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="146" file="0166" n="166" rhead="GNOMONICES"/>
            guli I E K, angulos{q́ue} contineant ęquales, erunt & </s>
            <s xml:id="echoid-s9405" xml:space="preserve">baſes E F, E K, æquales, & </s>
            <s xml:id="echoid-s9406" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s9407" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">trinque à meri-
            <lb/>
          die æquali tem
            <lb/>
          poris @patio di-
            <lb/>
          ſtant es in horo
            <lb/>
          logio hori@on-
            <lb/>
          tali, ſunt aqua-
            <lb/>
          lia.</note>
          <p style="it">
            <s xml:id="echoid-s9408" xml:space="preserve">POSTREMO ſequitur, ſatis eſſe ad deſcriptionem horologij Aſtronomici horizontalis, ſi vnus
              <lb/>
            quadrans circuli ex E, deſcripti, qualis eſt v.</s>
            <s xml:id="echoid-s9409" xml:space="preserve">g. </s>
            <s xml:id="echoid-s9410" xml:space="preserve">quadrans Mg, in ſex partes æquales diſtribuatur. </s>
            <s xml:id="echoid-s9411" xml:space="preserve">Nam du
              <lb/>
              <figure xlink:label="fig-0166-01" xlink:href="fig-0166-01a" number="122">
                <image file="0166-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0166-01"/>
              </figure>
              <note position="left" xlink:label="note-0166-02" xlink:href="note-0166-02a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0166-03" xlink:href="note-0166-03a" xml:space="preserve">20</note>
            ctis rectis occultis per puncta diuiſionum, & </s>
            <s xml:id="echoid-s9412" xml:space="preserve">centrum E, ſecantibus rectam F I, in punctis, per quę hora-
              <lb/>
              <note position="left" xlink:label="note-0166-04" xlink:href="note-0166-04a" xml:space="preserve">Satis eſt ad de-
                <lb/>
              ſoriptionẽ horo
                <lb/>
              logij horizonta
                <lb/>
              lis Aſtronomi-
                <lb/>
              ci, ſi unus dun-
                <lb/>
              taxat quadrans
                <lb/>
              circuli ex E, de-
                <lb/>
              ſcripti ſecetur
                <lb/>
              in 6. partes æ-
                <lb/>
              quales.</note>
            riæ lineæ ſunt ducendæ ex H; </s>
            <s xml:id="echoid-s9413" xml:space="preserve">ſi hæc puncta ex I, transferantur ad alteram partem lineę ęquinoctialis,
              <lb/>
              <note position="left" xlink:label="note-0166-05" xlink:href="note-0166-05a" xml:space="preserve">30</note>
            verſus K, habebuntur alia puncta, per quæ horariæ lineę ducendæ ſunt: </s>
            <s xml:id="echoid-s9414" xml:space="preserve">quandoquidem ſingula ſpatia ho-
              <lb/>
            raria in recta I F, æqualia ſunt ſingulis ſpatijs horarijs in recta I K, vt demonſtratum est. </s>
            <s xml:id="echoid-s9415" xml:space="preserve">Rurſus ductis
              <lb/>
            lineis horarijs ex H, per puncta rectæ I F, vel I K, vt reliquę altera ex parte accuratius ducãtur, tranſ-
              <lb/>
            ferenda erunt puncta circumferentiæ circuli ex H, deſcripti ex puncto, vbi linea meridiana, & </s>
            <s xml:id="echoid-s9416" xml:space="preserve">dicta cir-
              <lb/>
            cumferentia ſe mutuo interſecant, in partem alteram eiuſdem circumferentię. </s>
            <s xml:id="echoid-s9417" xml:space="preserve">Nam per hęctranſire de-
              <lb/>
            bent omnino horariæ lineę ex H, per puncta rectæ F K, eductę, cum arcus dicti circuli ex vna parte ęqua
              <lb/>
            les ſint ar cubus eiuſdem ex altera parte, vt oſtenſum eſt.</s>
            <s xml:id="echoid-s9418" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9419" xml:space="preserve">QVOD ſi axis H D, in triangulo D H I, ad planum horologij recto, intelligatur eſſe filum exten-
              <lb/>
              <note position="left" xlink:label="note-0166-06" xlink:href="note-0166-06a" xml:space="preserve">Quomodo ho-
                <lb/>
              rologiũ hotizõ
                <lb/>
              tale una cũ axe
                <lb/>
              mundi collocã
                <lb/>
              dum ſit, ut ho-
                <lb/>
              ras monſtret à
                <lb/>
              mer. vel med.
