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-div717" type="section" level="1" n="178">
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            <s xml:id="echoid-s14455" xml:space="preserve">
              <pb o="211" file="0231" n="231" rhead="LIBER SECVNDVS."/>
            Septentrionem, ſumendus erit arcus altitudinis poli B A, deorſum verſus, & </s>
            <s xml:id="echoid-s14456" xml:space="preserve">arcus complementi B C,
              <lb/>
            ſurſum verſus. </s>
            <s xml:id="echoid-s14457" xml:space="preserve">Ductis vero rectis D A, D C, ſecabitur meridiana linea in punctis H, & </s>
            <s xml:id="echoid-s14458" xml:space="preserve">I. </s>
            <s xml:id="echoid-s14459" xml:space="preserve">Poſt hæc in
              <lb/>
            I, excitabimus ad meridianam lineam perpendicularem F K, pro linea æquinoctiali. </s>
            <s xml:id="echoid-s14460" xml:space="preserve">Poſtremo ſumpta
              <lb/>
            recta I E, æquali ipſi I D, deſcribemus ex E, circulum cuiuſcunque magnitudinis, quo diuiſo in partes
              <lb/>
            24. </s>
            <s xml:id="echoid-s14461" xml:space="preserve">æquales, initio facto à linea meridiana, reliqua abſoluemus, vt ante docuimus ad initium hu-
              <lb/>
            ius propoſ.</s>
            <s xml:id="echoid-s14462" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14463" xml:space="preserve">DEMONSTRATIO huius deſcriptionis hæc eſt. </s>
            <s xml:id="echoid-s14464" xml:space="preserve">Si linea meridiana M N, proprium ſitum
              <lb/>
              <note position="right" xlink:label="note-0231-01" xlink:href="note-0231-01a" xml:space="preserve">Demonſtratio
                <lb/>
              huius deſcri-
                <lb/>
              ptionis.</note>
            habeat in plano, quod rectum eſt ad Horizontem, & </s>
            <s xml:id="echoid-s14465" xml:space="preserve">directo ad meridiem, vel boream ſpectat, ita vt M,
              <lb/>
            ſurſum verſus, & </s>
            <s xml:id="echoid-s14466" xml:space="preserve">N, deorſum verſus vergat, triangulum{q́ue} H D I, rectum ſtatuatur ad planum horo-
              <lb/>
            logii, ita vt in plano Meridiani ſitum ſit; </s>
            <s xml:id="echoid-s14467" xml:space="preserve">quoniam angulus H D G, per conſtructionem, æqualis eſt alti-
              <lb/>
              <note position="left" xlink:label="note-0231-02" xlink:href="note-0231-02a" xml:space="preserve">10</note>
            tudini poli, erit reliquus D H G, complemento altitudinis poli ęqualis. </s>
            <s xml:id="echoid-s14468" xml:space="preserve">Rurſus quia per conſtructionem
              <lb/>
            I D G, complemento altitudinis poli eſt æqualis, erit reliquus D I G, altitudini poli æqualis. </s>
            <s xml:id="echoid-s14469" xml:space="preserve">Sumpto igi-
              <lb/>
            tur D, vertice ſtyli pro centro mundi, erit D H, faciens cum linea meridiana in H, angulum complemen-
              <lb/>
            to altitudinis poli ęqualem axis mundi occurrens plano horologii in H, centro horologii. </s>
            <s xml:id="echoid-s14470" xml:space="preserve">Recta autem D I,
              <lb/>
            conſtituens cum eadem linea meridiana in I, angulum altitudinis poli, erit communis ſectio Meridiani at-
              <lb/>
            que Aequatoris, cum eiuſmodi ſectio inſphæra cum meridiana linca in Verticali efficiat ſemper angulum
              <lb/>
            altitudinis poli, cum axe vero angulum rectum, cuiuſmodi est angulus H D I, compoſitus ex angulo alti-
              <lb/>
            tudinis poli, & </s>
            <s xml:id="echoid-s14471" xml:space="preserve">angulo complementi eiuſdem altitudinis poli. </s>
            <s xml:id="echoid-s14472" xml:space="preserve">Occurrit igitur Aequator plano horolo-
              <lb/>
            gii in I, ac proinde, vt ſupra oſtenſum eſt, erit recta F K, linea æquinoctialis. </s>
            <s xml:id="echoid-s14473" xml:space="preserve">Recta autem D G, communis
              <lb/>
            ſectio erit Meridiani atque Horizontis. </s>
            <s xml:id="echoid-s14474" xml:space="preserve">Reliqua omnia demonſtr abuntur, vt prius.</s>
            <s xml:id="echoid-s14475" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s14476" xml:space="preserve">IDEM horologium deſcribemus ſine punctis in æquinoctiali linea inuentis, beneficio Ellipſis, vt & </s>
            <s xml:id="echoid-s14477" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0231-04" xlink:href="note-0231-04a" xml:space="preserve">Deſcriptio eiuſ
