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-s5899" xml:space="preserve">
              <pb o="102" file="0122" n="122" rhead="GNOMONICES"/>
            plementi arcus G I. </s>
            <s xml:id="echoid-s5900" xml:space="preserve">Quare ſi fiat, vt ſinus complementi altitudinis poli ſupra planum inclina-
              <lb/>
            tum, ad ſinum complementi arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5901" xml:space="preserve">polum, ita ſinus totus ad aliud, ha-
              <lb/>
            bebitur ſinus complementi arcus plani G I, qui angulo H, inclinationis Meridiani B D, ipſius pla-
              <lb/>
              <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a" number="88">
                <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0122-01"/>
              </figure>
              <note position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">10</note>
            ni inclinati ad Meridianum A C, ipſius Horizontis opponitur in triangulo G H I, eſtq́; </s>
            <s xml:id="echoid-s5902" xml:space="preserve">arcus pla
              <lb/>
            ni inclinati, qui interijcitur inter Meridianum Horizontis, & </s>
            <s xml:id="echoid-s5903" xml:space="preserve">dictum circulum maximum, hoc
              <lb/>
              <note position="left" xlink:label="note-0122-02" xlink:href="note-0122-02a" xml:space="preserve">10</note>
            eſt, Meridianum plani inclinati; </s>
            <s xml:id="echoid-s5904" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s5905" xml:space="preserve">arcus ipſe G I, cognitus erit.</s>
            <s xml:id="echoid-s5906" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5907" xml:space="preserve">IDEM & </s>
            <s xml:id="echoid-s5908" xml:space="preserve">facilius conſequemur, ſi planum inclinatum E F, tranſierit per verticem G, ita vt ſit
              <lb/>
            vnus ex circulis Verticalibus, velut in ſecunda figura apparet: </s>
            <s xml:id="echoid-s5909" xml:space="preserve">quia tunc arcus G H, Meridiani
              <lb/>
            inter planum, & </s>
            <s xml:id="echoid-s5910" xml:space="preserve">polum eſt complementum altitudinis poli ſupra Horizontem, & </s>
            <s xml:id="echoid-s5911" xml:space="preserve">complementũ
              <lb/>
            ipſius arcus G H, eſt ipſamet altitudo poli ſupra Horizontem, nempe arcus H C.</s>
            <s xml:id="echoid-s5912" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5913" xml:space="preserve">SIMILITER res facilis erit, ſi planum inclinatum E F, tranſierit per puncta A, C, vbi Ho-
              <lb/>
            rizon, & </s>
            <s xml:id="echoid-s5914" xml:space="preserve">Meridianus ſe mutuo interſecant, ita vt ſit vnus ex circulis poſitionum, velut in figura
              <lb/>
            tertia apparet: </s>
            <s xml:id="echoid-s5915" xml:space="preserve">quia tunc arcus Meridiani G H, inter planum, & </s>
            <s xml:id="echoid-s5916" xml:space="preserve">polum eſt altitudo poli ſupra Ho-
              <lb/>
            rizontem, nempe arcus H C. </s>
            <s xml:id="echoid-s5917" xml:space="preserve">Conſtat ergo id quod primo loco propoſitum eſt.</s>
            <s xml:id="echoid-s5918" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5919" xml:space="preserve">DEINDE quoniam eſt, per propoſ. </s>
            <s xml:id="echoid-s5920" xml:space="preserve">16. </s>
            <s xml:id="echoid-s5921" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5922" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5923" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s5924" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s5925" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s5926" xml:space="preserve">13.
              <lb/>
            </s>
            <s xml:id="echoid-s5927" xml:space="preserve">
              <note position="left" xlink:label="note-0122-03" xlink:href="note-0122-03a" xml:space="preserve">Inclinatio, quã
                <lb/>
              habet Meridia-
                <lb/>
              nus plani incli-
                <lb/>
              nati ad Meri-
                <lb/>
              dianũ Horizon
                <lb/>
              tis quo pacto re
                <lb/>
              per@atur.</note>
              <note position="left" xlink:label="note-0122-04" xlink:href="note-0122-04a" xml:space="preserve">30</note>
            lib. </s>
            <s xml:id="echoid-s5928" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5929" xml:space="preserve">Gebri, vel certè per propoſ. </s>
            <s xml:id="echoid-s5930" xml:space="preserve">41. </s>
            <s xml:id="echoid-s5931" xml:space="preserve">noſtrorum triangulorum ſphęricorum, vt ſinus arcus G H,
              <lb/>
            Meridiani inter planum, & </s>
            <s xml:id="echoid-s5932" xml:space="preserve">polum, ad ſinum anguli recti I, hoc eſt, ad ſinum totum, ita ſinus ar-
              <lb/>
            cus G I, ipſius plani inter duos Meridianos, quem iam inuenimus, ad ſinum anguli H, inclinatio-
              <lb/>
            nis circuli maximi B D, (qui eſt inſtar Meridiani ipſius plani) ad Horizontis Meridianum A C; </s>
            <s xml:id="echoid-s5933" xml:space="preserve">ſi
              <lb/>
            fiat, vt ſinus arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5934" xml:space="preserve">polum, ad ſinum totum, ita ſinus arcus G I, ipſius pla
              <lb/>
            ni inter duos Meridianos inuenti ad aliud, habebitur ſinus anguli H, inclinationis quęſitæ.
