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

Table of figures

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          <p style="it">
            <s xml:id="echoid-s1372" xml:space="preserve">
              <pb o="19" file="0039" n="39" rhead="LIBER PRIMVS."/>
            A B C D, pro Horizonte ſumatur, recta a d, in Horizonte communis ſectio ſit ipſius, & </s>
            <s xml:id="echoid-s1373" xml:space="preserve">paralleli Solis;
              <lb/>
            </s>
            <s xml:id="echoid-s1374" xml:space="preserve">adeo, vt ſol in d, oriatur, vel occidat, ſi Horizon propriam poſitionem habeat, it a vt B D, ſit linea Meri-
              <lb/>
            diana, hoc eſt, communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s1375" xml:space="preserve">Meridiani; </s>
            <s xml:id="echoid-s1376" xml:space="preserve">& </s>
            <s xml:id="echoid-s1377" xml:space="preserve">A C, communis ſectio Horizontis & </s>
            <s xml:id="echoid-s1378" xml:space="preserve">ver-
              <lb/>
            ticalis, at que adeò & </s>
            <s xml:id="echoid-s1379" xml:space="preserve">Acquatoris; </s>
            <s xml:id="echoid-s1380" xml:space="preserve">ita vt Sol in Aequatore exiſtens oriatur, vel occidat in A. </s>
            <s xml:id="echoid-s1381" xml:space="preserve">Quare
              <lb/>
            arcus d A, Horizontis inter d, ortũ, occaſumve paralleli Solis, & </s>
            <s xml:id="echoid-s1382" xml:space="preserve">A, ortum occaſumve Aequatoris,
              <lb/>
            latitudo ortiua erit, vel occidua, Sole parallelũ diametri M θ, deſcribente. </s>
            <s xml:id="echoid-s1383" xml:space="preserve">Eadem{q́ue} ratio de cæteris
              <lb/>
            habenda eſt. </s>
            <s xml:id="echoid-s1384" xml:space="preserve">Erit autem ſemper a d, in Analemmate æqualis rectæ a d, vel a e, in parallelo M d θ e, pro-
              <lb/>
            pterea quòd vtraque communis ſectio eſt Horizontis, & </s>
            <s xml:id="echoid-s1385" xml:space="preserve">paralleli, excurrens ex a, vſque ad ſuperficiem
              <lb/>
            Sphæræ, in qua ſibi mutuo congruunt, ſi & </s>
            <s xml:id="echoid-s1386" xml:space="preserve">Horizon, & </s>
            <s xml:id="echoid-s1387" xml:space="preserve">parallelus in propria poſitione concipiatur.</s>
            <s xml:id="echoid-s1388" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
        </div>
        <div xml:id="echoid-div66" type="section" level="1" n="19">
          <head xml:id="echoid-head22" xml:space="preserve">THEOREMA PRIMVM.
            <lb/>
          PROPOSITIO SECVNDA.</head>
          <p>
            <s xml:id="echoid-s1389" xml:space="preserve">IN quolibet horologio vertex ſtyli idem cenſeri debet, quod
              <lb/>
              <note position="right" xlink:label="note-0039-02" xlink:href="note-0039-02a" xml:space="preserve">Vert ex ſtyli cu
                <lb/>
              iusuis horologii
                <lb/>
              centrum mũdi
                <lb/>
              eſt, planum au-
                <lb/>
              tem horologij
                <lb/>
              extra centum
                <lb/>
              mundi exiſti@.</note>
            centrum mundi: </s>
            <s xml:id="echoid-s1390" xml:space="preserve">planum verò ipſius horologij tantum à
              <lb/>
            centro mundi abeſſe intelligendum eſt, quanta eſt ſtyli lon-
              <lb/>
              <note position="left" xlink:label="note-0039-03" xlink:href="note-0039-03a" xml:space="preserve">10</note>
            gitudo, æquidiſtareq; </s>
            <s xml:id="echoid-s1391" xml:space="preserve">circulo maximo, ad cuius planum
              <lb/>
            ſtylus rectus eſt, & </s>
            <s xml:id="echoid-s1392" xml:space="preserve">à quo nomen habet horologium.</s>
            <s xml:id="echoid-s1393" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1394" xml:space="preserve">SIT ſtylus horologij cuiuſpiam A B, inſiſtens ad angulos rectos plano horologij, quod per
              <lb/>
            rectam C D, duci intelligitur. </s>
            <s xml:id="echoid-s1395" xml:space="preserve">Quoniam igitur tota terra cum Sphæra Solis comparata eſt inſtar
              <lb/>
            puncti, ac centri, vt in commentarijs in Sphæram ex Ptolemæo, alijsq́ Aſtronomis oſtendimus,
              <lb/>
            nihil differet centrum mundi à puncto A, vertice
              <lb/>
              <figure xlink:label="fig-0039-01" xlink:href="fig-0039-01a" number="17">
                <image file="0039-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0039-01"/>
              </figure>
            gnomonis, ſeu ſtyli, quandoquidem à vertice A,
              <lb/>
            ad centrum terræ, quod idem eſt, quod centrum
              <lb/>
            mundi, vt in iiſdem commentarijs docuimus, nõ
              <lb/>
              <note position="left" xlink:label="note-0039-04" xlink:href="note-0039-04a" xml:space="preserve">30</note>
            eſt diſtantia notabilis, ſi ea conferatur cum diſtan-
              <lb/>
            tia, quam habet Sol ab eodem vertice; </s>
            <s xml:id="echoid-s1396" xml:space="preserve">atque adeo
              <lb/>