                <lb/>
              noc.</note>
            tum, vel etiam ferrum aliquod tenue, faciens in H, cum linea meridiana angulum æqualẽ angulo D H I,
              <lb/>
            & </s>
            <s xml:id="echoid-s9420" xml:space="preserve">cum recta C L, angulos rectos, vel certè ipſum triangulum D H I, conſtruatur ex materia aliqua ſoli-
              <lb/>
              <note position="left" xlink:label="note-0166-07" xlink:href="note-0166-07a" xml:space="preserve">40</note>
            da, statuaturq́, rectum ad planum horologij, indicabit vmbra axis D I, ſingulas horas à meridie, vel me-
              <lb/>
            dia nocte, ſi horologium in plano, quòd Horizonti æquidiſtet, ita statuatur, vt recta H I, lineam meridia-
              <lb/>
            nam (cuius inuentionem in plano, quod æquidiſtet Horizonti, tradidimus & </s>
            <s xml:id="echoid-s9421" xml:space="preserve">in commentarijs in ſphæram,
              <lb/>
            cum de Meridiano circulo ageremus, & </s>
            <s xml:id="echoid-s9422" xml:space="preserve">in ſcholio propoſ. </s>
            <s xml:id="echoid-s9423" xml:space="preserve">23. </s>
            <s xml:id="echoid-s9424" xml:space="preserve">ſuperioris lib.) </s>
            <s xml:id="echoid-s9425" xml:space="preserve">referat, punctum{q́ue} H, ad
              <lb/>
            auſtrum, at que I, ad boream vergat. </s>
            <s xml:id="echoid-s9426" xml:space="preserve">Cum enim omnes circuli horarum à meridie, vel media nocte ducan-
              <lb/>
            tur per axem mundi, fit vt radius Solis in quocunque illorum exiſtentis non recedat ab axe, & </s>
            <s xml:id="echoid-s9427" xml:space="preserve">communi
              <lb/>
            ſectione illius, ac plani horologij, cum & </s>
            <s xml:id="echoid-s9428" xml:space="preserve">axis, & </s>
            <s xml:id="echoid-s9429" xml:space="preserve">communis hęc ſectio, nempe linea eius horaria, in eodem
              <lb/>
              <note position="left" xlink:label="note-0166-08" xlink:href="note-0166-08a" xml:space="preserve">Si ſtylus D G,
                <lb/>
              in G, rectus ſit
                <lb/>
              ad planum ho-
                <lb/>
              rologit, indica-
                <lb/>
              bit umbra ſo-
                <lb/>
              lius uerticis D,
                <lb/>
              horas à mer. uel
                <lb/>
              med. noc.</note>
            circulo horario existant. </s>
            <s xml:id="echoid-s9430" xml:space="preserve">Quare vmbra axis in lineam horariam illius circuli proijcietur. </s>
            <s xml:id="echoid-s9431" xml:space="preserve">& </s>
            <s xml:id="echoid-s9432" xml:space="preserve">ſic de cęte-
              <lb/>
            ris. </s>
            <s xml:id="echoid-s9433" xml:space="preserve">Hinc fit, vt & </s>
            <s xml:id="echoid-s9434" xml:space="preserve">vmbra verticis D, ſtyli D G, recti ad planum horologij in puncto G, hoc eſt, vmbra cen
              <lb/>
            tri mundi (eſt enim vertex ſtyli idem, quod centrum mundi, per propoſ. </s>
            <s xml:id="echoid-s9435" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9436" xml:space="preserve">libri ſuperioris) in eaſdem li-
              <lb/>
              <note position="left" xlink:label="note-0166-09" xlink:href="note-0166-09a" xml:space="preserve">50</note>
            neas horarias proijciatur, quia & </s>
