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 Notes

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            <s xml:id="echoid-s10232" xml:space="preserve">
              <pb o="159" file="0179" n="179" rhead="LIBER SECVNDVS."/>
            tio huiuſce rei facilis eſt exconicis elementis Apollonii Pergęi, ſi rectè cõcipiantur coni in Analem
              <lb/>
            mate huius propoſ. </s>
            <s xml:id="echoid-s10233" xml:space="preserve">Nam ſectiones conicæ ſemper magis dilatantur verſus baſes conorum, vt ex
              <lb/>
            dictis elementis conicis patet.</s>
            <s xml:id="echoid-s10234" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10235" xml:space="preserve">QVOD ſi in Analemmate ſumatur longior ſtylus D M, & </s>
            <s xml:id="echoid-s10236" xml:space="preserve">per M, parallela ipſi B C, agatur
              <lb/>
              <note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">Qua ratione ex
                <lb/>
              Analemmate
                <lb/>
              huius propoſ. in
                <lb/>
              horologio de
                <lb/>
              ſcribãtur arcus
                <lb/>
              ſignorũ ad ma-
                <lb/>
              iorem, vel m i-
                <lb/>
              norem longitu
                <lb/>
              dinem gnomo-
                <lb/>
              nis.</note>
            ſecans diametros oppoſitorum ſignorum, habebuntur diametri aliarum conicarum ſectionum,
              <lb/>
            circa quas eodem modo ſectiones ipſæ conicæ deſcribi poſſunt pro maiori horologio, in quo qui-
              <lb/>
            dem eædem lineę horariæ omnino manent: </s>
            <s xml:id="echoid-s10237" xml:space="preserve">ſed æquinoctialis linea tanto ſpatio diſtare debet in
              <lb/>
            linea meridiana à centro H, quanta eſt portio illius parallelæ per M, ductæ, intercepta inter pun-
              <lb/>
            ctum, vbi ab axe C D, ſecatur, & </s>
            <s xml:id="echoid-s10238" xml:space="preserve">punctum, in quo eandem ſecat radius, ſiue diameter Aequatoris
              <lb/>
            F D. </s>
            <s xml:id="echoid-s10239" xml:space="preserve">Eadem ratione, ſi ſumatur minor ſtylus D M, minus horologium deſcribetur. </s>
            <s xml:id="echoid-s10240" xml:space="preserve">Itaque portio
              <lb/>
              <note position="left" xlink:label="note-0179-02" xlink:href="note-0179-02a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0179-03" xlink:href="note-0179-03a" xml:space="preserve">Portio Analem
                <lb/>
              matis inſtrumẽ
                <lb/>
              tum eſt ad ho-
                <lb/>
              rologia cuiuſuis
                <lb/>
              magnitudinis
                <lb/>
              deſcribenda.</note>
            illa Analemmatis in propoſ. </s>
            <s xml:id="echoid-s10241" xml:space="preserve">præcedenti deſcripta, eſt veluti inſtrumentum quoddam ad deſcri-
              <lb/>
            benda horologia cuiuſcunque magnitudinis, quod ad ſtylum, centrum horologii, lineam æquino
              <lb/>
            ctialem, & </s>
            <s xml:id="echoid-s10242" xml:space="preserve">ad lineas horarias attinet; </s>
            <s xml:id="echoid-s10243" xml:space="preserve">cum in ea aſſumi poſſit ſtylus cuiuſuis magnitudinis. </s>
            <s xml:id="echoid-s10244" xml:space="preserve">Quod
              <lb/>
            vero ſpectat ad arcus ſignorum, recurrendum erit ad Analemma in principio huius propoſ. </s>
            <s xml:id="echoid-s10245" xml:space="preserve">de-
              <lb/>
            ſcriptum, ex quo in horologio quocunque arcus ſignornm deſcribentur, vt dictum eſt.</s>
