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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        <div xml:id="echoid-div426" type="section" level="1" n="138">
          <p>
            <s xml:id="echoid-s8576" xml:space="preserve">
              <pb o="135" file="0155" n="155" rhead="LIBER PRIMVS."/>
            altitudinis poli, & </s>
            <s xml:id="echoid-s8577" xml:space="preserve">arcus anguli A.) </s>
            <s xml:id="echoid-s8578" xml:space="preserve">ad ſinum arcus k M, declinationis, ita ſinus anguli recti M,
              <lb/>
            hoc eſt, ita ſinus totus ad ſinum arcus A K, altitudinis poli. </s>
            <s xml:id="echoid-s8579" xml:space="preserve">Quare ſi fiat, vt ſinus altitudinis poli
              <lb/>
            ad ſinum declinationis, ita ſinus totus ad aliud, reperietur rurſus ſinus altitudinis Solis in Vertica-
              <lb/>
            li circulo. </s>
            <s xml:id="echoid-s8580" xml:space="preserve">Quod etiam ſupra demonſtrauimus ſine triangulis ſphæricis.</s>
            <s xml:id="echoid-s8581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8582" xml:space="preserve">INSVPER cum Sol in parallelis borealibus diſtat à meridie ſex horis, vt in ſexta figura, nul
              <lb/>
              <note position="right" xlink:label="note-0155-01" xlink:href="note-0155-01a" xml:space="preserve">Altitudo Solis,
                <lb/>
              cum Sol ſex ho-
                <lb/>
              ris abeſt à meri-
                <lb/>
              die in parallelis
                <lb/>
              borealibus, qua
                <lb/>
              rati one per ſphę
                <lb/>
              rica triangula
                <lb/>
              inueſtiganda.</note>
            lius erit negotij altitudinem eius in ueſtigare. </s>
            <s xml:id="echoid-s8583" xml:space="preserve">Quia enim in ſphærico triangulo E L N, figuræ
              <lb/>
            ſextæ angulus N, rectus eſt, per propoſ. </s>
            <s xml:id="echoid-s8584" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8585" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8586" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8587" xml:space="preserve">Theodoſij, quòd maximus circulus N A, per A,
              <lb/>
            polum Meridiani ductus ſit; </s>
            <s xml:id="echoid-s8588" xml:space="preserve">erit per propoſ. </s>
            <s xml:id="echoid-s8589" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8590" xml:space="preserve">lib 4. </s>
            <s xml:id="echoid-s8591" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8592" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8593" xml:space="preserve">de triangulis, vel per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s8594" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8595" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8596" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8597" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s8598" xml:space="preserve">43. </s>
            <s xml:id="echoid-s8599" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus comple-
              <lb/>
            menti arcus E N, hoc eſt, vt ſinus arcus E F, altitudinis poli, ad ſinum totum, ita ſinus comple-
              <lb/>
              <note position="left" xlink:label="note-0155-02" xlink:href="note-0155-02a" xml:space="preserve">10</note>
            menti arcus E L, hoc eſt, ita ſinus arcus L O, altitudinis Solis, ad ſinum complementi arcus N L,
              <lb/>
            id eſt, ad ſinum arcus L A, declinationis. </s>
            <s xml:id="echoid-s8600" xml:space="preserve">Conuertendo ergo erit quoque, vt ſinus totus ad ſinum
              <lb/>
            altitudinis poli, ita ſinus declinationis ad ſinum altitudinis Solis. </s>
            <s xml:id="echoid-s8601" xml:space="preserve">Quocirca ſi fiat, vt ſinus totus ad
              <lb/>
            ſinum altitudinis poli, ita ſinus declinationis ad aliud, habebitur linus altitudinis Solis. </s>
            <s xml:id="echoid-s8602" xml:space="preserve">Quod
              <lb/>
            etiam ſupra demonſtrauimus ſine triangulis ſphęricis.</s>
            <s xml:id="echoid-s8603" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8604" xml:space="preserve">ADHVC ſole puncta æquinoctiorũ poſſidente, ſine magno labore ex hora cognita, ſiue ex
              <lb/>
              <note position="right" xlink:label="note-0155-03" xlink:href="note-0155-03a" xml:space="preserve">Altitudo Solis
                <lb/>
              in ęquiuoctiis,
                <lb/>
              quo pacto ex da
                <lb/>
              ta hora per triã
                <lb/>
              gula ſphęrica in
                <lb/>
              daganda.</note>
            diſtantia Solis à meridie, altitudinem Solis eliciemus per ſphęrica triãgula hoc modo. </s>
            <s xml:id="echoid-s8605" xml:space="preserve">Intelligatur
              <lb/>
            in quinta figura Aequator eſle G H I, & </s>
            <s xml:id="echoid-s8606" xml:space="preserve">Sol exiſtere in k, ne cogamur nouam figurã deſcribere.