            <s xml:id="echoid-s9437" xml:space="preserve">vertex D, in axe exiſtit, cuius quidem omnium punctorum vmbrę in li-
              <lb/>
            neas horarias cadunt, vt dictum eſt: </s>
            <s xml:id="echoid-s9438" xml:space="preserve">quod etiam propoſ. </s>
            <s xml:id="echoid-s9439" xml:space="preserve">11. </s>
            <s xml:id="echoid-s9440" xml:space="preserve">pręcedentis lib. </s>
            <s xml:id="echoid-s9441" xml:space="preserve">demonſtrauimus. </s>
            <s xml:id="echoid-s9442" xml:space="preserve">Itaque vſus
              <lb/>
              <note position="left" xlink:label="note-0166-10" xlink:href="note-0166-10a" xml:space="preserve">Vſus horologij
                <lb/>
              Aſtronomici.</note>
            borologij Aſtronomici eſt, vt ex vmbra ſtyli in eius lineas horarias cadente intelligamus, quot horę tran-
              <lb/>
            ſactæ ſint à meridie, vel media nocte proxima, & </s>
            <s xml:id="echoid-s9443" xml:space="preserve">quot ſuperſint ad ſequentem meridiem, vel mediam no-
              <lb/>
            ctem. </s>
            <s xml:id="echoid-s9444" xml:space="preserve">Matutino enim tempore, ſi vmbra cadat v.</s>
            <s xml:id="echoid-s9445" xml:space="preserve">g. </s>
            <s xml:id="echoid-s9446" xml:space="preserve">in lineam horæ 7. </s>
            <s xml:id="echoid-s9447" xml:space="preserve">pro comperto habebimus, elapſas
              <lb/>
            eſſeſeptem horas à med. </s>
            <s xml:id="echoid-s9448" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s9449" xml:space="preserve">& </s>
            <s xml:id="echoid-s9450" xml:space="preserve">ſupcreſſe quinque vſque ad proximum meridiem, & </s>
            <s xml:id="echoid-s9451" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9452" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9453" xml:space="preserve">IAM verò ſi & </s>
            <s xml:id="echoid-s9454" xml:space="preserve">dimidiatas horas, & </s>
            <s xml:id="echoid-s9455" xml:space="preserve">earum quartas partes, immo & </s>
            <s xml:id="echoid-s9456" xml:space="preserve">octauas, vel quaſuis alias in
              <lb/>
              <note position="left" xlink:label="note-0166-11" xlink:href="note-0166-11a" xml:space="preserve">Qua ratione di
                <lb/>
              midia@æ horæ,
                <lb/>
              & earum quar-
                <lb/>
              tæ pattes, vel
                <lb/>
              quæcunque alię
                <lb/>
              in horologio de
                <lb/>
              ſeribantur.</note>
            horologio deſcribere placuerit, diuidendę erunt ſingulæ partes circuli ex E, deſcripti in dictas partes, vt
              <lb/>
            in duas, quatuor, octo, & </s>
            <s xml:id="echoid-s9457" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9458" xml:space="preserve">reliqua autem peragenda, vt prius. </s>
            <s xml:id="echoid-s9459" xml:space="preserve">Quod etiam, in alijs horologijs, quę ſequu@
              <lb/>
            tur, obſeruandum erit.</s>
            <s xml:id="echoid-s9460" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9461" xml:space="preserve">HIC autem, & </s>
            <s xml:id="echoid-s9462" xml:space="preserve">in ſequentibus omnibus, magnopere obſeruandum eſt, lineam quamcunque in </s>
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