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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              <pb o="387" file="0403" n="403" rhead="LIBER TERTIVS."/>
            putatus eſt uerſus dexteram, ſeu partes occidentales, quia eius plani Meridianus ſub Horizonte
              <lb/>
            orientalior eſt Meridiano Horizontis. </s>
            <s xml:id="echoid-s25520" xml:space="preserve">In ſexta denique figura nihil intereſt, utrum in hanc, uel in
              <lb/>
            illam partem arcus dictus a b, numerctur: </s>
            <s xml:id="echoid-s25521" xml:space="preserve">quia complectitur grad. </s>
            <s xml:id="echoid-s25522" xml:space="preserve">90. </s>
            <s xml:id="echoid-s25523" xml:space="preserve">ita ut recta ρ b, cum ρ a,
              <lb/>
            angulum conſtituat rectum in ρ, puncto.</s>
            <s xml:id="echoid-s25524" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25525" xml:space="preserve">POST hæc ex quocunque puncto rectæ ρ b, ut ex G, ducatur ad ipſam perpendicularis G H,
              <lb/>
            quę erit linea æquinoctialis, quia, ut mox oſtẽdemus, ρ b, eſt linea indicis, ad quam neceſlario per-
              <lb/>
            pendicularis eſt æquinoctialis linea, ut ſupra demonſtrauimus.</s>
            <s xml:id="echoid-s25526" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25527" xml:space="preserve">AD hæc in puncto ρ, cum recta ρ b, conſtituatur angulus G ρ I, altitudinis poli ſupra planum
              <lb/>
            propoſitũ inueatę, per propoſ. </s>
            <s xml:id="echoid-s25528" xml:space="preserve">29. </s>
            <s xml:id="echoid-s25529" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25530" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25531" xml:space="preserve">ut habeatur ρ I, axis mundi, ad quem ex puncto G, exci-
              <lb/>
            tetur perpendicularis G I, ac reliqua fiant, ut in prima deſcriptione, hoc eſt, rectæ G I, ſuma-
              <lb/>
              <note position="left" xlink:label="note-0403-01" xlink:href="note-0403-01a" xml:space="preserve">10</note>
            tur æqualis G L, & </s>
            <s xml:id="echoid-s25532" xml:space="preserve">circulus ex L, deſcriptus in 24 partes æquales ſecetur, initio facto à recta L M,
              <lb/>
            quę ex centro L, ducitur per punctum M, ubi æquinoctialis linea, & </s>
            <s xml:id="echoid-s25533" xml:space="preserve">meridiana ρ b, ſe interſecant
              <lb/>
            uel certè, quæ ex L, parallela ducitur ipſi meridianę lineę, quando æquinoctialis linea, & </s>
            <s xml:id="echoid-s25534" xml:space="preserve">meridia
              <lb/>
            na parallelę ſunt, ut in ſexta figura, &</s>
            <s xml:id="echoid-s25535" xml:space="preserve">c. </s>
            <s xml:id="echoid-s25536" xml:space="preserve">Gnomon erit I K, ex I, perpendicularis demiſſa ad ρ b,
              <lb/>
            vt prius.</s>
            <s xml:id="echoid-s25537" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25538" xml:space="preserve">QVOD autem recta ρ b, communis ſectio ſit plani horologii, & </s>
            <s xml:id="echoid-s25539" xml:space="preserve">Meridiani proprii eiuſdem
              <lb/>
            plani, ita demonſtrabimus. </s>
            <s xml:id="echoid-s25540" xml:space="preserve">Quoniam Meridianus Horizontis, & </s>
            <s xml:id="echoid-s25541" xml:space="preserve">Meridianus plani proprius per
              <lb/>
            axem mundi ducuntur, occurruntq́ue circulo maximo, cui horologium æquidiſtat, in centro mũ
              <lb/>
            di, utpote in I, uertice ſtyli, fit ut dicti Meridiani cum hoc circulo maximo faciant communes
              <lb/>
            ſectiones, rectas lineas, quæ in centro angulum contineant, cui ſubtenditur arcus eiuſdem circuli
              <lb/>
              <note position="left" xlink:label="note-0403-02" xlink:href="note-0403-02a" xml:space="preserve">20</note>