              <lb/>
            </s>
            <s xml:id="echoid-s8607" xml:space="preserve">Quia igitur in triangulo ſphærico E H K, angulus H, rectus eſt, erit per propoſ. </s>
            <s xml:id="echoid-s8608" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8609" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8610" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8611" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8612" xml:space="preserve">
              <lb/>
            Regiom. </s>
            <s xml:id="echoid-s8613" xml:space="preserve">vel per propoſ. </s>
            <s xml:id="echoid-s8614" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8615" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8616" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8617" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s8618" xml:space="preserve">43. </s>
            <s xml:id="echoid-s8619" xml:space="preserve">noſtrorum triangulorum ſphærico-
              <lb/>
              <note position="left" xlink:label="note-0155-04" xlink:href="note-0155-04a" xml:space="preserve">20</note>
            rum, vt ſinus complementiarcus E H, hoc eſt, vt ſinus arcus H B, altitudinis Aequatoris, vel com
              <lb/>
            plementi altitudinis poli, ad ſinum totum, ita ſinus complementi arcus E K, id eſt, ita ſinus arcus
              <lb/>
            K A, altitudinis Solis, ad ſinum complementi arcus H K, diſtantie Solis à meridie. </s>
            <s xml:id="echoid-s8620" xml:space="preserve">Quare erit etiã
              <lb/>
            conuertendo, vt ſinus totus ad ſinum complementi altitndinis poli, ita ſinus complementi diſtan-
              <lb/>
            tię Solis à meridie, ad ſinum altitudinis Solis; </s>
            <s xml:id="echoid-s8621" xml:space="preserve">Ac propterea ſi fiat, vt ſinus totus ad ſinum com-
              <lb/>
            plementi altitudinis poli, ita ſinus complementi diſtantię Solis à meridiead aliud, cognitus erit
              <lb/>
            ſinus altitudinis Solis.</s>
            <s xml:id="echoid-s8622" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8623" xml:space="preserve">ALIA quoque ratione per triangula ſphęrica, & </s>
            <s xml:id="echoid-s8624" xml:space="preserve">commodius fortaſſe, ſine circulo A L P, repe
              <lb/>
              <note position="right" xlink:label="note-0155-05" xlink:href="note-0155-05a" xml:space="preserve">Altitudo Solis
                <lb/>
              quomodo aliter
                <lb/>
              per ſphærica
                <lb/>
              triangula ex da-
                <lb/>
              ta hora inueſti-
                <lb/>
              ganda.</note>
            riemus altitudinem Solis ex hora cognita, quæ eiuſmodi eſt. </s>
            <s xml:id="echoid-s8625" xml:space="preserve">Producatur circulus declinationis
              <lb/>
            N L, ad partes L, donec Horizontem ſecet in Q. </s>
            <s xml:id="echoid-s8626" xml:space="preserve">Et quoniam angulus F N M, diſtantiæ Solis à
              <lb/>
              <note position="left" xlink:label="note-0155-06" xlink:href="note-0155-06a" xml:space="preserve">30</note>
            meridie cognitus eſt, erit & </s>
            <s xml:id="echoid-s8627" xml:space="preserve">Q N D, reliquus duorum rectorum notus. </s>
            <s xml:id="echoid-s8628" xml:space="preserve">Cum ergo in triangulo
              <lb/>
            ſphęrico D N Q, cuius angulus D, rectus, & </s>
            <s xml:id="echoid-s8629" xml:space="preserve">D N Q, notus eſt, vnà cum arcu D N, altitudinis po-
              <lb/>
            li, ſit per propoſ. </s>
            <s xml:id="echoid-s8630" xml:space="preserve">18 lib. </s>
            <s xml:id="echoid-s8631" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8632" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8633" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8634" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s8635" xml:space="preserve">14. </s>
            <s xml:id="echoid-s8636" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8637" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8638" xml:space="preserve">Gebri, vel per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s8639" xml:space="preserve">42. </s>
            <s xml:id="echoid-s8640" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus anguli D N Q, ad ſinum totum, ita ſinus
              <lb/>
            complementi anguli D Q N, ad ſinum complementi arcus D N, altitudinis poli; </s>
            <s xml:id="echoid-s8641" xml:space="preserve">erit conuerten-
              <lb/>
            do, vt ſinus totus ad ſinum anguli D N Q, ita ſinus complementi arcus D N, altitudinis poli
              <lb/>
            ad ſinum complementi anguli D Q N: </s>
            <s xml:id="echoid-s8642" xml:space="preserve">atque adeo angulus ipſe D Q N, cognitus erit. </s>
            <s xml:id="echoid-s8643" xml:space="preserve">Rurſus
              <lb/>
            quia in eodem triangulo ſphęrico D N Q, eſt per propoſ. </s>
            <s xml:id="echoid-s8644" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8645" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8646" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8647" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8648" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8649" xml:space="preserve">de triangulis, vel
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s8650" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8651" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8652" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8653" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s8654" xml:space="preserve">41. </s>
