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-div363" type="section" level="1" n="129">
          <pb o="105" file="0125" n="125" rhead="LIBER PRIMVS."/>
        </div>
        <div xml:id="echoid-div369" type="section" level="1" n="130">
          <head xml:id="echoid-head133" xml:space="preserve">PROBLEMA 11. PROPOSITIO 32.</head>
          <p>
            <s xml:id="echoid-s6242" xml:space="preserve">DATO plano ad Horizontem inclinato, & </s>
            <s xml:id="echoid-s6243" xml:space="preserve">declinante à Verticali,
              <lb/>
            quantus ſit arcus circuli maximi inclinationem ipſius ad Horizontem
              <lb/>
            metientis inter Horizontem, & </s>
            <s xml:id="echoid-s6244" xml:space="preserve">circulum horæ ſextæ à meridie, vel me-
              <lb/>
            dia nocte poſitus, explorare.</s>
            <s xml:id="echoid-s6245" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6246" xml:space="preserve">SIT Horizon A B C D; </s>
            <s xml:id="echoid-s6247" xml:space="preserve">Meridianus A C; </s>
            <s xml:id="echoid-s6248" xml:space="preserve">Verticalis B I D; </s>
            <s xml:id="echoid-s6249" xml:space="preserve">planum inclinatum ad Horizon-
              <lb/>
              <note position="left" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0125-02" xlink:href="note-0125-02a" xml:space="preserve">Arcus circuli
                <lb/>
              maximi, qui pla
                <lb/>
              ni à Verticali
                <lb/>
              declinantis in-
                <lb/>
              clinationem ad
                <lb/>
              Horizontẽ me-
                <lb/>
              titur, inter Ho-
                <lb/>
              rizon@ẽ. & circu
                <lb/>
              lum horæ 6. à
                <lb/>
              mer. uel med.
                <lb/>
              noc. poſitus, quo
                <lb/>
              pacto inueſtigã-
                <lb/>
              dus.</note>
            tem, & </s>
            <s xml:id="echoid-s6250" xml:space="preserve">à Verticali declinans E F; </s>
            <s xml:id="echoid-s6251" xml:space="preserve">circulus maximus eius inclinationem ſupra Horizontem metiẽs
              <lb/>
            G H, tranſiens per verticem, I, ſeu polum Horizontis, & </s>
            <s xml:id="echoid-s6252" xml:space="preserve">per polum plani inclinati M; </s>
            <s xml:id="echoid-s6253" xml:space="preserve">Circulus
              <lb/>
            denique horæ ſextæ à meridie, vel media nocte B K D, ductus
              <lb/>
              <figure xlink:label="fig-0125-01" xlink:href="fig-0125-01a" number="91">
                <image file="0125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0125-01"/>
              </figure>
            per polum mundi K, & </s>
            <s xml:id="echoid-s6254" xml:space="preserve">per B, D, communes ſectiones Hori-
              <lb/>
            zontis, & </s>
            <s xml:id="echoid-s6255" xml:space="preserve">Verticalis, ſecanſq́ue circulum G H, in L; </s>
            <s xml:id="echoid-s6256" xml:space="preserve">oporteatq́;
              <lb/>
            </s>
            <s xml:id="echoid-s6257" xml:space="preserve">arcum L H, explorare. </s>
            <s xml:id="echoid-s6258" xml:space="preserve">Quoniam in triangulo ſphærico D H L,
              <lb/>
            cuius angulus H, per propoſ. </s>
            <s xml:id="echoid-s6259" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6260" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6261" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6262" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s6263" xml:space="preserve">rectus eſt, quòd
              <lb/>
            circulus G H, per I, polum Horizontis A B C D, ducatur; </s>
            <s xml:id="echoid-s6264" xml:space="preserve">& </s>
            <s xml:id="echoid-s6265" xml:space="preserve">an-
              <lb/>
            gulus D, angulus altitudinis poli, cum D, polus ſit Meridiani,
              <lb/>
              <note position="left" xlink:label="note-0125-03" xlink:href="note-0125-03a" xml:space="preserve">20</note>
            (Hinc enim fit, vt per corol. </s>
            <s xml:id="echoid-s6266" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s6267" xml:space="preserve">16. </s>
            <s xml:id="echoid-s6268" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6269" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6270" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s6271" xml:space="preserve">arcus DC,
              <lb/>
            D k, quadrantes ſint, ac proinde arcus C k, altitudinis poli ſu-
              <lb/>
            pra Horizontem metiatut angulum C D k) eſt per propoſ. </s>
            <s xml:id="echoid-s6272" xml:space="preserve">18.
