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-s8898" xml:space="preserve">
              <pb o="138" file="0158" n="158" rhead="GNOMONICES"/>
            gulo E k N, figuræ quintæ angulus E, rectus eſt, erit per propoſ. </s>
            <s xml:id="echoid-s8899" xml:space="preserve">16. </s>
            <s xml:id="echoid-s8900" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8901" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8902" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8903" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8904" xml:space="preserve">de triangu
              <lb/>
            lis, vel per Propoſ. </s>
            <s xml:id="echoid-s8905" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8906" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8907" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8908" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s8909" xml:space="preserve">41. </s>
            <s xml:id="echoid-s8910" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt
              <lb/>
            ſinusarcus N k, complementi declinationis ad ſinum anguli recti E, id eſt, ad ſinum totum, ita ſi-
              <lb/>
            nus arcus E K, complementi altitudinis Solis ad ſinum anguli N, diſtantiæ Solis à meridie. </s>
            <s xml:id="echoid-s8911" xml:space="preserve">Itaque
              <lb/>
            ſi fiat, vt ſinus complementi declinationis ad ſinum to@um, ita ſinus complementi altitudinis So-
              <lb/>
            lis in Verticali circulo ad aliud, inueniet ur ſinus diſtantiæ Solis à meridie.</s>
            <s xml:id="echoid-s8912" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8913" xml:space="preserve">VNDE ſi quæratur, qua hora Sol in Verticali circulo reperiatur, inuenienda primum erit al-
              <lb/>
              <note position="left" xlink:label="note-0158-01" xlink:href="note-0158-01a" xml:space="preserve">Qua hora Sol
                <lb/>
              in Verticali cir
                <lb/>
              culo exiſtat.</note>
            titudo Solis in Verticali circulo, vt ſupra docuimus, etiamſi ignota ſit diſtantia Solis à meridie:
              <lb/>
            </s>
            <s xml:id="echoid-s8914" xml:space="preserve">Deinde ex hac altitudine exploranda diſtantia Solis à meridie, vt proxime oſtendimus.</s>
            <s xml:id="echoid-s8915" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8916" xml:space="preserve">SOLE in Aequatore exiſtente, facili etiam negotio ex altitudine Solis horam inquiremus.
              <lb/>
            </s>
            <s xml:id="echoid-s8917" xml:space="preserve">
              <note position="left" xlink:label="note-0158-02" xlink:href="note-0158-02a" xml:space="preserve">Hora qua via
                <lb/>
              in æquinoctijs
                <lb/>
              ex altiuidine
                <lb/>
              Solis nota explo
                <lb/>
              ianda.</note>
              <note position="left" xlink:label="note-0158-03" xlink:href="note-0158-03a" xml:space="preserve">10</note>
            Quoniam enim in ſphærico triangulo E H K, quintæ figurę, ſi intelligatur Aequator eſſe G H I, & </s>
            <s xml:id="echoid-s8918" xml:space="preserve">
              <lb/>
            Sol in K, vt ſupra diximus, angulus H, rectus eſt, erit per propoſ. </s>
            <s xml:id="echoid-s8919" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8920" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8921" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8922" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8923" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8924" xml:space="preserve">de trian-
              <lb/>
            gulis, vel per propoſ. </s>
            <s xml:id="echoid-s8925" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8926" xml:space="preserve">hb. </s>
            <s xml:id="echoid-s8927" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8928" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s8929" xml:space="preserve">43. </s>
            <s xml:id="echoid-s8930" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt
              <lb/>
            ſmus complementi arcus EH, altitudinis poli, ad ſinum totum, ita ſinus complementi arcus E K,
              <lb/>
            hoc eſt, ita ſinus arcus A K, altitudinis Solis, ad ſinum complementi arcus H K, diſtantię Solis à
              <lb/>
            meridie. </s>
            <s xml:id="echoid-s8931" xml:space="preserve">Quare ſi hat, vt ſinus complementi altitudinis poli ad ſinum totum, ita ſinus altitudinis
              <lb/>
            Solis ad aliud, inuenietur ſinus complementi diſtantię Solis à meridie.</s>
