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>
            <s xml:id="echoid-s5728" xml:space="preserve">
              <pb o="100" file="0120" n="120" rhead="GNOMONICES"/>
            propoſ. </s>
            <s xml:id="echoid-s5729" xml:space="preserve">13. </s>
            <s xml:id="echoid-s5730" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5731" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5732" xml:space="preserve">Gebri, vel certè ex propoſ. </s>
            <s xml:id="echoid-s5733" xml:space="preserve">41. </s>
            <s xml:id="echoid-s5734" xml:space="preserve">noſtrorum triangulorum ſphæricorum, ſinus ar-
              <lb/>
            cus H I, altitudinis poli ſupra planum, ad ſinum anguli G, inclinationis plani ad Meridianum; </s>
            <s xml:id="echoid-s5735" xml:space="preserve">erit
              <lb/>
            quoque conuertendo, vt ſinus totus anguli recti I, ad ſinum arcus Meridiani G H, inter planum, & </s>
            <s xml:id="echoid-s5736" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0120-01" xlink:href="fig-0120-01a" number="85">
                <image file="0120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0120-01"/>
              </figure>
              <note position="left" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">10</note>
            polum intercepti, ita ſinus anguli G, inclinationis plani ad Meridianum, ad ſinum arcus H I, alti-
              <lb/>
            tudinis poli ſupra planum. </s>
            <s xml:id="echoid-s5737" xml:space="preserve">Itaque inuento per corollarium præcedentis propoſ. </s>
            <s xml:id="echoid-s5738" xml:space="preserve">arcu Meridiani
              <lb/>
            inter planum inclinatum, & </s>
            <s xml:id="echoid-s5739" xml:space="preserve">polum mundi intercepto, nec non per propoſ. </s>
            <s xml:id="echoid-s5740" xml:space="preserve">27. </s>
            <s xml:id="echoid-s5741" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5742" xml:space="preserve">inclina-
              <lb/>
              <note position="left" xlink:label="note-0120-02" xlink:href="note-0120-02a" xml:space="preserve">20</note>
            tione plani ad Meridianum; </s>
            <s xml:id="echoid-s5743" xml:space="preserve">ſi fiat, vt ſinus totus ad ſinum arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5744" xml:space="preserve">po-
              <lb/>
            lum interiecti; </s>
            <s xml:id="echoid-s5745" xml:space="preserve">ita ſinus inclinationis plani ad Meridianum, ad aliud, habebitur ſinus altitudinis
              <lb/>
              <note position="left" xlink:label="note-0120-03" xlink:href="note-0120-03a" xml:space="preserve">Exem plum pri-
                <lb/>
              mum.</note>
            poli ſupra planum propoſitum. </s>
            <s xml:id="echoid-s5746" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s5747" xml:space="preserve">Ponatur arcus Meridiani inter planũ, & </s>
            <s xml:id="echoid-s5748" xml:space="preserve">polum grad.