              <lb/>
            </s>
            <s xml:id="echoid-s6273" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6274" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6275" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s6276" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s6277" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s6278" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6279" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6280" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6281" xml:space="preserve">Ge-
              <lb/>
            bri, vel certè per propoſ. </s>
            <s xml:id="echoid-s6282" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6283" xml:space="preserve">noſtrorum triangulorum ſphęri-
              <lb/>
            corum, vt ſinus anguli H D L, altitudinis poli, ad ſinum totum, ita ſinus complementi anguli L,
              <lb/>
            ad ſinum complementi arcus D H, hoc eſt, ad ſinum arcus C H, qui æqualis eſt declinationi pla
              <lb/>
            ni à Verticali; </s>
            <s xml:id="echoid-s6284" xml:space="preserve">(quoniam enim circulus G H, per polos Horizontis, & </s>
            <s xml:id="echoid-s6285" xml:space="preserve">circuli E F, ductus ſecat ar-
              <lb/>
            cus E N F, E H F, per propoſ. </s>
            <s xml:id="echoid-s6286" xml:space="preserve">9. </s>
            <s xml:id="echoid-s6287" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6288" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6289" xml:space="preserve">Theodoſij, bifariam; </s>
            <s xml:id="echoid-s6290" xml:space="preserve">Eſt autem arcus E H F, ſemicirculus,
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s6291" xml:space="preserve">11. </s>
            <s xml:id="echoid-s6292" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6293" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6294" xml:space="preserve">Theodoſij, erit E H, quadrans, atque adeò quadranti D C, æqualis. </s>
            <s xml:id="echoid-s6295" xml:space="preserve">Ablato
              <lb/>
              <note position="left" xlink:label="note-0125-04" xlink:href="note-0125-04a" xml:space="preserve">30</note>
            ergo communiarcu D H, erit reliquus arcus D E, declinationis plani à Verticali, æqualis arcui
              <lb/>
            reliquo C H.) </s>
            <s xml:id="echoid-s6296" xml:space="preserve">Erit conuertendo vt ſinus totus ad ſinum anguli H D L, altitudinis poli, ita ſinus
              <lb/>
            complementi arcus D H, hoc eſt, ſinus declinationis plani à Verticali, ad ſinum complementi an-
              <lb/>
            guli L. </s>
            <s xml:id="echoid-s6297" xml:space="preserve">Igitur ſi fiat, vt ſinus torus ad ſinum altitudinis poli ſupra Horizontem, ita ſinus declina-
              <lb/>
            tionis ad aliud, habebitur ſinus, cuius arcus ex quadrante ſubtractus relinquit angulum L, notũ.
