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-s20420" xml:space="preserve">
              <pb o="303" file="0319" n="319" rhead="LIBER TERTIVS."/>
            rallelum in arc{us} ſimiles, quòd illi circuli per horum polos non ducantur: </s>
            <s xml:id="echoid-s20421" xml:space="preserve">eadem{q́ue} ratio eſt de quocun-
              <lb/>
            que Verticali declinante, & </s>
            <s xml:id="echoid-s20422" xml:space="preserve">circulo, qui ei ęquidiſtet. </s>
            <s xml:id="echoid-s20423" xml:space="preserve">Quę cum ita ſint, non videntur æquales poſſe eſſe
              <lb/>
            duo illi anguli à dictis ſectionib{us} conſtituti; </s>
            <s xml:id="echoid-s20424" xml:space="preserve">quandoquidem, vt oſtendim{us}, non auferunt arcus ſimiles
              <lb/>
            ex circulo maximo, cui horologium æquidistat, & </s>
            <s xml:id="echoid-s20425" xml:space="preserve">ex ei{us} parallelo, quem in ſphæra planum horolo-
              <lb/>
            gii efficit.</s>
            <s xml:id="echoid-s20426" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20427" xml:space="preserve">HAEC ſunt, quę anxium reddere poſſent Lectoris animum: </s>
            <s xml:id="echoid-s20428" xml:space="preserve">Vnde clarius rem iſtã explanare opor-
              <lb/>
            tebit. </s>
            <s xml:id="echoid-s20429" xml:space="preserve">Libet autem hoc loco dubitationem hanc diſſoluere, (et ſi ſcio illam apud exercitatos in elementis
              <lb/>
            ſphæricis locum non habere) quia ex ea multæ aliæ ſimiles dubitationes poterunt explicari, vt ex iis, quę
              <lb/>
              <note position="right" xlink:label="note-0319-01" xlink:href="note-0319-01a" xml:space="preserve">Solutio dubi-
                <lb/>
              tationis ſupe-
                <lb/>
              rioris.</note>
            ſequuntur, fiet perſpicuum. </s>
            <s xml:id="echoid-s20430" xml:space="preserve">Dico ergo rectè à nobis eſſe demonſtratum, angulos illos æquales eſſe: </s>
            <s xml:id="echoid-s20431" xml:space="preserve">neque
              <lb/>
            verò obſtat, quòd illi arcus ſimiles non ſint; </s>
            <s xml:id="echoid-s20432" xml:space="preserve">quoniam enim axis mundi non cadit in centrum circuli, quẽ
              <lb/>
              <note position="left" xlink:label="note-0319-02" xlink:href="note-0319-02a" xml:space="preserve">10</note>
            planum horologii in ſphæra efficit, propterea quòd axis eius proprius, per propoſ. </s>
            <s xml:id="echoid-s20433" xml:space="preserve">10. </s>
            <s xml:id="echoid-s20434" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20435" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20436" xml:space="preserve">Theodoſii, in
              <lb/>
            ipſius centrum cadat, non erit punctum C, in quod cadit axis mundi, centrum illius circuli: </s>
            <s xml:id="echoid-s20437" xml:space="preserve">ac proinde fie-
              <lb/>
            ri non poteſt, vt lineæ rectæ angulum in plano horologii efficientes in C, auferant ex eo circulo arcum ſi-
              <lb/>
            milem ei, quem abſcindunt lineæ rectæ angulum æqualem comprehendentes ex circulo maximo, cui ille
              <lb/>
            æquidiſtat. </s>
            <s xml:id="echoid-s20438" xml:space="preserve">Soli enim anguli æquales ad centra circulorum, vel ad circumferentias conſtituti inſiſtunt
              <lb/>
            arcubus ſimilibus, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s20439" xml:space="preserve">33. </s>