            maximi inter illos Meridi
              <unsure/>
            anos interiectus: </s>
            <s xml:id="echoid-s25542" xml:space="preserve">Quia uerò ijdem Meridiani occurrunt plano horolo-
              <lb/>
              <note position="right" xlink:label="note-0403-03" xlink:href="note-0403-03a" xml:space="preserve">16. vndec.</note>
            gii in ρ, puncto, ubi axis eidem plano occurrit, faciuntq́ue cum eo ſectiones communes, lineas
              <lb/>
              <note position="right" xlink:label="note-0403-04" xlink:href="note-0403-04a" xml:space="preserve">10. vndec.</note>
            rectas, quę illis prioribus in maximo circulo ęquidiſtant, eo quòd eidem maximo circulo paral-
              <lb/>
            lelum eſt horologii planam; </s>
            <s xml:id="echoid-s25543" xml:space="preserve">comprehendent huiuſmodi lineæ in plano horologii angulũ æqua-
              <lb/>
            lem illi angulo, quem in circulo maximo priores illæ lineæ conſtituunt. </s>
            <s xml:id="echoid-s25544" xml:space="preserve">Quamobrem cum angu
              <lb/>
            lus a ρ b, in plano horologii ſit illi in maximo circulo æqualis, quòd arcus a b, ſimilis ſit arcui il-
              <lb/>
            lius circuli maximi inter duos Meridianos poſito, quandoquidem per conſtructionem totidem
              <lb/>
            gradus, ac Minuta continet: </s>
            <s xml:id="echoid-s25545" xml:space="preserve">ponatur autem ρ a, linea meridiana, erit ρ b, communis ſectio pla-
              <lb/>
            ni horologij, & </s>
            <s xml:id="echoid-s25546" xml:space="preserve">Meridiani ipſius proprii: </s>
            <s xml:id="echoid-s25547" xml:space="preserve">Ac proinde ſtylus in ea collocandus erit ad angulos re-
              <lb/>
            ctos, cum hac ratione à plano proprii huius Meridiani non recedat, ſed ad ipſum axem mundi in
              <lb/>
              <note position="left" xlink:label="note-0403-05" xlink:href="note-0403-05a" xml:space="preserve">30</note>
            eo exiſtentem pertingat. </s>
            <s xml:id="echoid-s25548" xml:space="preserve">Quare ρ b, linea indicis eſt, ſeu ſtyli. </s>
            <s xml:id="echoid-s25549" xml:space="preserve">Vnde reliqua conſtructio demon-
              <lb/>
            ſtrabitur, vt prima conſtructio huius propoſ. </s>
            <s xml:id="echoid-s25550" xml:space="preserve">Sed tertiam hanc deſcriptionem aliunde inchoare
              <lb/>
            poterimus, & </s>
            <s xml:id="echoid-s25551" xml:space="preserve">forſitan commodius, quàm tradidimus, vt in ſcholio ſequenti prope finem fere pla
              <lb/>
            num faciemus.</s>
            <s xml:id="echoid-s25552" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quando planũ
            <lb/>
          horologii axi
            <lb/>
          æquidiſtat.</note>
          <p>
            <s xml:id="echoid-s25553" xml:space="preserve">PORRO in plano ex parte boreali ad Horizontem inclinato, quod nec arcum habeat inter-
              <lb/>
            poſitum inter dictos duos Meridianos, neque altitudinem poli ſortiatur, vt contingit in planis,
              <lb/>
            quæ æquidiſtant circulis maximis per axem mundi ductis, quale eſt planum tertiæ figuræ, con-
              <lb/>
            ſtruendum erit horologium, vt in antecedenti conſtructione; </s>
            <s xml:id="echoid-s25554" xml:space="preserve">vel ſi prius ducatur vtcunque recta
              <lb/>
            quæpiam linea E ε, pro linea meridiana, ita procedendum erit. </s>
            <s xml:id="echoid-s25555" xml:space="preserve">Excitetur ad E ε, in quouis pun-
              <lb/>
            cto, vt in M, perpendicularis M H, pro linea æquinoctiali. </s>
            <s xml:id="echoid-s25556" xml:space="preserve">Deinde in M, conſtituatur angulus
              <lb/>
              <note position="left" xlink:label="note-0403-07" xlink:href="note-0403-07a" xml:space="preserve">40</note>
