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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[Figure 241]
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[265] 1. figura
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[266] 2. figura.
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[267] 3. figura.
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[268] 4. figura
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[269] 5. figura
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[270] 6. figura
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            <s xml:id="echoid-s25958" xml:space="preserve">
              <pb o="394" file="0410" n="410" rhead="GNOMONICES"/>
            nus ille per H ρ, axem ductus, occurrit plano horologij in ρ, centro horologij, ducenda erit communis ei{us}
              <lb/>
            cum horologio ſectio per ρ. </s>
            <s xml:id="echoid-s25959" xml:space="preserve">Rurſus quia idem Meridianus ad planum horologij rectus eſt, tranſibit ne-
              <lb/>
            ceſſario per stylum, cum omnia plana per stylum ducta ſint recta ad planum horologij; </s>
            <s xml:id="echoid-s25960" xml:space="preserve">atque adeo di-
              <lb/>
              <note position="left" xlink:label="note-0410-01" xlink:href="note-0410-01a" xml:space="preserve">18. vndec.</note>
            cta communis ſectio, hoc eſt, linea ſtyli per K, ducenda erit, cuiuſmodi eſt recta ρ K, quæ æquinoctialem
              <lb/>
            lineam ſecabit ad angulos rectos,
              <lb/>
            vt in ſuperioribus demonstratum
              <lb/>
              <figure xlink:label="fig-0410-01" xlink:href="fig-0410-01a" number="270">
                <image file="0410-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0410-01"/>
                <caption xml:id="echoid-caption6" xml:space="preserve">6. figura</caption>
              </figure>
            est. </s>
            <s xml:id="echoid-s25961" xml:space="preserve">Nam quia tam planum Ae- quatoris, quàm planum horologij rectum eſt ad Meridianum pro- prium plani horologij, erit quoque
              <note position="left" xlink:label="note-0410-02" xlink:href="note-0410-02a" xml:space="preserve">10</note>
            communis eorum ſectio, nempe æquinoctialis linea α M, ad eun- dem recta, atque adeo, per defin.</s>
            <s xml:id="echoid-s25962" xml:space="preserve">
              <note position="left" xlink:label="note-0410-03" xlink:href="note-0410-03a" xml:space="preserve">19. vndec.</note>
            3. </s>
            <s xml:id="echoid-s25963" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25964" xml:space="preserve">11. </s>
            <s xml:id="echoid-s25965" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s25966" xml:space="preserve">ad lineam ſtyli ρ K, in eodem Meridiano exiſten- tem perpendicularis. </s>
            <s xml:id="echoid-s25967" xml:space="preserve">Quod ſi cen tro careat horologium, ducenda erit linea styli per K, locum styli parallela lineæ meridianæ, & </s>
            <s xml:id="echoid-s25968" xml:space="preserve">ad æquinoctialem lineam perpendi-
              <note position="left" xlink:label="note-0410-04" xlink:href="note-0410-04a" xml:space="preserve">20</note>
            cularis. </s>
            <s xml:id="echoid-s25969" xml:space="preserve">Quia enim tunc pla- num horologii axi mundi, quem non ſecat, hoc eſt, communi ſe- ctioni Meridiani Horizontis, et Meridiani proprij ipſius horolo- gij, æquidiſtat, erunt per propoſ.</s>
            <s xml:id="echoid-s25970" xml:space="preserve"> 18. </s>
            <s xml:id="echoid-s25971" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25972" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25973" xml:space="preserve">communes ſectiones pla ni horologii, & </s>
            <s xml:id="echoid-s25974" xml:space="preserve">ipſorum Meridia- norum, hoc est, linea meridiana,& </s>
            <s xml:id="echoid-s25975" xml:space="preserve">linea ſtyli, parallelæ inter ſe, ſecabit{q́ue}
              <unsure/>
            linea styli lineam æquinoctialem ad angulos rectos, vt proxi- me demonſtr auim{us}.</s>
            <s xml:id="echoid-s25976" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p style="it">
            <s xml:id="echoid-s25977" xml:space="preserve">QVOD autem recta ρ I, ſit axis mundi, ita vt cum linea ſtyli ρ K, quæ communis ſectio eſt Meri-
              <lb/>
            diani proprii plani inclinati, & </s>
            <s xml:id="echoid-s25978" xml:space="preserve">plani horologii, comprehendat angulum I ρ K, altitudinis poli ſupra pla
              <lb/>
            num inclinatum, manifestum eſt. </s>
            <s xml:id="echoid-s25979" xml:space="preserve">Si enim triangulum I K ρ, circa K ρ, moueatur, donec rectum fiat ad
              <lb/>
            planum horologii, & </s>
            <s xml:id="echoid-s25980" xml:space="preserve">ſtylus I K, ad idem rectus, ac idcirco punctum I, centro mundi congruat, erit recta
              <lb/>
            ρ I, axis mundi, quandoquidem axis mundi per centrum mundi, & </s>
            <s xml:id="echoid-s25981" xml:space="preserve">centrum horologij ducitur. </s>
            <s xml:id="echoid-s25982" xml:space="preserve">Quod etiã
              <lb/>
            hac ratione perſpicuum fiet. </s>
            <s xml:id="echoid-s25983" xml:space="preserve">quoniam circumuoluto triangulo ρ H E, circa meridianam lineam ρ E, do-
              <lb/>
            nec cum plano Meridiani coniungatur, punctum H, centro mundi congruit, vt ſupra oſtendim{us}, at que