            <s xml:id="echoid-s20440" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20441" xml:space="preserve">6. </s>
            <s xml:id="echoid-s20442" xml:space="preserve">Euclidis, demonſtr auimus: </s>
            <s xml:id="echoid-s20443" xml:space="preserve">quales non ſunt duo prædi-
              <lb/>
            cti anguli. </s>
            <s xml:id="echoid-s20444" xml:space="preserve">Nam ille in circulo maximo, cui horologium æquidiſtat, conſtituitur in eius centro, put a in cen
              <lb/>
            tro mundi, alter verò in circulo, qui illi par allelus est, extra centrum, nempe in puncto C, quod oſtendi-
              <lb/>
            m{us} iam centrum illius non eſſe. </s>
            <s xml:id="echoid-s20445" xml:space="preserve">V erum tamen eſt, ſi ex C, in plano horologii circulus deſcribatur, arcum
              <lb/>
            quem dictus angul{us} D C P, abſcindit, qualis in noſtro exemplo eſt arcus D P, ſimilem fore arcui, quẽ
              <lb/>
              <note position="left" xlink:label="note-0319-03" xlink:href="note-0319-03a" xml:space="preserve">20</note>
            æqualis angulus ex circulo maximo, cui horologium æquidiſtat, in centro eius conſtitutus aufert: </s>
            <s xml:id="echoid-s20446" xml:space="preserve">ſed ille
              <lb/>
            circulus parallelo, quem planum horologii facit in ſphæra, concentricus non eſt, vt oſtendimus. </s>
            <s xml:id="echoid-s20447" xml:space="preserve">Non ergo
              <lb/>
            locum habet dubitatio propoſita hoc loco.</s>
            <s xml:id="echoid-s20448" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quomodo ho-
            <lb/>
          rologium decli
            <lb/>
          nans à Vertica
            <lb/>
          li collocandum
            <lb/>
          ſit, vt horas mõ
            <lb/>
          ſtret.</note>
          <p style="it">
            <s xml:id="echoid-s20449" xml:space="preserve">IAM verò ſi horologium declinans hactenus delineatum ita collocetur in plano declinante, vt li-
              <lb/>
            nea meridiana, ſeu horæ 12. </s>
            <s xml:id="echoid-s20450" xml:space="preserve">C D, ad Horizontem perpendicularis ſit, & </s>
            <s xml:id="echoid-s20451" xml:space="preserve">recta A B, illam ad angulos
              <lb/>
            rectos ſecans Horizonti æquidiſtet, & </s>
            <s xml:id="echoid-s20452" xml:space="preserve">præterea punctum C, in iis, quæ à meridie declinant, ſurſum, & </s>
            <s xml:id="echoid-s20453" xml:space="preserve">
              <lb/>
            punctum D, deorſum verſus statuatur; </s>
            <s xml:id="echoid-s20454" xml:space="preserve">in illis verò, quæ deflectunt à borea, punctum C, deorſum, & </s>
            <s xml:id="echoid-s20455" xml:space="preserve">D,
              <lb/>
            ſurſum verſus ponatur; </s>
            <s xml:id="echoid-s20456" xml:space="preserve">nec non in puncto K, ad angulos rectos infigatur ſtylus I K, vel triangulũ C I G,
              <lb/>
            rectum ſtatuatur ad planum horologij, indicabit extremum vmbræ à vertice ſtyli proiectæ, veltota vm-
              <lb/>
            bra totius axis C I, horas à meridie, vel media nocte, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s20457" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20458" xml:space="preserve">ſuperioris libri oſtendim{us}.</s>
            <s xml:id="echoid-s20459" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p style="it">
            <s xml:id="echoid-s20460" xml:space="preserve">QVOD ſi in ipſo muro declinante horologium deſcribendum ſit, non autem in quopiam alio plano,