              <lb/>
            </s>
            <s xml:id="echoid-s5935" xml:space="preserve">Quod eſt ſecundum.</s>
            <s xml:id="echoid-s5936" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5937" xml:space="preserve">EXEMPLVM vtriuſque. </s>
            <s xml:id="echoid-s5938" xml:space="preserve">Ponatur altitudo poli ſupra planum grad. </s>
            <s xml:id="echoid-s5939" xml:space="preserve">16. </s>
            <s xml:id="echoid-s5940" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5941" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5942" xml:space="preserve">Arcus ve-
              <lb/>
              <note position="left" xlink:label="note-0122-05" xlink:href="note-0122-05a" xml:space="preserve">Exemplum pri-
                <lb/>
              mum.</note>
            rò Meridiani inter planum, & </s>
            <s xml:id="echoid-s5943" xml:space="preserve">polum grad. </s>
            <s xml:id="echoid-s5944" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5945" xml:space="preserve">Si igitur fiat, vt 9579 S. </s>
            <s xml:id="echoid-s5946" xml:space="preserve">ſinus complementi altitu-
              <lb/>
            dinis poli ſupra planum ad 86602. </s>
            <s xml:id="echoid-s5947" xml:space="preserve">ſinum complementi arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5948" xml:space="preserve">polum,
              <lb/>
              <note position="left" xlink:label="note-0122-06" xlink:href="note-0122-06a" xml:space="preserve">40</note>
            ita 100000. </s>
            <s xml:id="echoid-s5949" xml:space="preserve">ſinus totus ad aliud, habebitur hic ferè ſinus 90401. </s>
            <s xml:id="echoid-s5950" xml:space="preserve">cuius arcus continet grad. </s>
            <s xml:id="echoid-s5951" xml:space="preserve">64.
              <lb/>
            </s>
            <s xml:id="echoid-s5952" xml:space="preserve">min. </s>
            <s xml:id="echoid-s5953" xml:space="preserve">41. </s>
            <s xml:id="echoid-s5954" xml:space="preserve">quo detracto ex quadrante, remanebit arcus ipſius plani inter duos Meridianos, grad. </s>
            <s xml:id="echoid-s5955" xml:space="preserve">25. </s>
            <s xml:id="echoid-s5956" xml:space="preserve">
              <lb/>
            min. </s>
            <s xml:id="echoid-s5957" xml:space="preserve">19. </s>
            <s xml:id="echoid-s5958" xml:space="preserve">quod eſt primum. </s>
            <s xml:id="echoid-s5959" xml:space="preserve">Poſt hęc, ſi fiat, vt 50000. </s>
            <s xml:id="echoid-s5960" xml:space="preserve">ſinus arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5961" xml:space="preserve">po-
              <lb/>
            lum, ad 100000. </s>
            <s xml:id="echoid-s5962" xml:space="preserve">ſinum totum, ita 42762. </s>
            <s xml:id="echoid-s5963" xml:space="preserve">ſinus arcus inter duos Meridianos inuenti ad aliud, in-
              <lb/>
            uenietur hic ſinus 85524. </s>
            <s xml:id="echoid-s5964" xml:space="preserve">cuius arcus, nempe inclinatio Meridiani ipſius plani ad Meridianum
              <lb/>
            Horizontis, continet grad. </s>
            <s xml:id="echoid-s5965" xml:space="preserve">58. </s>
            <s xml:id="echoid-s5966" xml:space="preserve">min. </s>
            <s xml:id="echoid-s5967" xml:space="preserve">47. </s>
            <s xml:id="echoid-s5968" xml:space="preserve">quod eſt ſecundum.</s>
            <s xml:id="echoid-s5969" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5970" xml:space="preserve">RVRSVS ponatur altitudo poli ſupra planum grad. </s>
            <s xml:id="echoid-s5971" xml:space="preserve">66. </s>
            <s xml:id="echoid-s5972" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5973" xml:space="preserve">47 arcus verò Meridiani inter
              <lb/>
            planum & </s>
            <s xml:id="echoid-s5974" xml:space="preserve">polum grad. </s>
            <s xml:id="echoid-s5975" xml:space="preserve">90. </s>
            <s xml:id="echoid-s5976" xml:space="preserve">vt contingit in plano declinante à Verticali, à ſeptentrione in ortum
              <lb/>
            grad. </s>
            <s xml:id="echoid-s5977" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5978" xml:space="preserve">inclinato verò ad Horizontem grad. </s>
