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-s35468" xml:space="preserve">
              <pb o="550" file="0566" n="566" rhead="GNOMONICES"/>
            ponatur rectus ad Meridianum. </s>
            <s xml:id="echoid-s35469" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s35470" xml:space="preserve">E Q, ipſi O P, ſinui circun ferentiæ deſcenſiuæ æqua-
              <lb/>
            lis erit. </s>
            <s xml:id="echoid-s35471" xml:space="preserve">Quia vero in triangulis E Q N, E S V, @ſt, vt E Q, ſinus circunferentiæ deſcenſiuæ, id eſt,
              <lb/>
            ſinus complementi altitudinis Solis ſupra Horizontem, ad Q N, hoc eſt, ad K L, illi æqualem, ſi-
              <lb/>
            num diſtantiæ Solis à meridie, ita E S, ſinus totus ad S V, ſinum complementi horizontalis cir-
              <lb/>
              <note position="left" xlink:label="note-0566-01" xlink:href="note-0566-01a" xml:space="preserve">Horizontalis.</note>
            cunferentiæ A S; </s>
            <s xml:id="echoid-s35472" xml:space="preserve">Si fiat, vt ſinus circunferentiæ deſcenſiuæ, hoc eſt, vt ſinus complementi altitu-
              <lb/>
            dinis Solis ſupra Horizontem, ad ſinum diſtantiæ Solis à meridie, ita ſinus totus ad aliud, repe-
              <lb/>
            rietur ſinus complementi circunferentiæ horizontalis. </s>
            <s xml:id="echoid-s35473" xml:space="preserve">Hoc ergo complementum, vna cum cir-
              <lb/>
            cunferentia horizontali, cognitum erit.</s>
            <s xml:id="echoid-s35474" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s35475" xml:space="preserve">PER triangula ſphærica ita eaſdẽ ſex circunferentias inquiremus, Sole extra Aequatorẽ exiſtẽ
              <lb/>
              <note position="left" xlink:label="note-0566-02" xlink:href="note-0566-02a" xml:space="preserve">Inuentio earũ-
                <lb/>
              dem ſex circun-
                <lb/>
              ferentiarum per
                <lb/>
              triangula ſphæ-
                <lb/>
              rica, Sole exiſtẽ-
                <lb/>
              te in quouis pa-
                <lb/>
              rallelo extra
                <lb/>
              Aequatorem,
                <lb/>
              dummodo ſit
                <lb/>
              in parallelo bo-
                <lb/>
              reali vltra Ver-
                <lb/>
              @icalem ex par-
                <lb/>
              t
                <unsure/>
              e auſtrali.</note>
              <figure xlink:label="fig-0566-01" xlink:href="fig-0566-01a" number="351">
                <image file="0566-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0566-01"/>
              </figure>
            te in quouis parallelo.
              <lb/>
            </s>
            <s xml:id="echoid-s35476" xml:space="preserve">
              <note position="left" xlink:label="note-0566-03" xlink:href="note-0566-03a" xml:space="preserve">10</note>
            Sit Horizon A B C D;
              <lb/>
            </s>
            <s xml:id="echoid-s35477" xml:space="preserve">Meridianus B E D; </s>
            <s xml:id="echoid-s35478" xml:space="preserve">
              <lb/>
            Aequator A F C; </s>
            <s xml:id="echoid-s35479" xml:space="preserve">Ver-
              <lb/>
            ticalis A E C; </s>
            <s xml:id="echoid-s35480" xml:space="preserve">Paralle-
              <lb/>
            lus Solis L M, ſiue au-
              <lb/>
            ſtralis, ſiue bore alis: </s>
            <s xml:id="echoid-s35481" xml:space="preserve">
              <lb/>
            ponaturq́ue primum
              <lb/>
            Sol in puncto G, vltra
              <lb/>
            Verticalem circulum,
              <lb/>
            vt contingit in omni-
              <lb/>
              <note position="left" xlink:label="note-0566-04" xlink:href="note-0566-04a" xml:space="preserve">20</note>
            bus horis paralleli au-
              <lb/>
            ſtralis ſupra Horizon-
              <lb/>
            tem; </s>
            <s xml:id="echoid-s35482" xml:space="preserve">in illis autẽ dun-
              <lb/>
            taxat horis paralleli bo
              <lb/>
            realis, quę minorem
              <lb/>
            diſtantiam habent à
              <lb/>
            Meridiano, quàm cum Sol in Verticali exiſtit, ſi tamen parallelus Solis Verticalem interſecat; </s>
            <s xml:id="echoid-s35483" xml:space="preserve">quæ
              <lb/>
            quidem diſtantia Solis à meridie in Verticali exiſtentis inuenietur ex ijs, quæ in propoſ. </s>
            <s xml:id="echoid-s35484" xml:space="preserve">36. </s>