              <lb/>
            </s>
            <s xml:id="echoid-s5749" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5750" xml:space="preserve">inclinatio verò plani ad Meridianũ grad. </s>
            <s xml:id="echoid-s5751" xml:space="preserve">35. </s>
            <s xml:id="echoid-s5752" xml:space="preserve">Si igitur fiat, vt 100000. </s>
            <s xml:id="echoid-s5753" xml:space="preserve">ſinus totus ad 50000. </s>
            <s xml:id="echoid-s5754" xml:space="preserve">
              <lb/>
            ſinum arcus inter planum, & </s>
            <s xml:id="echoid-s5755" xml:space="preserve">polum poſiti, ita 57357. </s>
            <s xml:id="echoid-s5756" xml:space="preserve">ſinus grad. </s>
            <s xml:id="echoid-s5757" xml:space="preserve">35. </s>
            <s xml:id="echoid-s5758" xml:space="preserve">hoc eſt, inclinationis ad Me-
              <lb/>
            ridianum, ad aliud, inuenietur hic ferè ſinus 28678 {1/2}, cuius arcus grad. </s>
            <s xml:id="echoid-s5759" xml:space="preserve">16. </s>
            <s xml:id="echoid-s5760" xml:space="preserve">min. </s>
            <s xml:id="echoid-s5761" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5762" xml:space="preserve">altitudinem
              <lb/>
            poli ſupra planum propoſitum dimetitur.</s>
            <s xml:id="echoid-s5763" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5764" xml:space="preserve">SIMILITER ponatur arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5765" xml:space="preserve">polum poſitus grad. </s>
            <s xml:id="echoid-s5766" xml:space="preserve">90. </s>
            <s xml:id="echoid-s5767" xml:space="preserve">vt contin
              <lb/>
              <note position="left" xlink:label="note-0120-04" xlink:href="note-0120-04a" xml:space="preserve">Exemplum ſe-
                <lb/>
              cundum.</note>
            git, quando planum & </s>
            <s xml:id="echoid-s5768" xml:space="preserve">Aequator in vno eodemq́; </s>
            <s xml:id="echoid-s5769" xml:space="preserve">puncto Meridianum interſecant: </s>
            <s xml:id="echoid-s5770" xml:space="preserve">Inclinatio ve-
              <lb/>
            rò plani ad Meridianum grad. </s>
            <s xml:id="echoid-s5771" xml:space="preserve">66. </s>
            <s xml:id="echoid-s5772" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5773" xml:space="preserve">47. </s>
            <s xml:id="echoid-s5774" xml:space="preserve">Itaque ſi fiat vt 100000. </s>
            <s xml:id="echoid-s5775" xml:space="preserve">ſinus totus ad 100000. </s>
            <s xml:id="echoid-s5776" xml:space="preserve">ſinũ
              <lb/>
              <note position="left" xlink:label="note-0120-05" xlink:href="note-0120-05a" xml:space="preserve">30</note>
            arcus inter planum, & </s>
            <s xml:id="echoid-s5777" xml:space="preserve">polum, ita 91902. </s>
            <s xml:id="echoid-s5778" xml:space="preserve">ſinus inclinationis ad Meridianum, ad aliud, inuenietur
              <lb/>
            idem ſinus 91902. </s>
            <s xml:id="echoid-s5779" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s5780" xml:space="preserve">66. </s>
            <s xml:id="echoid-s5781" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5782" xml:space="preserve">47. </s>
            <s xml:id="echoid-s5783" xml:space="preserve">altitudinem poli ſupra planum propoſitum con
              <lb/>
            tinet. </s>
            <s xml:id="echoid-s5784" xml:space="preserve">Vbi vides altitudinem poli ſupra planum ęqualem eſſe inclinationi eius ad Meridianum:
              <lb/>
            </s>
            <s xml:id="echoid-s5785" xml:space="preserve">quoniam quando planum, & </s>
            <s xml:id="echoid-s5786" xml:space="preserve">Aequator in eodem puncto Meridianum interſecant, idem arcus
              <lb/>
            circuli maximi per polos mundi, & </s>
            <s xml:id="echoid-s5787" xml:space="preserve">per polos plani ducti metitur & </s>
            <s xml:id="echoid-s5788" xml:space="preserve">altitudinem poli ſupra pla-
              <lb/>
            num, & </s>
            <s xml:id="echoid-s5789" xml:space="preserve">inclinationem eiuſdem plani ad Meridianum, vt perſpicuum eſt, cum per propoſ. </s>
            <s xml:id="echoid-s5790" xml:space="preserve">15. </s>
            <s xml:id="echoid-s5791" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5792" xml:space="preserve">
              <lb/>
            1. </s>
            <s xml:id="echoid-s5793" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s5794" xml:space="preserve">ſit rectus ad planum inclinatum. </s>
            <s xml:id="echoid-s5795" xml:space="preserve">Hinc enim fit, vt metiatur altitudinem poli ſupra pla-
              <lb/>
            num, veluti proprius quidam Meridianus ipſius plani inclinati. </s>
            <s xml:id="echoid-s5796" xml:space="preserve">Idem quoque circulus maximus
              <lb/>
            menſurat inclinationem eiuſdem plani ad Meridianum, quia rectus quoque eſt ad Meridianum; </s>
            <s xml:id="echoid-s5797" xml:space="preserve">
              <lb/>
            quod ita planum fiet. </s>
            <s xml:id="echoid-s5798" xml:space="preserve">Quoniam enim tranſit per polos plani, & </s>
            <s xml:id="echoid-s5799" xml:space="preserve">per polos Aequatoris, tranſibunt
              <lb/>
              <note position="left" xlink:label="note-0120-06" xlink:href="note-0120-06a" xml:space="preserve">40</note>
            quoque viciſsim planum propoſitum, & </s>
            <s xml:id="echoid-s5800" xml:space="preserve">Aequator per illius polos, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s5801" xml:space="preserve">15. </s>
            <s xml:id="echoid-s5802" xml:space="preserve">libri 1.