            <s xml:id="echoid-s5979" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5980" xml:space="preserve">min. </s>
            <s xml:id="echoid-s5981" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5982" xml:space="preserve">ex parte auſtrali, in latitudine grad. </s>
            <s xml:id="echoid-s5983" xml:space="preserve">42. </s>
            <s xml:id="echoid-s5984" xml:space="preserve">vt
              <lb/>
            ex præcedentibus colligi poteſt. </s>
            <s xml:id="echoid-s5985" xml:space="preserve">Si igitur fiat, vt 39420. </s>
            <s xml:id="echoid-s5986" xml:space="preserve">ſinus complementi altitudinis poli ſupra
              <lb/>
              <note position="left" xlink:label="note-0122-07" xlink:href="note-0122-07a" xml:space="preserve">50</note>
            planum inclinatum ad ſinum complementi arcus Meridiani inter planum & </s>
            <s xml:id="echoid-s5987" xml:space="preserve">polum, quod nul
              <lb/>
            lum eſt, ita 100000. </s>
            <s xml:id="echoid-s5988" xml:space="preserve">ſinus totus ad aliud, habebitur hic ſinus o, cuius arcus grad. </s>
            <s xml:id="echoid-s5989" xml:space="preserve">0. </s>
            <s xml:id="echoid-s5990" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5991" xml:space="preserve">0. </s>
            <s xml:id="echoid-s5992" xml:space="preserve">detra-
              <lb/>
            ctus ex grad. </s>
            <s xml:id="echoid-s5993" xml:space="preserve">90. </s>
            <s xml:id="echoid-s5994" xml:space="preserve">relinquit arcum ipſius plani inter duos Meridianos grad. </s>
            <s xml:id="echoid-s5995" xml:space="preserve">90. </s>
            <s xml:id="echoid-s5996" xml:space="preserve">quod eſt primum.
              <lb/>
            </s>
            <s xml:id="echoid-s5997" xml:space="preserve">Rurſus ſi fiat, vt 100000. </s>
            <s xml:id="echoid-s5998" xml:space="preserve">ſinus arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5999" xml:space="preserve">polum, ad 100000. </s>
            <s xml:id="echoid-s6000" xml:space="preserve">ſinum totum,
              <lb/>
            ita 100000. </s>
            <s xml:id="echoid-s6001" xml:space="preserve">ſinus arcus plani inter duos Meridianos inuẽti, ad aliud, reperietur ſinus hic 100000. </s>
            <s xml:id="echoid-s6002" xml:space="preserve">
              <lb/>
            cuius arcus grad. </s>
            <s xml:id="echoid-s6003" xml:space="preserve">90. </s>
            <s xml:id="echoid-s6004" xml:space="preserve">erit inclinatio Meridiani ipſius ad Meridianum Horizontis. </s>
            <s xml:id="echoid-s6005" xml:space="preserve">quæ res cum ſu-
              <lb/>
            perioribus conſentit. </s>
            <s xml:id="echoid-s6006" xml:space="preserve">Quia enim polus Meridiani ipſius plani inclinati eſt punctum, vbi Aequa-
              <lb/>
            tor Meridianum interſecat, vt in pręcedenti propoſ. </s>
            <s xml:id="echoid-s6007" xml:space="preserve">diximus, neceſſe eſt ex coroll. </s>
            <s xml:id="echoid-s6008" xml:space="preserve">propoſitionis
              <lb/>
            16. </s>
            <s xml:id="echoid-s6009" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6010" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6011" xml:space="preserve">Theodoſij, arcum ipſius plani à polo dicto vſq; </s>
            <s xml:id="echoid-s6012" xml:space="preserve">ad Meridianũ ipſius eſſe quadrantẽ, &</s>
            <s xml:id="echoid-s6013" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6014" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6015" xml:space="preserve">ALIVD exemplũ pro ſecunda figura. </s>
            <s xml:id="echoid-s6016" xml:space="preserve">Ponatur planũ E F, declinare à meridie in ortum, vel à
              <lb/>
              <note position="left" xlink:label="note-0122-08" xlink:href="note-0122-08a" xml:space="preserve">Exemplum ſe-
                <lb/>
              cundum.</note>
            ſeptentrione in occaſum, grad. </s>
            <s xml:id="echoid-s6017" xml:space="preserve">30. </s>
            <s xml:id="echoid-s6018" xml:space="preserve">in Horizonte Romano, vel vbi polus ſupra Horizõtem </s>
          </p>
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