              <lb/>
              <note position="right" xlink:label="note-0319-06" xlink:href="note-0319-06a" xml:space="preserve">Quomodo in
                <lb/>
              plano ſtabili,
                <lb/>
              quod à Vertica
                <lb/>
              li declinet, ho-
                <lb/>
              rologium Aſtro
                <lb/>
              nomicum de-
                <lb/>
              ſcribendũ ſit.</note>
            ex quo in murum transferatur, vt hactenus fecim{us}; </s>
            <s xml:id="echoid-s20461" xml:space="preserve">ducenda erit in muro recta C D, officio perpendicu-
              <lb/>
            li ad Horizontem perpendicularis, & </s>
            <s xml:id="echoid-s20462" xml:space="preserve">ad hanc in eodem muro perpendicularis ducenda A B, quæ Hori-
              <lb/>
            zonti æquidiſtabit: </s>
            <s xml:id="echoid-s20463" xml:space="preserve">Vel ſi mauis, per libellam, & </s>
            <s xml:id="echoid-s20464" xml:space="preserve">perpendiculum ducenda erit recta A B, Horizonti
              <lb/>
            æquidiſtans, & </s>
            <s xml:id="echoid-s20465" xml:space="preserve">ad hanc excitanda perpendicularis C D, quæ ad Horizontem perpendicularis erit. </s>
            <s xml:id="echoid-s20466" xml:space="preserve">Cæte-
              <lb/>
            ra autem conſtruenda, vt in prima deſcriptione horologij declinantis; </s>
            <s xml:id="echoid-s20467" xml:space="preserve">Nimirum ducenda linea declina-
              <lb/>
            tionis E F, & </s>
            <s xml:id="echoid-s20468" xml:space="preserve">ad A B, perpendicularis F G, & </s>
            <s xml:id="echoid-s20469" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20470" xml:space="preserve">Si autem alijs duob{us} modis vti malueris, ducenda
              <lb/>
            quoque erit ante omnia recta C D, ad Horizontem perpendicularis. </s>
            <s xml:id="echoid-s20471" xml:space="preserve">Deinde ducenda recta C P, ita vt
              <lb/>
            C D, C P, intercipiant arcum D P, vt in tertio modo dixim{us}, ea tamen lege, vt attentè conſideretur,
              <lb/>
            verſus quam partem arcas D P, per propoſ. </s>
            <s xml:id="echoid-s20472" xml:space="preserve">30. </s>
            <s xml:id="echoid-s20473" xml:space="preserve">primi libri repert{us} numerari debeat, quemadmodum
              <lb/>
              <note position="left" xlink:label="note-0319-07" xlink:href="note-0319-07a" xml:space="preserve">40</note>
            in tertio modo præſcripſimus. </s>
            <s xml:id="echoid-s20474" xml:space="preserve">Reliqua omnino conficienda, vt pri{us}: </s>
            <s xml:id="echoid-s20475" xml:space="preserve">hoc eſt, ducenda æquinoctialis linea
              <lb/>
            G H, perpendicularis ad C P, & </s>
            <s xml:id="echoid-s20476" xml:space="preserve">c.</s>
            <s xml:id="echoid-s20477" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Qua ratione li
            <lb/>
          neæ horarię du
            <lb/>
          ci poſſint ſecũ-
            <lb/>
          dum Andream
            <lb/>
          Schonerum,
            <lb/>
          etiamſi earum
            <lb/>
          puncta in æqui
            <lb/>
          noctiali inuen-
            <lb/>
          ta non ſint.</note>
          <p style="it">
            <s xml:id="echoid-s20478" xml:space="preserve">QVONIAM verò aliquando contingit, vt aliquę lineæ horariæ aut nunquam, aut certè valde
              <lb/>
            procul æquinoctialem lineam ſecent, quod ideo cuenit, quòd interdum rectæ per centrum L, & </s>