                <lb/>
              dem horologii
                <lb/>
              benefie
                <unsure/>
              io Elli-
                <lb/>
              pſis.</note>
            borizontale deſcripſimus in ſcholio propoſ. </s>
            <s xml:id="echoid-s14478" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14479" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14480" xml:space="preserve">hoc modo. </s>
            <s xml:id="echoid-s14481" xml:space="preserve">Ex H, centro horologii deſcribantur
              <lb/>
            duo circuli, vnus ad interuallum H I, alter vero ad interuallum I D: </s>
            <s xml:id="echoid-s14482" xml:space="preserve">Vel ſi hę ſemidiametri nimis bre-
              <lb/>
            ues videantur, ſumatur punctum in axe remotius à puncto H, quàm D, (vt & </s>
            <s xml:id="echoid-s14483" xml:space="preserve">in horizontali horologio
              <lb/>
            factum eſt) à quo ad axem perpendicularis ducatur ſecans meridianam lineam in puncto, quod maioris
              <lb/>
            circuli ſemidiametrum terminabit: </s>
            <s xml:id="echoid-s14484" xml:space="preserve">pro minoris autem circuli ſemidiametro accipiatur ſegmentũ illius
              <lb/>
            perpendicularis inter idem punctum, & </s>
            <s xml:id="echoid-s14485" xml:space="preserve">axem interpoſitum. </s>
            <s xml:id="echoid-s14486" xml:space="preserve">Diuiſo deinde vtroque circulo in 24. </s>
            <s xml:id="echoid-s14487" xml:space="preserve">par-
              <lb/>
            tes ęquales, initio facto à linea meridiana, inueniemus beneficio punctorum diuiſionum in plano horologii
              <lb/>
            puncta Ellipſis, per quæ ducendę ſunt lineę horariæ ex puncto H, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s14488" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14489" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14490" xml:space="preserve">tradi-
              <lb/>
            dimus. </s>
            <s xml:id="echoid-s14491" xml:space="preserve">Eadem enim demonſtratio huc afferri poterit. </s>
            <s xml:id="echoid-s14492" xml:space="preserve">Exemplum huius deſcriptionis non ponimus, quia
              <lb/>
              <note position="left" xlink:label="note-0231-05" xlink:href="note-0231-05a" xml:space="preserve">30</note>
            luce clarius res ipſa intelligi potest ex figura, quam in dicto ſcholio propoſ. </s>
            <s xml:id="echoid-s14493" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14494" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14495" xml:space="preserve">depinximus. </s>
            <s xml:id="echoid-s14496" xml:space="preserve">Ea
              <lb/>
            enim figura refert Verticale horologium ad latitudinem loci gr. </s>
            <s xml:id="echoid-s14497" xml:space="preserve">48. </s>
            <s xml:id="echoid-s14498" xml:space="preserve">quæ nimirum cum ea latitudine, pro
              <lb/>
            qua illud horologium horizontale conſtructum eſt, grad. </s>
            <s xml:id="echoid-s14499" xml:space="preserve">90. </s>
            <s xml:id="echoid-s14500" xml:space="preserve">conficit; </s>
            <s xml:id="echoid-s14501" xml:space="preserve">dummodo numeri horarum mutentur
              <lb/>
            in earum complementa vſque ad 12. </s>
            <s xml:id="echoid-s14502" xml:space="preserve">Eſt enim Verticalis proprie dictus cuiusuis Horizontis inſtar cuiuſ-
              <lb/>
              <note position="right" xlink:label="note-0231-06" xlink:href="note-0231-06a" xml:space="preserve">Horologiũ ho-
                <lb/>
              rizontale ad
                <lb/>
              quamcunque la
                <lb/>
              titudinem con-
                <lb/>
              ſtructũ
                <unsure/>
              , eſt Ver-
                <lb/>
              ticale in regio-
                <lb/>
              ne, cuius latitu-
                <lb/>
              do complemen
                <lb/>
              tum eſt illius
                <lb/>
              latitudinis, &
                <lb/>
              contra Vertica
                <lb/>
              le illius eſt hori
                <lb/>
              @ontale huius.</note>
            dam Horizontis, ſupra quem polus attollitur tot gradibus, quot deſunt latitudini loci, ad quam horizon-
              <lb/>
            tale horologium conſtructum eſt, ad explendum numerum grad. </s>
            <s xml:id="echoid-s14503" xml:space="preserve">90. </s>