            <s xml:id="echoid-s35485" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35486" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s35487" xml:space="preserve">demonſtrata ſunt. </s>
            <s xml:id="echoid-s35488" xml:space="preserve">Ducatur ex E, vertice capitis per G, locum Solis Deſcenſiuus circulus E G H; </s>
            <s xml:id="echoid-s35489" xml:space="preserve">
              <lb/>
            &</s>
            <s xml:id="echoid-s35490" xml:space="preserve">ex A, polo Meridiani per idem punctum G, Hectemorion A G I; </s>
            <s xml:id="echoid-s35491" xml:space="preserve">Ex polis tandem B, D, Verti-
              <lb/>
              <note position="left" xlink:label="note-0566-05" xlink:href="note-0566-05a" xml:space="preserve">30</note>
            calis circuli per idem punctum G, Horarius circulus B G K D. </s>
            <s xml:id="echoid-s35492" xml:space="preserve">Erit igitur A G, circunferentia he-
              <lb/>
            ctemoria; </s>
            <s xml:id="echoid-s35493" xml:space="preserve">B G, horaria; </s>
            <s xml:id="echoid-s35494" xml:space="preserve">E G, deſcenſiua; </s>
            <s xml:id="echoid-s35495" xml:space="preserve">B I, meridiana; </s>
            <s xml:id="echoid-s35496" xml:space="preserve">E K, Verticalis; </s>
            <s xml:id="echoid-s35497" xml:space="preserve">& </s>
            <s xml:id="echoid-s35498" xml:space="preserve">A H, horizontalis, quas
              <lb/>
            omnes hoc pacto ſupputabimus, ducto prius ex polo mundi O, ſiue auſtrali, ſiue boreali per G,
              <lb/>
            circulo maximo O G P, qui declinationem paralleli dati metitur, & </s>
            <s xml:id="echoid-s35499" xml:space="preserve">ex Aequatore abſcindit arcũ
              <lb/>
            F P, qui diſtantiam Solis à meridie metitur, cum per propoſ. </s>
            <s xml:id="echoid-s35500" xml:space="preserve">10. </s>
            <s xml:id="echoid-s35501" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35502" xml:space="preserve">2. </s>
            <s xml:id="echoid-s35503" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s35504" xml:space="preserve">ſimilis ſit arcui pa-
              <lb/>
            ralleli inter Meridianum, & </s>
            <s xml:id="echoid-s35505" xml:space="preserve">punctum G, ſeu circulum O G P.</s>
            <s xml:id="echoid-s35506" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s35507" xml:space="preserve">QVONIAM in triangulo ſphærico A G P, angulus P, rectus eſt, erit, per propoſ. </s>
            <s xml:id="echoid-s35508" xml:space="preserve">19. </s>
            <s xml:id="echoid-s35509" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35510" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s35511" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s35512" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s35513" xml:space="preserve">de triang. </s>
            <s xml:id="echoid-s35514" xml:space="preserve">vel per propoſ. </s>
            <s xml:id="echoid-s35515" xml:space="preserve">15. </s>
            <s xml:id="echoid-s35516" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35517" xml:space="preserve">1. </s>
            <s xml:id="echoid-s35518" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s35519" xml:space="preserve">43. </s>
            <s xml:id="echoid-s35520" xml:space="preserve">noſtrorum triang. </s>
            <s xml:id="echoid-s35521" xml:space="preserve">
              <lb/>
            ſphær. </s>
            <s xml:id="echoid-s35522" xml:space="preserve">vt ſinus complementi arcus A P, hoc eſt, vt ſinus arcus F P, diſtantiæ Solis à meridie, ad
              <lb/>
            ſinum totum, ita ſinus complementi hectemoriæ circunferentiæ A G, ad ſinum complementi ar-
              <lb/>
              <note position="left" xlink:label="note-0566-06" xlink:href="note-0566-06a" xml:space="preserve">40</note>
            cus declinationis G P: </s>
            <s xml:id="echoid-s35523" xml:space="preserve">Et conuertendo, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus
              <lb/>
            complementi declinationis ad ſinum complementi circunferentiæ hectemoriæ. </s>
            <s xml:id="echoid-s35524" xml:space="preserve">Quapropter ſi
              <lb/>
            fiat, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus complementi declinationis ad
              <lb/>
              <note position="left" xlink:label="note-0566-07" xlink:href="note-0566-07a" xml:space="preserve">Hectemoria.</note>
            aliud, inuenietur ſinus complementi hectemoriæ circunferentiæ; </s>
            <s xml:id="echoid-s35525" xml:space="preserve">ac proinde complementũ iſtud,
              <lb/>