            <s xml:id="echoid-s20479" xml:space="preserve">puncta di-
              <lb/>
            uiſionum circuli ex L, deſcripti emiſſę vel ſunt parallelę ipſi ęquinoctiali lineę, vel in punctis remotiſſi-
              <lb/>
            mis eam interſecant; </s>
            <s xml:id="echoid-s20480" xml:space="preserve">excogitauit Andre{as} Schoner{us} rationem ſanè ingenioſam, qua eædem lineæ hora-
              <lb/>
            riæ ex C, centro horologii duci poſſint, nulla habita ratione lineę æquinoctialis. </s>
            <s xml:id="echoid-s20481" xml:space="preserve">Id quod in horologio ho-
              <lb/>
            rizontali etiam fecit, & </s>
            <s xml:id="echoid-s20482" xml:space="preserve">in Verticali. </s>
            <s xml:id="echoid-s20483" xml:space="preserve">Hoc autem ſe modo ferè habet eius conſtructio. </s>
            <s xml:id="echoid-s20484" xml:space="preserve">Ex puncto E,
              <lb/>
            ad rect{as} β C, E F, perpendiculares ducantur E Y, E Q, ſit {q́ue} E Q, ipſi E Y, æqualis. </s>
            <s xml:id="echoid-s20485" xml:space="preserve">Ducta autem
              <lb/>
            recta Q F, quæ rectam A B, ſecet in R, ducatur per R, ad A B, perpendicularis R S, vel ipſi C D, pa-
              <lb/>
              <note position="left" xlink:label="note-0319-09" xlink:href="note-0319-09a" xml:space="preserve">50</note>
            rallela, ſecans lineam C α, horæ 6. </s>
            <s xml:id="echoid-s20486" xml:space="preserve">in S. </s>
            <s xml:id="echoid-s20487" xml:space="preserve">Rurſus per S, ad R S, ducta perpendiculari S T, vel parallela
              <lb/>
            ipſi A B, ſumpta{q́ue} S T, ipſi R S, æquali, ducatur per T, ad S T, perpendicularis, vel ipſi R S, paralle-
              <lb/>
            la. </s>
            <s xml:id="echoid-s20488" xml:space="preserve">Postremo ſi ex T, centro ſemicirculus deſcriptus in partes 12. </s>
            <s xml:id="echoid-s20489" xml:space="preserve">æquales diſtribuatur, initio facto à re-
              <lb/>
            cta T S, ſecabunt rectæ ex T, per puncta diuiſionum emiſſæ rectam R S, in punctis, per quæ rectæ ex C,
              <lb/>
            centro horologii egredientes dabunt horari{as} line{as}, vt pri{us}. </s>
            <s xml:id="echoid-s20490" xml:space="preserve">Quòd ſi hæc ratio deſcriptionis cum prio-
              <lb/>
            rib{us} coniungatur, accuratè admodum, exquiſite{q́ue} omnes lineæ horariæ deſcribentur. </s>
            <s xml:id="echoid-s20491" xml:space="preserve">Nam quæ in pun-
              <lb/>
            ctis remotis rectam R S, ſecant, eæ non longè à puncto G, ęquinoctialem lineam diuident, vt in hora 11.
              <lb/>
            </s>
            <s xml:id="echoid-s20492" xml:space="preserve">apparet: </s>
            <s xml:id="echoid-s20493" xml:space="preserve">Et quę ęgrè lineam ęquinoctialem ſecant, eę commodiſſimè rectam R S, interſecant, vt in ho-
              <lb/>
            ra 4. </s>
            <s xml:id="echoid-s20494" xml:space="preserve">perſpicuum eſt.</s>
            <s xml:id="echoid-s20495" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20496" xml:space="preserve">VERVM quia ad hanc deſcriptionem neceſſarium eſt, vt pri{us} ducatur linea horę 6.</s>
            <s xml:id="echoid-s20497" xml:space="preserve">1 ex C, centro
              <lb/>
            horologij per punctum α, rectæ A B. </s>
            <s xml:id="echoid-s20498" xml:space="preserve">in quod cadit recta F α, ad lineam declinationis E F, </s>
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