            <s xml:id="echoid-s8655" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus an-
              <lb/>
            guli D Q N, noti iam facti ad ſinum arcus D N, altitudinis poli, ita ſinus totus anguli recti D, ad
              <lb/>
              <note position="left" xlink:label="note-0155-07" xlink:href="note-0155-07a" xml:space="preserve">40</note>
            ſinum arcus N Q; </s>
            <s xml:id="echoid-s8656" xml:space="preserve">cognitus erit ſinus arcus N Q, ex quo perueſtig@bimus arcũ ipſum N Q, hac
              <lb/>
            ratione. </s>
            <s xml:id="echoid-s8657" xml:space="preserve">Quando in ſignis borealibus diſtantia Solis à meridie maior fuerit, quàm hor. </s>
            <s xml:id="echoid-s8658" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8659" xml:space="preserve">vt in
              <lb/>
            tertia figura accidit, dabit arcus ex tabula ſinum erutus arcum N Q; </s>
            <s xml:id="echoid-s8660" xml:space="preserve">quia arcus N Q, minor
              <lb/>
            quadrante tunc eſt, propterea quòd arcus ex polo N, per Q, vſque ad Aequatorem productus qua-
              <lb/>
            drans eſt. </s>
            <s xml:id="echoid-s8661" xml:space="preserve">Quando vero diſtantia Solis à meridie minor fuerit, quàm hor. </s>
            <s xml:id="echoid-s8662" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8663" xml:space="preserve">vt in figura prima, ſe-
              <lb/>
            cunda, & </s>
            <s xml:id="echoid-s8664" xml:space="preserve">quarta apparet, in quocunque parallelo ſiue boreali, ſiue auſtrali Sol commoretur, erit
              <lb/>
            arcus N Q, quadrante maior: </s>
            <s xml:id="echoid-s8665" xml:space="preserve">quoniam vero, vt in tractatu ſinuum oſtendimus, idem ſinus eſt ar-
              <lb/>
            cus N Q, & </s>
            <s xml:id="echoid-s8666" xml:space="preserve">reliqui ex ſemicirculo, auferemus arcum ſinus inuenti ex ſemicirculo, vt habeamus
              <lb/>
            arcum N Q. </s>
            <s xml:id="echoid-s8667" xml:space="preserve">Quando denique diſtantia Solis à meridie comprehendit hor. </s>
            <s xml:id="echoid-s8668" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8669" xml:space="preserve">nihil hic pręcipi-
              <lb/>
            mus, quia tunc, vt in fra docebimus, multo facilius altitudo Solis inquiritur: </s>
            <s xml:id="echoid-s8670" xml:space="preserve">Eſſet tamen tuncarcus
              <lb/>
              <note position="left" xlink:label="note-0155-08" xlink:href="note-0155-08a" xml:space="preserve">50</note>
            NQ, quadrans, quia punctũ Q, caderet in punctũ A Inuento autem hac ratione arcu N Q, repe
              <lb/>
            riendus eſt ex eo arcus L Q, hoc modo. </s>
            <s xml:id="echoid-s8671" xml:space="preserve">In parallelis borealibus ex arcu inuento N Q, detrahatur
              <lb/>
            arcus N L, cõplementi declinationis; </s>
            <s xml:id="echoid-s8672" xml:space="preserve">In auſtralibus autem parallelis ex eodem arcu inuento N Q,
              <lb/>
            auferatur arcus N L, compoſitus ex quadrante N M, & </s>
            <s xml:id="echoid-s8673" xml:space="preserve">arcu declinationis M L, vt in quarta figura
              <lb/>
            apparet. </s>
            <s xml:id="echoid-s8674" xml:space="preserve">Semper enim reliquus erit arcus L Q. </s>
            <s xml:id="echoid-s8675" xml:space="preserve">Iam vero quoniam in triangulo ſphærico L O Q,
              <lb/>
            angulus O, rectus eſt, & </s>
            <s xml:id="echoid-s8676" xml:space="preserve">L Q O, notus paulo ante factus, vna cum arcu L Q; </s>
            <s xml:id="echoid-s8677" xml:space="preserve">eſtq́; </s>
            <s xml:id="echoid-s8678" xml:space="preserve">per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s8679" xml:space="preserve">16. </s>
            <s xml:id="echoid-s8680" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8681" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8682" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8683" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8684" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s8685" xml:space="preserve">13. </s>
            <s xml:id="echoid-s8686" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8687" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8688" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s8689" xml:space="preserve">41. </s>
            <s xml:id="echoid-s8690" xml:space="preserve">noſtrorũ
              <lb/>
            triangulorum ſphæricorum, vt ſinus totus anguli recti O, ad ſinum arcus L Q, noti, ita ſinus an-
              <lb/>
            guli L Q O. </s>
            <s xml:id="echoid-s8691" xml:space="preserve">noti ad ſinum arcus L O, altitudinis Solis; </s>
            <s xml:id="echoid-s8692" xml:space="preserve">cognita fiet Solis altitudo. </s>
            <s xml:id="echoid-s8693" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0155-09" xlink:href="note-0155-09a" xml:space="preserve">Inuentum pri-
                <lb/>
              mum.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s8694" xml:space="preserve">ITAQVE ſi fiat, vt ſinus totus ad ſinum anguli D N Q, qui relinquitur, ablato angulo di-
              <lb/>
            ſtantiæ Solis à meridie ex duobus rectis, ita ſinus complementi altitudinis poli ad aliud, </s>
          </p>
        </div>
      </text>
    </echo>
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