            <s xml:id="echoid-s10246" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10247" xml:space="preserve">PARALLELI iidem, ſiue arcus ſignorum Zodiaci, hac etiam ratione in horologio deſcri-
              <lb/>
              <note position="right" xlink:label="note-0179-04" xlink:href="note-0179-04a" xml:space="preserve">Alia deſcriptio
                <lb/>
              arcuum ſigno-
                <lb/>
              rum Zodiaci in
                <lb/>
              horologio hori-
                <lb/>
              zontali.</note>
            bi poſſunt. </s>
            <s xml:id="echoid-s10248" xml:space="preserve">Circa rectam A λ, vtcunque ductam, quæ axem mundi referat, ex quolibet puncto D,
              <lb/>
            vt centro, ſemicircu
              <lb/>
            lus deſcribatur cuinſ
              <lb/>
              <figure xlink:label="fig-0179-01" xlink:href="fig-0179-01a" number="132">
                <image file="0179-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0179-01"/>
              </figure>
            cunque magnitudi-
              <lb/>
              <note position="left" xlink:label="note-0179-05" xlink:href="note-0179-05a" xml:space="preserve">20</note>
            nis; </s>
            <s xml:id="echoid-s10249" xml:space="preserve">ſitq́ D H, ex par
              <lb/>
            te ſiniſtra ipſius D,
              <lb/>
            æqualis aſſumpto axi
              <lb/>
            D H, in portione A-
              <lb/>
            nalemmatis præcedẽ
              <lb/>
            tis propoſ. </s>
            <s xml:id="echoid-s10250" xml:space="preserve">vel in triã
              <lb/>
            gulo H D I, ex quo in
              <lb/>
            ſcholio eiuſdem pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s10251" xml:space="preserve">horologium ſine
              <lb/>
            portione Analemma
              <lb/>
              <note position="left" xlink:label="note-0179-06" xlink:href="note-0179-06a" xml:space="preserve">30</note>
            tis deſcripſimus; </s>
            <s xml:id="echoid-s10252" xml:space="preserve">du-
              <lb/>
            ctaq́; </s>
            <s xml:id="echoid-s10253" xml:space="preserve">D C, perpendi
              <lb/>
            culariad axem D H,
              <lb/>
            ſumatur D I, æquino
              <lb/>
            ctiali lineę D I, eiuſ-
              <lb/>
            dem portionis Ana-
              <lb/>
            lemmatis, vel dicti
              <lb/>
            trianguli, ęqualis, du-
              <lb/>
            caturq́; </s>
            <s xml:id="echoid-s10254" xml:space="preserve">recta H I, ad
              <lb/>
            partes I, quantumlibet; </s>
            <s xml:id="echoid-s10255" xml:space="preserve">vel certè (ne in ducenda linea H I, error committatur, quòd punctum H,
              <lb/>
              <note position="left" xlink:label="note-0179-07" xlink:href="note-0179-07a" xml:space="preserve">40</note>
            fortaſſe nimis propinquum ſit puncto I) ex H, arcus deſcribatur ad partes D, in quo ſumatur A B,
              <lb/>
            verſus rectam D C, æqualis arcui altitudinis poli, & </s>
            <s xml:id="echoid-s10256" xml:space="preserve">per B, recta H B, educatur, ſecans D C, æqui-
              <lb/>
            noctialem in I. </s>
            <s xml:id="echoid-s10257" xml:space="preserve">Erit triangulum D H I, æquale prorſus triangulo D H I, prędictę portionis Ana-
              <lb/>
            lemmatis, vel triangulo horologij ſine portione Analemmatis deſcripti, & </s>
            <s xml:id="echoid-s10258" xml:space="preserve">H I, ęqualis lineę me-
              <lb/>
            ridianæ eiuſdem portionis Analemmatis, vel dicti horologij, vt ex conſtructione vtraque huius
              <lb/>
            trianguli in hac figura perſpicuum eſſe poteſt. </s>
            <s xml:id="echoid-s10259" xml:space="preserve">Ex priori enim conſtructione, ſunt duo latera D H,
