſt,
              <lb/>
              <note position="left" xlink:label="note-0338-04" xlink:href="note-0338-04a" xml:space="preserve">30</note>
            ſit angul{us} declinationis, quẽ nimirum facit Verticalis propriè dictus cum plano declinante, & </s>
            <s xml:id="echoid-s21636" xml:space="preserve">A B D,
              <lb/>
            eiuſdem complementum, quem videlicet Meridianus cum eodem plano conſtituit. </s>
            <s xml:id="echoid-s21637" xml:space="preserve">Vnde neceſſe eſt, angu-
              <lb/>
            lum reliquum B A D, in triangulo A B D, eſſe rectum. </s>
            <s xml:id="echoid-s21638" xml:space="preserve">Id quod luce clari{us} etiam conſtat ex horologio,
              <lb/>
            quod in ſcholio propoſ. </s>
            <s xml:id="echoid-s21639" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21640" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s21641" xml:space="preserve">ad datam ſtyli longitudinem conſtruximus. </s>
            <s xml:id="echoid-s21642" xml:space="preserve">Ibi enim linea F E, re-
              <lb/>
            ſpondet hic lineæ A B, & </s>
            <s xml:id="echoid-s21643" xml:space="preserve">linea F α, ibi eadem eſt, quæ hic linea A D.</s>
            <s xml:id="echoid-s21644" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s21645" xml:space="preserve">IN nostro quoque exemplo Verticalis grad. </s>
            <s xml:id="echoid-s21646" xml:space="preserve">60. </s>
            <s xml:id="echoid-s21647" xml:space="preserve">tranſit præcisè per K, locum ſtyli: </s>
            <s xml:id="echoid-s21648" xml:space="preserve">quia Verticalis
              <lb/>
            ille, qui per ſtylum ducitur, atque adeò rectus eſt ad planum declinans, recedit à Meridiano gradibus 30.
              <lb/>
            </s>
            <s xml:id="echoid-s21649" xml:space="preserve">quot nimirum gradibus planum declinans à Verticali recedit. </s>
            <s xml:id="echoid-s21650" xml:space="preserve">Manifestum autem eſt, Verticalem grad. </s>
            <s xml:id="echoid-s21651" xml:space="preserve">
              <lb/>
            60. </s>
            <s xml:id="echoid-s21652" xml:space="preserve">declinare à Meridiano grad. </s>
            <s xml:id="echoid-s21653" xml:space="preserve">30. </s>
            <s xml:id="echoid-s21654" xml:space="preserve">Eadem ratione in omni horologio declinante per locum ſtyli ille Ver
              <lb/>
            ticalis ducendus erit, qui tot gradibus à Meridiano abeſt, quot continet declinatio plani declinantis à
              <lb/>
              <note position="left" xlink:label="note-0338-05" xlink:href="note-0338-05a" xml:space="preserve">40</note>
            Verticali circulo.</s>
            <s xml:id="echoid-s21655" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1106" type="section" level="1" n="262">
          <head xml:id="echoid-head271" xml:space="preserve">PROBLEMA 5. PROPOSITIO 5.</head>
          <p>
            <s xml:id="echoid-s21656" xml:space="preserve">PARALLELOS Horizontis in eodem horologio declinante
              <lb/>
            figurare.</s>
            <s xml:id="echoid-s21657" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21658" xml:space="preserve">HOS parallelos in horologio declinante eiſdem rationibus deſcribemus, quibus in Verticali
              <lb/>
              <note position="left" xlink:label="note-0338-06" xlink:href="note-0338-06a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              rallelorum Ho
                <lb/>
              rizontis in eo-
                <lb/>
              dem horologio
                <lb/>
              declinante à
                <lb/>
              Verticali.</note>
            horologio deſcripti ſunt propoſ. </s>
            <s xml:id="echoid-s21659" xml:space="preserve">17. </s>
            <s xml:id="echoid-s21660" xml:space="preserve">ſuperioris libri, his, quæ ſequuntur, mutatis. </s>
            <s xml:id="echoid-s21661" xml:space="preserve">In priore ratio-
              <lb/>
              <note position="left" xlink:label="note-0338-07" xlink:href="note-0338-07a" xml:space="preserve">50</note>
            ne circulus Analemmatis referet hic non Meridianum, vt ibi, ſed Verticalem illum circulum, qui
              <lb/>
            ad planum declinans rectus eſt, qui nimirum tranſit per K, locum gnomonis, facitq́ue cum pla-
              <lb/>
            no horologij ſectionem cõmunem, quæ in puncto K, ad angulos rectos ſecat horizontalem lineã.
              <lb/>
            </s>
            <s xml:id="echoid-s21662" xml:space="preserve">Talis eſt in noſtro exemplo Verticalis grad. </s>
            <s xml:id="echoid-s21663" xml:space="preserve">60. </s>
            <s xml:id="echoid-s21664" xml:space="preserve">& </s>
            <s xml:id="echoid-s21665" xml:space="preserve">diſtans à Meridiano ex parte auſtri verſus or-
              <lb/>
            tum grad. </s>
            <s xml:id="echoid-s21666" xml:space="preserve">30. </s>
            <s xml:id="echoid-s21667" xml:space="preserve">faciensq́ue in horologio ſectionem A K, vt in præcedenti ſcholio diximus. </s>
            <s xml:id="echoid-s21668" xml:space="preserve">Paral-
              <lb/>
            leli autem Horizontis non mutantur. </s>
            <s xml:id="echoid-s21669" xml:space="preserve">Rurſus recta G O, erit communis ſectio plani horologii, & </s>
            <s xml:id="echoid-s21670" xml:space="preserve">
              <lb/>
            Verticalis illius per ſtylum ducti, ita tamen, vt diſtet à centro E, pro magnitudine ſtyli I k, vel A K. </s>
            <s xml:id="echoid-s21671" xml:space="preserve">
              <lb/>
            Puncta denique K, L, M, N, transferenda hic ſunt non in meridianam lineam horologii, vt ibi,
              <lb/>
            ſed in rectam, quæ per K, ad horizontalem lineam perpendicularis eſt ducta, hoc eſt, in commu-
              <lb/>
            nem ſectionem dicti Verticalis, & </s>
            <s xml:id="echoid-s21672" xml:space="preserve">plani horologii. </s>
            <s xml:id="echoid-s21673" xml:space="preserve">Transſerenda ſunt autem hæc puncta ex loco
              <lb/>
            ſtyli tam infra lineam horizontalem, quàm ſupra, vt habeantur etiam paralleli Horizontis in </s>
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