            circulus per verticem A, ductus, planoq́; </s>
            <s xml:id="echoid-s1397" xml:space="preserve">horolo-
              <lb/>
            gii per C D, ducto æquidiſtans pro circulo maxi-
              <lb/>
            mo ſumi non immerito poterit. </s>
            <s xml:id="echoid-s1398" xml:space="preserve">Quare iure op
              <lb/>
            timo ii, qui de horologiorum deſcriptione agunt,
              <lb/>
            vt rationem umbrarum, quas Sol quouis momen
              <lb/>
            to temporis efficit, demonſtrare poſſint, concipiũt
              <lb/>
            verticem ſtyli in centro mundi ſtatui, ad quod om
              <lb/>
            nes radii Solis incidentes proiiciunt per gnomo-
              <lb/>
              <note position="left" xlink:label="note-0039-05" xlink:href="note-0039-05a" xml:space="preserve">40</note>
            nis verticem vmbram in planum horologii; </s>
            <s xml:id="echoid-s1399" xml:space="preserve">vt fi-
              <lb/>
            gura demonſtrat, in qua vmbra eſt B G, in horolo-
              <lb/>
            gii plano, Sole habente altitudinem E H, ſupra cir
              <lb/>
            culum maximum EF, cui planum C D, in quod vmbra cadit, æquidiſtat, Cum enim H A G, ra-
              <lb/>
            dius Solis in puncto H, exiſtentis perueniat ad punctum G, & </s>
            <s xml:id="echoid-s1400" xml:space="preserve">ſtylus ſit opacus, erit totum trian-
              <lb/>
            gulum A B G, vmbroſum, quòd in eius aream radij Solis non cadant; </s>
            <s xml:id="echoid-s1401" xml:space="preserve">atque adeo B G, longitudo
              <lb/>
            erit vmbræ in plano horologij, reliquæ verò omnes partes, vt G D, & </s>
            <s xml:id="echoid-s1402" xml:space="preserve">B C, à Sole illuſtrabuntur.
              <lb/>
            </s>
            <s xml:id="echoid-s1403" xml:space="preserve">Eodem modo longitudinem vmbræ quolibet tempore inueſtigare poterimus, ſi altitudinem So-
              <lb/>
            lis ſupra circulum maximũ, qui plano horologij æquidiſtet, cognouerimus, vt ſuo loco dicemus. </s>
            <s xml:id="echoid-s1404" xml:space="preserve">
              <lb/>
            Ex his manifeſtum eſt, planum horologij per rectam C D, ductum tantum abeſſe à centro mun-
              <lb/>
              <note position="left" xlink:label="note-0039-06" xlink:href="note-0039-06a" xml:space="preserve">50</note>
            di, quanta eſt longitudo gnomonis A B, quandoquidem vertex A, in cẽtro collocatur, vt diximus.
              <lb/>
            </s>
            <s xml:id="echoid-s1405" xml:space="preserve">Quod ſi per rectam E A F, circulus maximus intelligatur duci, ad quem Gnomon A B, rectus ſit,
              <lb/>
            æquidiſtans erit planum horologij huic circulo; </s>
            <s xml:id="echoid-s1406" xml:space="preserve">cum gnomon A B, & </s>
            <s xml:id="echoid-s1407" xml:space="preserve">ad planum circuli per re-
              <lb/>
              <note position="right" xlink:label="note-0039-07" xlink:href="note-0039-07a" xml:space="preserve">14. undec.</note>
            ctam E F, & </s>
            <s xml:id="echoid-s1408" xml:space="preserve">ad planum horologij per rectam C D, ductum rectus ponatur.</s>
            <s xml:id="echoid-s1409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1410" xml:space="preserve">HABET autem horologium nomen à circulo diametri E F, cui æquidiſtat. </s>
            <s xml:id="echoid-s1411" xml:space="preserve">Nam ſi circu-
              <lb/>
              <note position="right" xlink:label="note-0039-08" xlink:href="note-0039-08a" xml:space="preserve">Horologium
                <lb/>
              quodcunq; no-
                <lb/>
              men accipit à
                <lb/>
              circulo maxi-
                <lb/>
              mo, cui ęquidi-
                <lb/>
              ſtat.</note>
            lus ille fuerit Horizon, horologium dicitur Horizontale. </s>
            <s xml:id="echoid-s1412" xml:space="preserve">Si Verticalis, Verticale: </s>
            <s xml:id="echoid-s1413" xml:space="preserve">ſi Meridianus,
              <lb/>
            Meridianum: </s>
            <s xml:id="echoid-s1414" xml:space="preserve">Si Aequinoctialis, Aequinoctiale: </s>
            <s xml:id="echoid-s1415" xml:space="preserve">& </s>
            <s xml:id="echoid-s1416" xml:space="preserve">ſic de reliquis, vt ſupra diximus, cum varia ho-
              <lb/>
            rologiorũ genera explicaremus. </s>
            <s xml:id="echoid-s1417" xml:space="preserve">Tot enim horologia fieri poſſunt, quot circuli maximi in Sphæ-
              <lb/>
            ra per centrum mundi poſſunt duci, cũ ſingulis plana parallela poſſint duci ad interuallum lon-
              <lb/>
            gitudinis ſtyli, in quibus horologia deſcribantur, vt perſpicuum eſt. </s>
            <s xml:id="echoid-s1418" xml:space="preserve">In quolibet ergo horologio
              <lb/>
            vertex ſtyli, &</s>
            <s xml:id="echoid-s1419" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1420" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s1421" xml:space="preserve"/>
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