            <s xml:id="echoid-s8932" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8933" xml:space="preserve">IDEM quoque aliter demonſtrabimus. </s>
            <s xml:id="echoid-s8934" xml:space="preserve">Quia enim in triangulo ſphærico A G K, angulus A,
              <lb/>
            rectus eſt, per propoſ. </s>
            <s xml:id="echoid-s8935" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8936" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8937" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8938" xml:space="preserve">Theodoſii, quòd circulus maximus E A, per polum Horizontis E,
              <lb/>
            ductus ſit, erit per propoſ. </s>
            <s xml:id="echoid-s8939" xml:space="preserve">16. </s>
            <s xml:id="echoid-s8940" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8941" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8942" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8943" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8944" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s8945" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8946" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8947" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8948" xml:space="preserve">Gebri,
              <lb/>
              <note position="left" xlink:label="note-0158-04" xlink:href="note-0158-04a" xml:space="preserve">20</note>
            vel per propoſ. </s>
            <s xml:id="echoid-s8949" xml:space="preserve">41. </s>
            <s xml:id="echoid-s8950" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus anguli G, complementi altitu-
              <lb/>
            dinis poli, (Si enim Aequator ponatur G H I, erit angulus G, reſpondens arcui H B, altitudinis
              <lb/>
            Aequatoris, ſeu complementi altitudinis poli) ad ſinum arcus A k, altitudinis Solis, ita ſinus an-
              <lb/>
            guli A, recti, id eſt, ita ſinus totus, ad ſinum arcus Gk, altitudinis Solis, ita ſinus an-
              <lb/>
            Si igitur fiat, vt ſinus complementi altitudinis poli, ad ſinum altitudinis Solis, ita ſinus totusad
              <lb/>
            aliud, notus fiet ſinus complementi diſtantiæ Solis à meridie.</s>
            <s xml:id="echoid-s8951" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8952" xml:space="preserve">POSTREMO in ſphæra recta ita procedemus. </s>
            <s xml:id="echoid-s8953" xml:space="preserve">Sole exiſtente in æquinoctiis, accipiemus
              <lb/>
              <note position="left" xlink:label="note-0158-05" xlink:href="note-0158-05a" xml:space="preserve">Quo pacto in
                <lb/>
              ſphæra recta rẽ-
                <lb/>
              pore ęquinoctio
                <lb/>
              rum reperienda
                <lb/>
              ſit hora ex alti-
                <lb/>
              dine Solis.</note>
              <figure xlink:label="fig-0158-01" xlink:href="fig-0158-01a" number="115">
                <image file="0158-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0158-01"/>
              </figure>
            cõplementum altitudinis Solis pro diſtantia eiuſdẽ
              <lb/>
            à meridie. </s>
            <s xml:id="echoid-s8954" xml:space="preserve">Nã in appoſita figura, quam pro ſphæra
              <lb/>
            recta conſtruximus, arcus EI, diſtantiæ Solis à meri
              <lb/>
              <note position="left" xlink:label="note-0158-06" xlink:href="note-0158-06a" xml:space="preserve">30</note>
            die, complementũ eſt arcus A I, altitudinis Solis.</s>
            <s xml:id="echoid-s8955" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8956" xml:space="preserve">QVANDO verò Sol in aliquo alio parallelo
              <lb/>
              <note position="left" xlink:label="note-0158-07" xlink:href="note-0158-07a" xml:space="preserve">Qua ratione in
                <lb/>
              ſphæra recta ſit
                <lb/>
              indaganda ho-
                <lb/>
              ra ex al titudine
                <lb/>
              Solis in quocũ-
                <lb/>
              que parallelo
                <lb/>
              exiſtentis.</note>
            exiſtit, vt in K; </s>
            <s xml:id="echoid-s8957" xml:space="preserve">quoniã in triangulo ſphærico E I K,
              <lb/>
            angulus I, rectus eſt, erit per propoſ. </s>
            <s xml:id="echoid-s8958" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8959" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8960" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8961" xml:space="preserve">Ioan.
