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-s5264" xml:space="preserve">
              <pb o="94" file="0114" n="114" rhead="GNOMONICES"/>
            per propoſ. </s>
            <s xml:id="echoid-s5265" xml:space="preserve">23. </s>
            <s xml:id="echoid-s5266" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5267" xml:space="preserve">eiuſdem plani inclinatione ad Horizontem, inueniatur ex propoſ. </s>
            <s xml:id="echoid-s5268" xml:space="preserve">25. </s>
            <s xml:id="echoid-s5269" xml:space="preserve">hu
              <lb/>
            ius lib. </s>
            <s xml:id="echoid-s5270" xml:space="preserve">minor diameter Ellipſis, quam perpendiculares à circunferentia plani inclinati (quod in
              <lb/>
              <figure xlink:label="fig-0114-01" xlink:href="fig-0114-01a" number="79">
                <image file="0114-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0114-01"/>
              </figure>
            ſphæra circulũ facit, ex propoſ. </s>
            <s xml:id="echoid-s5271" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5272" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5273" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5274" xml:space="preserve">Theod.)
              <lb/>
            </s>
            <s xml:id="echoid-s5275" xml:space="preserve">ad Horizontis planum demiſſę, ex propoſ. </s>
            <s xml:id="echoid-s5276" xml:space="preserve">24. </s>
            <s xml:id="echoid-s5277" xml:space="preserve">
              <lb/>
            huius lib. </s>
            <s xml:id="echoid-s5278" xml:space="preserve">faciunt, quæ ſit HI, maiorem diame-
              <lb/>
            trum F G, ſecans in centro E, ad angulos rectos. </s>
            <s xml:id="echoid-s5279" xml:space="preserve">
              <lb/>
            lam ex coroll. </s>
            <s xml:id="echoid-s5280" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s5281" xml:space="preserve">26. </s>
            <s xml:id="echoid-s5282" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5283" xml:space="preserve">circa dia-
              <lb/>
            metros F G, H I, datas deſcribatur Ellipſis, vel
              <lb/>
            certè eius pars, ſecans A C, communem ſectio-
              <lb/>
            nem Horizontis, ac Meridiani in K, puncto, per
              <lb/>
              <note position="left" xlink:label="note-0114-01" xlink:href="note-0114-01a" xml:space="preserve">10</note>
            quod ipſi A C, perpendicularis ducatur K L, ſe-
              <lb/>
            cãs Horizontis circunferentiã in L. </s>
            <s xml:id="echoid-s5284" xml:space="preserve">Dico arcum
              <lb/>
            C L, æqualẽ eſſe arcui Meridiani circuli inter
              <lb/>
            Horizontem, & </s>
            <s xml:id="echoid-s5285" xml:space="preserve">planum inclinatum interpoſito.
              <lb/>
            </s>
            <s xml:id="echoid-s5286" xml:space="preserve">Intelligatur enim ſemicirculus Meridiani AMC,
              <lb/>
            ad Horizontẽ A B C D, rectus; </s>
            <s xml:id="echoid-s5287" xml:space="preserve">& </s>
            <s xml:id="echoid-s5288" xml:space="preserve">M, punctum,
              <lb/>
            in quo planum inclinatum ſecat Meridianum,
              <lb/>
            ita vt arcus C M, ſit inter Horizontem, & </s>
            <s xml:id="echoid-s5289" xml:space="preserve">pla-
              <lb/>
            num ipſum. </s>
            <s xml:id="echoid-s5290" xml:space="preserve">Ducantur quoque rectæ E L,
              <lb/>
            E M, C L, C M. </s>
            <s xml:id="echoid-s5291" xml:space="preserve">Quoniam igitur perpendicularis ex M, ad Horizontem demiſſa cadit in rectam
              <lb/>
              <note position="left" xlink:label="note-0114-02" xlink:href="note-0114-02a" xml:space="preserve">38. vndec.</note>
              <note position="left" xlink:label="note-0114-03" xlink:href="note-0114-03a" xml:space="preserve">20</note>
            A C, communem ſectionem Horizontis, ac Meridiani, quòd Meridianus ad Horizontem rectus
              <lb/>
            ſit; </s>
            <s xml:id="echoid-s5292" xml:space="preserve">cadit autem, per propoſ. </s>
            <s xml:id="echoid-s5293" xml:space="preserve">24. </s>
            <s xml:id="echoid-s5294" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5295" xml:space="preserve">& </s>
            <s xml:id="echoid-s5296" xml:space="preserve">in Ellipſim, quam perpendiculares à punctis circunfe
              <lb/>
            rentiæ plani inclinati, quorum vnum eſt M, in planum Horizontis cadentes efficiunt; </s>
            <s xml:id="echoid-s5297" xml:space="preserve">perſpicuũ
              <lb/>
            eſt, perpendicularem ex M, cadere in punctum K, vbi Ellipſis rectam A C, ſecat. </s>
            <s xml:id="echoid-s5298" xml:space="preserve">Cadat ergo, & </s>
            <s xml:id="echoid-s5299" xml:space="preserve">
              <lb/>
            ſit M K, eritq́ue propterea tam angulus E K M, quàm C K M, rectus, per definitionem 3. </s>
            <s xml:id="echoid-s5300" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5301" xml:space="preserve">11.
