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-s8240" xml:space="preserve">
              <pb o="132" file="0152" n="152" rhead="GNOMONICES"/>
            mentum arcus A M. </s>
            <s xml:id="echoid-s8241" xml:space="preserve">Solum quando diſtantia Solis à meridie in ſignis borealibus excedit ſex ho-
              <lb/>
            ras, vt in tertia figura contingit, complementum arcus A M, eſt diſtantia Solis à media nocte, nem-
              <lb/>
            pearcus Aequatoris inſra Horizontem inter M, & </s>
            <s xml:id="echoid-s8242" xml:space="preserve">Meridianum; </s>
            <s xml:id="echoid-s8243" xml:space="preserve">ſed hic arcus eundem ſinum ha-
              <lb/>
              <figure xlink:label="fig-0152-01" xlink:href="fig-0152-01a" number="111">
                <image file="0152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0152-01"/>
              </figure>
              <note position="left" xlink:label="note-0152-01" xlink:href="note-0152-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0152-02" xlink:href="note-0152-02a" xml:space="preserve">20</note>
            bet, quem arcus F M, diſtantiæ Solis à meridie, vt in tractatu ſinuũ explicauimus. </s>
            <s xml:id="echoid-s8244" xml:space="preserve">Conficiunt enim
              <lb/>
              <note position="left" xlink:label="note-0152-03" xlink:href="note-0152-03a" xml:space="preserve">30</note>
            hi duo arcus ſemicirculum) ad ſinum totum, ita ſinus complementi arcus A L, ad ſinum comple
              <lb/>
            menti arcus L M, declinationis paralleli. </s>
            <s xml:id="echoid-s8245" xml:space="preserve">Conuertendo ergo erit quoque vt ſinus totus ad ſinum
              <lb/>
            diſtantiæ Solis à meridie, ita ſinus complementi declinationis propoſiti paralleli ad ſinum
              <lb/>
            complementi arcus A L; </s>
            <s xml:id="echoid-s8246" xml:space="preserve">atque adeò ex tribus primis notis quartum cognoſcetur, nempe com-
              <lb/>
            plementum arcus A L, hoc eſt, ipſe arcus L P; </s>
            <s xml:id="echoid-s8247" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s8248" xml:space="preserve">arcus A L, cognitus erit, qui dicatur
              <lb/>
            Primum Inuentum.</s>
            <s xml:id="echoid-s8249" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Pri@um inuen
            <lb/>
          @m.</note>
          <p>
            <s xml:id="echoid-s8250" xml:space="preserve">RVRSVS quia in triangulo ſphærico N L P, earundem quatuor priorum ſigurarum, angu-
              <lb/>
            lus P, rectus eſt, per propoſ. </s>
            <s xml:id="echoid-s8251" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8252" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8253" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8254" xml:space="preserve">Theodoſij, quòd circulus maximus A P, ductus eſt per A, po-
              <lb/>
            lum Meridiani B E D; </s>
            <s xml:id="echoid-s8255" xml:space="preserve">erit per eandem propoſ. </s>
            <s xml:id="echoid-s8256" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8257" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8258" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8259" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8260" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8261" xml:space="preserve">de triangulis, vel per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s8262" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8263" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8264" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8265" xml:space="preserve">Gebri, uel per propoſ. </s>
            <s xml:id="echoid-s8266" xml:space="preserve">43. </s>
            <s xml:id="echoid-s8267" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus comple-
              <lb/>
              <note position="left" xlink:label="note-0152-05" xlink:href="note-0152-05a" xml:space="preserve">40</note>
            menti arcus N L, hoc eſt, vt ſinus arcus L M, declinationis paralleli, ad ſinum complementi arcus
              <lb/>
            L P, hoc eſt, ad ſinum arcus A L, quem diximus Primum inuentum, ita ſinus complementi arcus
              <lb/>
            N P, ad ſinum totum. </s>
            <s xml:id="echoid-s8268" xml:space="preserve">Conuertendo igitur erit quoque, vt ſinus arcus, quem diximus Primum
              <lb/>
            inuentum, ad ſinum declinationis paralleli propoſiti, ita ſinus totus ad ſinum complementi arcus
              <lb/>
            N P, atque adeò ex primis tribus notis quartum cognoſcetur, ńempe complementum arcus NP,
              <lb/>
            id eſt, ipſe arcus F P, in prima, ſecunda, & </s>
            <s xml:id="echoid-s8269" xml:space="preserve">quarta figura, cum N F, quadrans ſit. </s>
            <s xml:id="echoid-s8270" xml:space="preserve">Solum quando di-
              <lb/>
            ſtantia Solis à meridie in borealibus ſignis ſuperat ſex horas, vt in tertia figura accidit, cõplementũ
              <lb/>
            arcus N P, eſt arcus à P, tendens per D, vſque ad Aequatorem ſub Horizonte; </s>
            <s xml:id="echoid-s8271" xml:space="preserve">(Quia enim tunc
              <lb/>
            P, cadit inter N, polum, & </s>
            <s xml:id="echoid-s8272" xml:space="preserve">Horizontẽ, propterea quòd circulus A L P, ſecat circulum declinationis
              <lb/>
            N M, in L, cum N L M, ſecet Aequatorem in M, vltra punctum A, ſub Horizonte, propter arcum
              <lb/>
              <note position="left" xlink:label="note-0152-06" xlink:href="note-0152-06a" xml:space="preserve">50</note>
            F M, diſtantiæ Solis à meridie, quæ maior ponitur quàm 6. </s>
            <s xml:id="echoid-s8273" xml:space="preserve">horarum, ſeu quàm quadrans F A;
              <lb/>
            </s>
            <s xml:id="echoid-s8274" xml:space="preserve">efficitur, vt cum arcus ex polo N, per D, tendens vſque ad Aequatorẽ ſub Horizonte ſit quadrans,
              <lb/>
            dictus arcus tendens ex P, per D, vſque ad Aequatorem ſub Horizonte, complementum exiſtat ip-
              <lb/>
            ſius arcus N P,) quo complemento cognito cognoſcetur quoque arcus F P, reliquus ex ſemicircu-
              <lb/>
            lo. </s>
            <s xml:id="echoid-s8275" xml:space="preserve">Iam verò ſi arcus F P, inuentus, Sole exiſtente boreali, vt in prima, ſecunda, & </s>
            <s xml:id="echoid-s8276" xml:space="preserve">tertia figura ap-
              <lb/>
            paret, adijciatur ad arcũ F B, altitudinis Aequatoris, vel cõplementi altitudinis poli, cognitus erit
              <lb/>
            totus arcus B P: </s>
            <s xml:id="echoid-s8277" xml:space="preserve">Sole autem auſtralia ſigna percurrente, ſi idem arcus inuentus F P, detrahatur ex
              <lb/>
            arcu F B, complementi altitudin is poli, idem arcus B P, notus relinquetur, vt in quarta figura eſt
              <lb/>
            manifeſtum. </s>
            <s xml:id="echoid-s8278" xml:space="preserve">Hic autem arcus B P, dicatur ſecundum Inuentum.</s>
            <s xml:id="echoid-s8279" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Secundum in-
            <lb/>
          uentum.</note>
          <p>
            <s xml:id="echoid-s8280" xml:space="preserve">POSTREMO, quoniam in triangulo ſphærico E L P, angulus P, rectus eſt, vt proximè di-
              <lb/>
            ximus, erit per eandem propoſ. </s>
            <s xml:id="echoid-s8281" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8282" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8283" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8284" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8285" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8286" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s8287" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8288" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8289" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8290" xml:space="preserve"/>
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