            E M L, inclinationis Meridiani proprii ipſius plani ad Meridianum Horizontis inuentæ per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s25557" xml:space="preserve">30. </s>
            <s xml:id="echoid-s25558" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25559" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25560" xml:space="preserve">verſus quidem ſiniſtrã, ſi planum à meridie in ortum, at dextrã verſus, ſi à meridie
              <lb/>
            in occaſum declinet. </s>
            <s xml:id="echoid-s25561" xml:space="preserve">Sumpto autem in recta M L, puncto L, vt libet, ducatur per illud ipſi E ε,
              <lb/>
            parallela L G, ſecans æquinoctialem lineam in G, quæ communis ſectio erit proprii Meridiani, & </s>
            <s xml:id="echoid-s25562" xml:space="preserve">
              <lb/>
            plani horologii, & </s>
            <s xml:id="echoid-s25563" xml:space="preserve">ipſa L G, longitudo gnomonis. </s>
            <s xml:id="echoid-s25564" xml:space="preserve">Deſcripto autem circulo ex L, diuiſoq́ue in
              <lb/>
            partes 24. </s>
            <s xml:id="echoid-s25565" xml:space="preserve">æquales, initio ſumpto à recta M L, ſi ex punctis diuiſionum per L, rectæ ducantur, ſe-
              <lb/>
            cabitur æquinoctialis linea in punctis, per quæ ducendæ ſunt lineæ horariæ ad æquinoctialem li-
              <lb/>
            neam perpendiculares, & </s>
            <s xml:id="echoid-s25566" xml:space="preserve">inter ſe parallelæ, vt prius. </s>
            <s xml:id="echoid-s25567" xml:space="preserve">Nam hac ratione deſcriptum erit huiuſmo-
              <lb/>
            di horologium non aliter, atque in præcedenti deſcriptione, quando prius linea ſtyli G N, duce-
              <lb/>
            batur: </s>
            <s xml:id="echoid-s25568" xml:space="preserve">quia angulus N L O, æqualis eſt angulo E M L, inclinationis Meridianorum, externus in-
              <lb/>
              <note position="right" xlink:label="note-0403-08" xlink:href="note-0403-08a" xml:space="preserve">29. primi.</note>
            terno. </s>
            <s xml:id="echoid-s25569" xml:space="preserve">Horologium igitur Aſtronomicum, & </s>
            <s xml:id="echoid-s25570" xml:space="preserve">à Verticali declinans, & </s>
            <s xml:id="echoid-s25571" xml:space="preserve">ad Horizontem inclinatũ
              <lb/>
              <note position="left" xlink:label="note-0403-09" xlink:href="note-0403-09a" xml:space="preserve">50</note>
            conſtruximus, &</s>
            <s xml:id="echoid-s25572" xml:space="preserve">c. </s>
            <s xml:id="echoid-s25573" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s25574" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1299" type="section" level="1" n="317">
          <head xml:id="echoid-head328" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s25575" xml:space="preserve">TOTAM hanc deſcriptionem horologij à Verticali declinantis, & </s>
            <s xml:id="echoid-s25576" xml:space="preserve">ſimul ad Horizontem inclinati
              <lb/>
            ſex figuris abſoluimus, vt omnis varietas in huiuſmodi horologijs patefieret: </s>
            <s xml:id="echoid-s25577" xml:space="preserve">quarum priores tres ad ea
              <lb/>
            borologia ſuperiorapertinent, quæ auſtrum reſpiciunt, in quibus centrum horologij uel eſt infra æquinoctia
              <lb/>
            lem lineam, vel ſupra eandem, uel certe omnes lineæ horariæ ſunt parallelæ ſecantes lineam æquinoctia-
              <lb/>
            lem ad angulos rectos, horologium{q́ue} centro caret; </s>
            <s xml:id="echoid-s25578" xml:space="preserve">poſteriores uerò tres referunt ea horologia ſuperiora,
              <lb/>
            quæ ad boreã ſpectant, in quibus linea horæ 12. </s>
            <s xml:id="echoid-s25579" xml:space="preserve">vel meridiana æquinoctialẽ lineam ſecat, uel infra </s>
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