            vna cum circunferentia hectemoria, ignotum non erit.</s>
            <s xml:id="echoid-s35526" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s35527" xml:space="preserve">DEINDE quia in triangulo O G I, angulus I, rectus eſt, erit per propoſ. </s>
            <s xml:id="echoid-s35528" xml:space="preserve">19. </s>
            <s xml:id="echoid-s35529" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35530" xml:space="preserve">4. </s>
            <s xml:id="echoid-s35531" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s35532" xml:space="preserve">Re-
              <lb/>
            giom. </s>
            <s xml:id="echoid-s35533" xml:space="preserve">de triang. </s>
            <s xml:id="echoid-s35534" xml:space="preserve">vel per propoſ. </s>
            <s xml:id="echoid-s35535" xml:space="preserve">15. </s>
            <s xml:id="echoid-s35536" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35537" xml:space="preserve">1. </s>
            <s xml:id="echoid-s35538" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s35539" xml:space="preserve">43. </s>
            <s xml:id="echoid-s35540" xml:space="preserve">noſtrorum triang. </s>
            <s xml:id="echoid-s35541" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s35542" xml:space="preserve">vt ſi-
              <lb/>
            nus complementi arcus O G, hoc eſt, vt ſinus arcus declinationis G P, ad ſinum complementi ar-
              <lb/>
            cus G I, hoc eſt, ad ſinum hectemoriæ circunferentiæ A G, ita ſinus complementi arcus O I, hoc
              <lb/>
            eſt, ſinus arcus F I, inter Aequatorem, & </s>
            <s xml:id="echoid-s35543" xml:space="preserve">Hectemorion, ad ſinum totum: </s>
            <s xml:id="echoid-s35544" xml:space="preserve">Et conuertendo,
              <unsure/>
            vt ſinus
              <lb/>
              <note position="left" xlink:label="note-0566-08" xlink:href="note-0566-08a" xml:space="preserve">50</note>
            circunferentiæ hectemorię ad ſinum declinationis, ita ſinus totus ad arcum Meridiani inter Ae-
              <lb/>
            quatorem, & </s>
            <s xml:id="echoid-s35545" xml:space="preserve">Hectemorion. </s>
            <s xml:id="echoid-s35546" xml:space="preserve">Si ergo fiat, vt ſinus circunferentię hectemoriæ ad ſinum declina-
              <lb/>
              <note position="left" xlink:label="note-0566-09" xlink:href="note-0566-09a" xml:space="preserve">Met
                <unsure/>
              idiana.</note>
            tionis, ita ſinus totus ad aliud, proueniet ſinusarcus Meridiani F I, inter Aequatorem, & </s>
            <s xml:id="echoid-s35547" xml:space="preserve">Hecte-
              <lb/>
            morion, qui in parallelis borealibus additus ad arcum B F, altitudinis Aequatoris, hoc eſt, ad com
              <lb/>
            plementum altitudinis poli, in auſtralibus vero parallelis ablatus ex eodem arcu B F, altitudinis
              <lb/>
            Aequatoris, hoc eſt, ex complemento altitudinis poli, dabit circunferentiam meridianam B I.
              <lb/>
            </s>
            <s xml:id="echoid-s35548" xml:space="preserve">Itaque vt inueniatur circunferentia meridiana per triangula ſphęrica, inueſtiganda prius erit
              <lb/>
            hectemoria.</s>
            <s xml:id="echoid-s35549" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s35550" xml:space="preserve">RVRSVS, cũ in triangulo E G I, angulus I, rectus ſit, erit per propoſ. </s>
            <s xml:id="echoid-s35551" xml:space="preserve">19. </s>
            <s xml:id="echoid-s35552" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35553" xml:space="preserve">4. </s>
            <s xml:id="echoid-s35554" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s35555" xml:space="preserve">Regiom.
              <lb/>
            </s>
            <s xml:id="echoid-s35556" xml:space="preserve">de triang. </s>
            <s xml:id="echoid-s35557" xml:space="preserve">vel per propoſ. </s>
            <s xml:id="echoid-s35558" xml:space="preserve">15. </s>
            <s xml:id="echoid-s35559" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35560" xml:space="preserve">1. </s>
            <s xml:id="echoid-s35561" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s35562" xml:space="preserve">43. </s>
            <s xml:id="echoid-s35563" xml:space="preserve">noſtrorũ triang. </s>
            <s xml:id="echoid-s35564" xml:space="preserve">ſphęr. </s>
            <s xml:id="echoid-s35565" xml:space="preserve">vt ſinus cõple-
              <lb/>
            menti arcus GI, hoc eſt, vt ſinus circunferentię hectemorię A G, ad ſinũ totum, ita ſinus </s>
          </p>
        </div>
      </text>
    </echo>
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