              <lb/>
            </s>
            <s xml:id="echoid-s5302" xml:space="preserve">Euclidis. </s>
            <s xml:id="echoid-s5303" xml:space="preserve">Quare tam quadratum ex E L, quadratis ex E K, K L, quàm quadratum ex E M, quadra
              <lb/>
              <note position="left" xlink:label="note-0114-04" xlink:href="note-0114-04a" xml:space="preserve">47. primi.</note>
            tis ex E K, K M, æquale erit: </s>
            <s xml:id="echoid-s5304" xml:space="preserve">Ac propterea, cum quadrata rectarum æqualium E L, E M, (Ducun-
              <lb/>
            tur enim ex centro ſphæræ ad eius ſuperficiem.) </s>
            <s xml:id="echoid-s5305" xml:space="preserve">æqualia ſint; </s>
            <s xml:id="echoid-s5306" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s5307" xml:space="preserve">quadrata ex E K, K L, qua-
              <lb/>
            dratis ex E K, K M, æqualia; </s>
            <s xml:id="echoid-s5308" xml:space="preserve">Et dempto quadrato ex E K, cõmuni, æquale erit quadratum ex K L,
              <lb/>
            quadrato ex K M, atq; </s>
            <s xml:id="echoid-s5309" xml:space="preserve">adeò & </s>
            <s xml:id="echoid-s5310" xml:space="preserve">recta K L, rectæ K M, æqualis erit. </s>
            <s xml:id="echoid-s5311" xml:space="preserve">Itaque cum in triangulis C K L,
              <lb/>
              <note position="left" xlink:label="note-0114-05" xlink:href="note-0114-05a" xml:space="preserve">30</note>
            C K M, latera K L, K C, lateribus K M, K C, ſint ęqualia, angulosq́ue contineant ęquales, vtpo-
              <lb/>
              <note position="left" xlink:label="note-0114-06" xlink:href="note-0114-06a" xml:space="preserve">4. primi.</note>
            te rectos; </s>
            <s xml:id="echoid-s5312" xml:space="preserve">ęqualis erit baſis C L, baſi C M, ac idcirco & </s>
            <s xml:id="echoid-s5313" xml:space="preserve">arcus C L, arcui C M, Meridiani inter Ho
              <lb/>
              <note position="left" xlink:label="note-0114-07" xlink:href="note-0114-07a" xml:space="preserve">28. tertij.</note>
            rizontem, & </s>
            <s xml:id="echoid-s5314" xml:space="preserve">planum inclinatum poſito ęqualis erit. </s>
            <s xml:id="echoid-s5315" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s5316" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5317" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s5318" xml:space="preserve">Sit Horizon A B C D, Meridianus A C G, planum & </s>
            <s xml:id="echoid-s5319" xml:space="preserve">ad Horizontem, & </s>
            <s xml:id="echoid-s5320" xml:space="preserve">ad
              <lb/>
              <note position="left" xlink:label="note-0114-08" xlink:href="note-0114-08a" xml:space="preserve">Arcus Metidia
                <lb/>
              ni inter Hori-
                <lb/>
              zontẽ & planũ
                <lb/>
              inclinatum po-
                <lb/>
              ſitus, quomodo
                <lb/>
              inquiratur per
                <lb/>
              ſinus.</note>
            Meridianum inclinatum E F, ſecans Meridianum in G, ſiue infra Horizontem, ſiue ſupra, vt C G,
              <lb/>
              <figure xlink:label="fig-0114-02" xlink:href="fig-0114-02a" number="80">
                <image file="0114-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0114-02"/>
              </figure>
            arcus ſit inter Horizontem, & </s>
            <s xml:id="echoid-s5321" xml:space="preserve">pla-
              <lb/>
            num inclinatum interpoſitus. </s>
            <s xml:id="echoid-s5322" xml:space="preserve">Quo
              <lb/>
            niam igitur in ſphęrico triangulo
              <lb/>
            C F G, cuius angulus C, rectus eſt,
              <lb/>
            quòd Meridianus rectus ſit ad Ho-
              <lb/>
              <note position="left" xlink:label="note-0114-09" xlink:href="note-0114-09a" xml:space="preserve">40</note>
            rizontem; </s>
            <s xml:id="echoid-s5323" xml:space="preserve">vt ſinus arcus C F, nem-
              <lb/>
            pe cõplementi declinationis D F,
              <lb/>
            à Verticali circulo, ad ſinum angu-