              <lb/>
            D I, huius trianguli duobus lateribus D H, D I, illius ęqualia, angulosq́; </s>
            <s xml:id="echoid-s10260" xml:space="preserve">comprehendunt æqua-
              <lb/>
            les, vtpote rectos. </s>
            <s xml:id="echoid-s10261" xml:space="preserve">Igitur tota triangula ęqualia erunt. </s>
            <s xml:id="echoid-s10262" xml:space="preserve">Ex conſtructione autem poſteriori, ſunt duo
              <lb/>
              <note position="right" xlink:label="note-0179-08" xlink:href="note-0179-08a" xml:space="preserve">4. primi.</note>
            anguli H D I, D H I, vnius trianguli duobus angulis H D I, D H I, alterius trianguli æquales, (quòd
              <lb/>
            in vtroque triangulo prior angulus rectus ſit, & </s>
            <s xml:id="echoid-s10263" xml:space="preserve">poſterior æqualis altitudini poli) eſtq́; </s>
            <s xml:id="echoid-s10264" xml:space="preserve">latus D H,
              <lb/>
              <note position="left" xlink:label="note-0179-09" xlink:href="note-0179-09a" xml:space="preserve">50</note>
            vnius lateri D H, alterius æquale. </s>
            <s xml:id="echoid-s10265" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s10266" xml:space="preserve">latera D I, H I, vnius æqualia ſunt lateribus D I, H I, al-
              <lb/>
              <note position="right" xlink:label="note-0179-10" xlink:href="note-0179-10a" xml:space="preserve">26. primi.</note>
            terius, &</s>
            <s xml:id="echoid-s10267" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10268" xml:space="preserve">Ex centro deinde E, Aequatoris in horologio, ex quo videlicet circulus fuit deſcriptus,
              <lb/>
            diuiſusq́; </s>
            <s xml:id="echoid-s10269" xml:space="preserve">in partes 24. </s>
            <s xml:id="echoid-s10270" xml:space="preserve">æquales, &</s>
            <s xml:id="echoid-s10271" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10272" xml:space="preserve">transferantur omnia interualla inter centrum E, & </s>
            <s xml:id="echoid-s10273" xml:space="preserve">lineas ho-
              <lb/>
            rarias in æquinoctiali linea F k, poſita in lineam D C, huius figuræ, quam nunc conſtruimus, à
              <lb/>
            puncto D; </s>
            <s xml:id="echoid-s10274" xml:space="preserve">nempe interuallo E F, vel E K, in horologio, quod ante hanc figuram proxime conſtru
              <lb/>
            ctum eſt, (Sunt enim rectæ E F, E K, in horologio dicto inter ſe æquales, vt in ſcholio præcedentis
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s10275" xml:space="preserve">demonſtratum eſt: </s>
            <s xml:id="echoid-s10276" xml:space="preserve">quemadmodum & </s>
            <s xml:id="echoid-s10277" xml:space="preserve">reliqua interualla quæcunque inter E, & </s>
            <s xml:id="echoid-s10278" xml:space="preserve">binas ho-
              <lb/>
            ras æquali temporis interuallo à linea meridiana remotas ęqualia oſtenſa ſunt) æqualis ſit in hac
              <lb/>
            figura recta D C; </s>
            <s xml:id="echoid-s10279" xml:space="preserve">& </s>
            <s xml:id="echoid-s10280" xml:space="preserve">interuallo E R, vel E S, eiuſdem horologij æqualis ſit recta D T, in hac fi-
              <lb/>
            gura, &</s>
            <s xml:id="echoid-s10281" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10282" xml:space="preserve">Per puncta autem C, T, & </s>
            <s xml:id="echoid-s10283" xml:space="preserve">reliqua in linea D C, notata, ex H, emittantur rectæ, qui-
              <lb/>
            bus aſcribantur numeri horarum reſpondentes translatis interuallis; </s>
            <s xml:id="echoid-s10284" xml:space="preserve">ita vt recta H C, ſit linea </s>
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