              <lb/>
            adeo & </s>
            <s xml:id="echoid-s25984" xml:space="preserve">puncto I, congruet quoque recta ρ H, rectæ ρ I: </s>
            <s xml:id="echoid-s25985" xml:space="preserve">Oſtendimus autem ρ H, eſſe axem mundi. </s>
            <s xml:id="echoid-s25986" xml:space="preserve">Igi-
              <lb/>
            tur & </s>
            <s xml:id="echoid-s25987" xml:space="preserve">ρ I, axis mundi erit. </s>
            <s xml:id="echoid-s25988" xml:space="preserve">In horologijs, quæ centro carent, ducend{us} eſt axis mundi per I, lineæ ſtyli
              <lb/>
            æquidiſtans, quia ſi ipſam ſecaret, eſſet punctum ſectionis centrum horologij, vt manifeſtum eſt. </s>
            <s xml:id="echoid-s25989" xml:space="preserve">Reliqua
              <lb/>
              <note position="left" xlink:label="note-0410-06" xlink:href="note-0410-06a" xml:space="preserve">40</note>
            perſpicua ſunt ex demonſtratione primæ deſcriptionis in hac propoſ. </s>
            <s xml:id="echoid-s25990" xml:space="preserve">traditæ.</s>
            <s xml:id="echoid-s25991" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s25992" xml:space="preserve">POSTREMO idem horologium declinans ſimul & </s>
            <s xml:id="echoid-s25993" xml:space="preserve">inclinatum deſcribemus beneficio Ellipſis in
              <lb/>
            horologij plano deſcriptæ, non ſec{us} ac docuimus in ſcholio propoſ. </s>
            <s xml:id="echoid-s25994" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25995" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s25996" xml:space="preserve">Semidiametri circulorũ,
              <lb/>
              <note position="left" xlink:label="note-0410-07" xlink:href="note-0410-07a" xml:space="preserve">Eiuſdem horo-
                <lb/>
              logii deſcriptio
                <unsure/>
                <lb/>
              ex Ellipſi.</note>
            qui determinant longitudinem & </s>
            <s xml:id="echoid-s25997" xml:space="preserve">latitudinem Ellipſis, ex centro horologij ρ, deſcribendorum ſunt ρ G,
              <lb/>
            G I: </s>
            <s xml:id="echoid-s25998" xml:space="preserve">Vel ſi maiores deſiderentur, ſumatur pro maiore ſemidiametro quant acunque portio ex linea ſtyli,
              <lb/>
            nempe ρ L, pro minore autem recta, quæ ex puncto, quod maiorem terminat, vt ex L, cadit in axem ρ I,
              <lb/>
            perpendicularis: </s>
            <s xml:id="echoid-s25999" xml:space="preserve">Et quod ad demonſtrationem attinet, circa G I, vel illam perpendicularem ex L, caden
              <lb/>
            tem in axem, deſcribendus eſt circulus in plano Aequatoris ex cẽtro mundi, quod in axe eſt, pro baſe cy-
              <lb/>
            lindri. </s>
            <s xml:id="echoid-s26000" xml:space="preserve">Diuiſio autem circulorum ex
              <unsure/>
            ρ, deſcriptorum inchoanda eſt à recta, quæ in cẽtro ρ, cum linea ſty-
              <lb/>
            li verſus lineam meridianam angulum comprehendat angulo ρ L M, nempe inclinationi Meridiani pro-
              <lb/>
              <note position="left" xlink:label="note-0410-08" xlink:href="note-0410-08a" xml:space="preserve">50</note>
            prii ipſius plani inclinati ad Meridianum Horizontis, æqualem. </s>
            <s xml:id="echoid-s26001" xml:space="preserve">Vnde quoniam in ſexta figura inclina-
              <lb/>
            tio Meridianorum complectitur grad. </s>
            <s xml:id="echoid-s26002" xml:space="preserve">90. </s>
            <s xml:id="echoid-s26003" xml:space="preserve">& </s>
            <s xml:id="echoid-s26004" xml:space="preserve">recta L M, cum linea ſtyli angulum efficit rectum, initium
              <lb/>
            habebit diuiſio circulorum ex ρ, deſcriptorum à linea meridiana, cum hæc cum linea ſl
              <unsure/>
            yli rectos etiã con-
              <lb/>
            tineat angulos, vt ex ſuperioribus conſtat. </s>
            <s xml:id="echoid-s26005" xml:space="preserve">Hæc porro deſcriptio locum non habet in horologiis centro cæ
              <lb/>
            rentibus, vt in tertia figura: </s>
            <s xml:id="echoid-s26006" xml:space="preserve">quia planum horologij, cum axi mundi, ſiue cylindri, ex cuius ſectione Elli-
              <lb/>
            pſis illa oritur, æquidiſtet, non efficit Ellipſim, ſed parallelogrammum, vt à Sereno Antinſenſi demon-
              <lb/>
            ſtratur lib. </s>
            <s xml:id="echoid-s26007" xml:space="preserve">1. </s>
            <s xml:id="echoid-s26008" xml:space="preserve">de ſectione cylindri.</s>
            <s xml:id="echoid-s26009" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26010" xml:space="preserve">IAM verò ſi horologium quodcunque ſuperi{us} inuertatur, ita vt ſuperior pars euadat inferior, & </s>
            <s xml:id="echoid-s26011" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0410-09" xlink:href="note-0410-09a" xml:space="preserve">Qua ratione ex
                <lb/>
              horologio Su-
                <lb/>
              periori genere-
                <lb/>
              tur Inferius.</note>
            quæ poſt hanc inuerſionem nobis dextra eſt, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s26012" xml:space="preserve">è contrario, vt in præcedentibus non ſemel de-
              <lb/>
            clarauim{us}, habebim{us} horologium in facie plani oppoſita, ac inferiori collocandum, vt </s>
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