              <lb/>
            li G, inclinationis plani E F, ad Me
              <lb/>
            ridianum, ita eſt, per propoſ. </s>
            <s xml:id="echoid-s5324" xml:space="preserve">16. </s>
            <s xml:id="echoid-s5325" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s5326" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5327" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s5328" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s5329" xml:space="preserve">de triangulis, vel
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s5330" xml:space="preserve">13. </s>
            <s xml:id="echoid-s5331" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5332" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5333" xml:space="preserve">Gebri, vel cer-
              <lb/>
            tè ex propoſ. </s>
            <s xml:id="echoid-s5334" xml:space="preserve">41. </s>
            <s xml:id="echoid-s5335" xml:space="preserve">noſtrorum trian-
              <lb/>
            gulorum ſphęricorum, ſinus arcus
              <lb/>
            C G, inter Horizontem, & </s>
            <s xml:id="echoid-s5336" xml:space="preserve">planũ
              <lb/>
              <note position="left" xlink:label="note-0114-10" xlink:href="note-0114-10a" xml:space="preserve">50</note>
            inclinatum, ad ſinũ anguli F, inclinationis plani ad Horizontẽ; </s>
            <s xml:id="echoid-s5337" xml:space="preserve">erit quoque conuertendo, vt ſinus
              <lb/>
            anguli G, inclinationis ad Meridianũ, ad ſinum arcus C F, complementi declinationis à Verticali,
              <lb/>
            ita ſinus anguli F, inclinationis ad Horizontẽ, ad ſinum arcus Meridiani C G, inter Horizontem,
              <lb/>
            & </s>
            <s xml:id="echoid-s5338" xml:space="preserve">planum inclinatum intercepti. </s>
            <s xml:id="echoid-s5339" xml:space="preserve">Quamobrem, inuenta per propoſ. </s>
            <s xml:id="echoid-s5340" xml:space="preserve">23, huius lib. </s>
            <s xml:id="echoid-s5341" xml:space="preserve">declinatione pla
              <lb/>
            ni propoſiti à circulo Verticali, atque inclinatione eiuſdem ad Horizontem. </s>
            <s xml:id="echoid-s5342" xml:space="preserve">Item inclinatione
              <lb/>
            eiuſdem ad Meridianum, ex propoſ. </s>
            <s xml:id="echoid-s5343" xml:space="preserve">antecedente; </s>
            <s xml:id="echoid-s5344" xml:space="preserve">ſi fiat, vt ſinus inclinationis ad Meridianum ad
              <lb/>
            ſinum cõplementi declinationis à Verticali, ita ſinus inclinationis ad Horizontem, ad aliud, habe-
              <lb/>
            bitur ſinus illius arcus Meridiani, qui inter Horizontem, & </s>
            <s xml:id="echoid-s5345" xml:space="preserve">planum inclinatum interiicitur.</s>
            <s xml:id="echoid-s5346" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5347" xml:space="preserve">EXEMPLVM. </s>
            <s xml:id="echoid-s5348" xml:space="preserve">Ponatur inclinatio ad Meridianum grad. </s>
            <s xml:id="echoid-s5349" xml:space="preserve">66. </s>
            <s xml:id="echoid-s5350" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5351" xml:space="preserve">47. </s>
            <s xml:id="echoid-s5352" xml:space="preserve">Declinatio à Vertica-
              <lb/>
            li grad. </s>
            <s xml:id="echoid-s5353" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5354" xml:space="preserve">& </s>
            <s xml:id="echoid-s5355" xml:space="preserve">inclinatio ad Horizontem grad. </s>
            <s xml:id="echoid-s5356" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5357" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5358" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5359" xml:space="preserve">Si igitur fiat, vt 91902. </s>
            <s xml:id="echoid-s5360" xml:space="preserve">ſinus inclinatio-
              <lb/>
            nis ad Meridianum ad 86602. </s>
            <s xml:id="echoid-s5361" xml:space="preserve">ſinum complementi declinationis à Verticali, ita 78854. </s>
            <s xml:id="echoid-s5362" xml:space="preserve">ſinus </s>
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