              <lb/>
            </s>
            <s xml:id="echoid-s8962" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8963" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s8964" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8965" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8966" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8967" xml:space="preserve">Ge-
              <lb/>
            bri, vel per propoſ. </s>
            <s xml:id="echoid-s8968" xml:space="preserve">43. </s>
            <s xml:id="echoid-s8969" xml:space="preserve">noſtrorum triangulorũ ſphæ
              <lb/>
            ricorum, vt ſinus complemẽti arcus Ik, declinatio-
              <lb/>
            nis paralleli propoſiti, ad ſinum totum, ita ſinus cõ-
              <lb/>
            plementi arcus E K, hoc eſt, ita ſinus arcus K L, alti
              <lb/>
            tudinis Solis, ad ſinum complementi arcus E I, di-
              <lb/>
              <note position="left" xlink:label="note-0158-08" xlink:href="note-0158-08a" xml:space="preserve">40</note>
            ſtantiæ Solis à meridie. </s>
            <s xml:id="echoid-s8970" xml:space="preserve">Quamobrem ſi fiat, vt ſinus
              <lb/>
            complementi declinationis Solis ad ſinum totum,
              <lb/>
            ita ſinus altitudinis Solis ad aliud, notus fiet ſinus
              <lb/>
            cõplementi diſtantiæ Solis à meridie. </s>
            <s xml:id="echoid-s8971" xml:space="preserve">Igitur ex co-
              <lb/>
            gnita diei hora altitudinem Solis ſupra Horizontem: </s>
            <s xml:id="echoid-s8972" xml:space="preserve">Et contra ex altitudine Solis nota horam dioi
              <lb/>
            cognouimus. </s>
            <s xml:id="echoid-s8973" xml:space="preserve">Quod erar faciendum.</s>
            <s xml:id="echoid-s8974" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div491" type="section" level="1" n="139">
          <head xml:id="echoid-head142" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s8975" xml:space="preserve">QVANDO inueniendæ ſunt altitudines Solis pro ſingulis horis duorum parallelorum oppoſito-
              <lb/>
              <note position="left" xlink:label="note-0158-09" xlink:href="note-0158-09a" xml:space="preserve">50</note>
            rum, quales ſunt v. </s>
            <s xml:id="echoid-s8976" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8977" xml:space="preserve">duo tropici à principijs ♋, & </s>
            <s xml:id="echoid-s8978" xml:space="preserve">♑, deſcripti, quod non rarò vſu venit in conſtruen-
              <lb/>
            dis inſtrumentis horarijs, & </s>
            <s xml:id="echoid-s8979" xml:space="preserve">in deſcriptionibus horologiorum, perfacile reddetur totum negotium, ſi ea,
              <lb/>
            quæ iamiam explicabimus, attentè conſiderentur.</s>
            <s xml:id="echoid-s8980" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8981" xml:space="preserve">NAM ſi primo velimus modo vti, permanebit pro ſingulis horis vtriuſque paralleli eadem medietas
              <lb/>
              <note position="left" xlink:label="note-0158-10" xlink:href="note-0158-10a" xml:space="preserve">Qui numeti nõ
                <lb/>
              mutentur un-
                <lb/>
              quam, ſi per pri
                <lb/>
              mum modum
                <lb/>
              traditum inue-
                <lb/>
              ſtigentur altitu
                <lb/>
              dines S olis pro
                <lb/>
              ſingulis. horis
                <lb/>
              duorum paralle
                <lb/>
              lotum oppoſito
                <lb/>
              rum.</note>
            rectæ compoſitæ ex ſinu altitudinis meridianæ, & </s>
            <s xml:id="echoid-s8982" xml:space="preserve">ſinu depreſſionis meridianæ, ita vt ſemel inuenta huiuſ-
              <lb/>
            modi medietas adbibeatur ad omnium horarum altitudines perueſtigandas in duobus parallelis oppoſi-
              <lb/>
            tis. </s>
            <s xml:id="echoid-s8983" xml:space="preserve">Quia enim, vt in ſcholio antecedentis propoſ. </s>
            <s xml:id="echoid-s8984" xml:space="preserve">oſtendimus, depreſſio meridiana cuiuſcunque paralleli
              <lb/>
            æqualis eſt altitudini meridianæ paralleli oppoſiti, fit vt recta compoſita ex ſinu altitudinis meridianæ, et
              <lb/>
            ſinu depreſſionis meridianæ vnius paralleli, ſit æqualis rectæ compoſitæ ex ſinu altitudinis meridianæ, & </s>
            <s xml:id="echoid-s8985" xml:space="preserve">
              <lb/>
            ſinu depreſſionis meridianæ alterius paralleli oppoſiti, quandoquidem depreſſio meridiana illius æqualis
              <lb/>
            eſt altitudini meridianæ huius, & </s>
            <s xml:id="echoid-s8986" xml:space="preserve">huius meridiana depreſſio ęqualis illius altitudini meridianæ. </s>
            <s xml:id="echoid-s8987" xml:space="preserve">Vnde &</s>
            <s xml:id="echoid-s8988" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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