            <s xml:id="echoid-s14504" xml:space="preserve">vt perſpicuum eſt ex portione Ana-
              <lb/>
            lemmatis in principio huius propoſ. </s>
            <s xml:id="echoid-s14505" xml:space="preserve">deſcripta, in qua angulus D H G, complementum anguli H D G, alti-
              <lb/>
            tudinis poli ſupra Horizontem B C, constituit altitudinem poli ſupra Verticalem H I, tanquam ſupra Ho
              <lb/>
            rizontem quempiam: </s>
            <s xml:id="echoid-s14506" xml:space="preserve">Ita vt quodcunque horologium horizontale ad quamcunque latitudinem loci fabri
              <lb/>
            catum, ſit Verticale in regione eius latitudinis, quæ illius complementum eſt: </s>
            <s xml:id="echoid-s14507" xml:space="preserve">Et quodlibet horologium
              <lb/>
              <note position="left" xlink:label="note-0231-07" xlink:href="note-0231-07a" xml:space="preserve">40</note>
            Verticale in priore latitudine ſit viciſſim horizontale in poſteriore; </s>
            <s xml:id="echoid-s14508" xml:space="preserve">ſi numeri horarum mutentur in ea-
              <lb/>
            rum complementa vſque ad 12. </s>
            <s xml:id="echoid-s14509" xml:space="preserve">vt diximus.</s>
            <s xml:id="echoid-s14510" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div733" type="section" level="1" n="179">
          <head xml:id="echoid-head182" xml:space="preserve">PROBLEMA 14. PROPOSITIO 14.</head>
          <p>
            <s xml:id="echoid-s14511" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in Verticali ho-
              <lb/>
            rologio prædicto deſcribere.</s>
            <s xml:id="echoid-s14512" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <p>
            <s xml:id="echoid-s14513" xml:space="preserve">REPETATVR portio Analemmatis præcedentis propoſ. </s>
            <s xml:id="echoid-s14514" xml:space="preserve">cõpleaturq́; </s>
            <s xml:id="echoid-s14515" xml:space="preserve">Meridianus A B C,
              <lb/>
              <note position="right" xlink:label="note-0231-09" xlink:href="note-0231-09a" xml:space="preserve">Deſcriptio a@-
                <lb/>
              cuum ſignorũ
                <lb/>
              Zodiaci in ho-
                <lb/>
              rologio Vertica
                <lb/>
              li, ex Anal@-
                <lb/>
              mate.</note>
            in quo, iuxta Analemma propoſ. </s>
            <s xml:id="echoid-s14516" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14517" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s14518" xml:space="preserve">conſtructum, ducantur parallelorum diametri,
              <lb/>
            vnà cum diametris oppoſita ſigna coniungentibus, facientibusq́; </s>
            <s xml:id="echoid-s14519" xml:space="preserve">in conis, quorum baſes ſunt pa-
              <lb/>
            ralleli, vertex autem communis centrum D, triangula per axem. </s>
            <s xml:id="echoid-s14520" xml:space="preserve">Erit igitur ex demonſtratis in
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s14521" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14522" xml:space="preserve">5. </s>
            <s xml:id="echoid-s14523" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14524" xml:space="preserve">& </s>
            <s xml:id="echoid-s14525" xml:space="preserve">7. </s>
            <s xml:id="echoid-s14526" xml:space="preserve">præcedentis libri K R, diameter conicæ ſectionis, quam Sol in principio ♋,
              <lb/>
            exiſtens deſcribit: </s>
            <s xml:id="echoid-s14527" xml:space="preserve">L R, diameter ſectionis, quam Sol in principio ♊, & </s>
            <s xml:id="echoid-s14528" xml:space="preserve">♌, percurrit: </s>
            <s xml:id="echoid-s14529" xml:space="preserve">M R, dia-
              <lb/>
            meter ſectionis deſcriptæ à radio Solis in primo puncto ♉, & </s>
            <s xml:id="echoid-s14530" xml:space="preserve">♍, exiſtentis. </s>
            <s xml:id="echoid-s14531" xml:space="preserve">At verò N Q, O Q,
              <lb/>
            P Q, erunt diametri ſectionum conicarum, quas radii Solis in oppoſitis parallelis exiſtentis
              <lb/>
            deſcribunt.</s>
            <s xml:id="echoid-s14532" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14533" xml:space="preserve">HAE autem diametri conicarum ſectionum reperientur etiam in quocunque alio Analem-
              <lb/>
            mate, quod vel maius ſit, vel minus hoc propoſito, etiamſi horologium ſine portione </s>
          </p>
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