              <lb/>
            </s>
            <s xml:id="echoid-s5803" xml:space="preserve">Theodoſij. </s>
            <s xml:id="echoid-s5804" xml:space="preserve">Quare puncta, vbi ſe interſecant planum, & </s>
            <s xml:id="echoid-s5805" xml:space="preserve">Aequator in Meridiano, poli ſunt illius
              <lb/>
            circuli, ac proinde Meridianus per hos polos ductus, erit per propoſ. </s>
            <s xml:id="echoid-s5806" xml:space="preserve">15. </s>
            <s xml:id="echoid-s5807" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5808" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5809" xml:space="preserve">Theodoſij, ad illum
              <lb/>
            rectus. </s>
            <s xml:id="echoid-s5810" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s5811" xml:space="preserve">viciſſim ille ad Meridianum rectus erit, quod erat oſtendendum.</s>
            <s xml:id="echoid-s5812" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5813" xml:space="preserve">EODEM modo ſupra planum ad Meridianum tantum inclinatum, quod nimirum per ver
              <lb/>
              <note position="left" xlink:label="note-0120-07" xlink:href="note-0120-07a" xml:space="preserve">Quando planũ
                <lb/>
              ad Meridianũ
                <lb/>
              tan tum inclina
                <lb/>
              tum eſt. Vel ad
                <lb/>
              Meridianum &
                <lb/>
              Horizõtem, re-
                <lb/>
              ctum autem ad
                <lb/>
              Verti@alem.</note>
              <figure xlink:label="fig-0120-02" xlink:href="fig-0120-02a" number="86">
                <image file="0120-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0120-02"/>
              </figure>
            ticem loci tranſit, altitudo poli in-
              <lb/>
            uenietur, nec non ſupra planum,
              <lb/>
            quod ad Verticalem circulum eſt
              <lb/>
            rectum, & </s>
            <s xml:id="echoid-s5814" xml:space="preserve">tam ad Meridianum,
              <lb/>
            quam ad Horizõtem inclinatum.
              <lb/>
            </s>
            <s xml:id="echoid-s5815" xml:space="preserve">
              <note position="left" xlink:label="note-0120-08" xlink:href="note-0120-08a" xml:space="preserve">50</note>
            Cuiuſmodi eſt planum, quod per
              <lb/>
            communes ſectiones Horizontis,
              <lb/>
            ac Meridiani incedit. </s>
            <s xml:id="echoid-s5816" xml:space="preserve">Id quod faci
              <lb/>
            le intelligi poteſt ex his duabus ſi-
              <lb/>
            guris, in quarum priori Verticalis
              <lb/>
            eſt k L, planum ad Meridianum
              <lb/>
            tantum inclinatum E F, tranſiens
              <lb/>
            per verticem G, ſiue polum Hori
              <lb/>
            zontis, ac propterea rectum exi-
              <lb/>
            ſtens ad Horizontem, ita vtarcus
              <lb/>
            Meridiani G H, inter planum & </s>
            <s xml:id="echoid-s5817" xml:space="preserve">polum æqualis ſit complemento altitudinis poli ſupra </s>
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