              <lb/>
            </s>
            <s xml:id="echoid-s6298" xml:space="preserve">Quia verò per propoſ. </s>
            <s xml:id="echoid-s6299" xml:space="preserve">16. </s>
            <s xml:id="echoid-s6300" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6301" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6302" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s6303" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s6304" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s6305" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6306" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6307" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6308" xml:space="preserve">Gebri, vel cer
              <lb/>
            tè per propoſ. </s>
            <s xml:id="echoid-s6309" xml:space="preserve">41. </s>
            <s xml:id="echoid-s6310" xml:space="preserve">noſtrorum triangulorum ſphęricorum, in eodem triangulo eſt, vt ſinus anguli
              <lb/>
            L, proximè inuenti, ad ſinum arcus D H, complementi declinationis, ita ſinus anguli H D L, al-
              <lb/>
            titudinis poli, ad ſinum arcus L H; </s>
            <s xml:id="echoid-s6311" xml:space="preserve">Si fiat, vt ſinus anguli L, inuenti ad ſinum complementi decli
              <lb/>
            nationis, ita ſinus altitudinis poli ſupra Horizontem ad aliud, habebitur ſinus arcus L H, quæſiti.</s>
            <s xml:id="echoid-s6312" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Exemplum pri-
            <lb/>
          mum.</note>
          <p>
            <s xml:id="echoid-s6313" xml:space="preserve">EXEMPLVM. </s>
            <s xml:id="echoid-s6314" xml:space="preserve">Ponatur planum inclinatum ad Horizontem grad. </s>
            <s xml:id="echoid-s6315" xml:space="preserve">30. </s>
            <s xml:id="echoid-s6316" xml:space="preserve">declinãs verò à Ver-
              <lb/>
              <note position="left" xlink:label="note-0125-06" xlink:href="note-0125-06a" xml:space="preserve">40</note>
            ticali grad. </s>
            <s xml:id="echoid-s6317" xml:space="preserve">20. </s>
            <s xml:id="echoid-s6318" xml:space="preserve">Fiat vt 100000. </s>
            <s xml:id="echoid-s6319" xml:space="preserve">ſinus totus, ad 66913. </s>
            <s xml:id="echoid-s6320" xml:space="preserve">ſinum altitudinis poli, ita 34202. </s>
            <s xml:id="echoid-s6321" xml:space="preserve">ſinus de-
              <lb/>
            clinationis ad aliud, reperietur hic ferè ſinus 22885 cuius arcus grad. </s>
            <s xml:id="echoid-s6322" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6323" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6324" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6325" xml:space="preserve">à quadrante
              <lb/>
            demptus relinquit angulum L, grad. </s>
            <s xml:id="echoid-s6326" xml:space="preserve">76. </s>
            <s xml:id="echoid-s6327" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6328" xml:space="preserve">46. </s>
            <s xml:id="echoid-s6329" xml:space="preserve">Rurſus fiat, vt 97344. </s>
            <s xml:id="echoid-s6330" xml:space="preserve">ſinus anguli L, inuenti,
              <lb/>
            ad 93969. </s>
            <s xml:id="echoid-s6331" xml:space="preserve">ſinum complementi declinationis, ita 66913. </s>
            <s xml:id="echoid-s6332" xml:space="preserve">ſinus altitudinis poliad aliud, habebi-
              <lb/>
            turq́ue hic propemodum ſinus 64593. </s>
            <s xml:id="echoid-s6333" xml:space="preserve">cui reſpondent grad. </s>
            <s xml:id="echoid-s6334" xml:space="preserve">40. </s>
            <s xml:id="echoid-s6335" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6336" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6337" xml:space="preserve">pro arcu L H. </s>
            <s xml:id="echoid-s6338" xml:space="preserve">quęſito.</s>
            <s xml:id="echoid-s6339" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6340" xml:space="preserve">RVRSVS ponatur planum inclinatum ad Horizontem grad. </s>
            <s xml:id="echoid-s6341" xml:space="preserve">52. </s>
            <s xml:id="echoid-s6342" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6343" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6344" xml:space="preserve">declinans autem à
              <lb/>
              <note position="right" xlink:label="note-0125-07" xlink:href="note-0125-07a" xml:space="preserve">Exemplum ſe-
                <lb/>
              cundum.</note>
            Verticali grad. </s>
            <s xml:id="echoid-s6345" xml:space="preserve">30. </s>
            <s xml:id="echoid-s6346" xml:space="preserve">Fiat vt 100000. </s>
            <s xml:id="echoid-s6347" xml:space="preserve">ſinus totus ad 66913. </s>
            <s xml:id="echoid-s6348" xml:space="preserve">ſinum altitudinis poli, ita 50000. </s>
            <s xml:id="echoid-s6349" xml:space="preserve">ſinus
              <lb/>
            declinationis ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s6350" xml:space="preserve">hic fermè ſinus 33456. </s>
            <s xml:id="echoid-s6351" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s6352" xml:space="preserve">19. </s>
            <s xml:id="echoid-s6353" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6354" xml:space="preserve">33. </s>
            <s xml:id="echoid-s6355" xml:space="preserve">à qua-
              <lb/>
            drante ablatus relinquit angulum L, quem circulus maximus inclinationem plani ad Horizontẽ
              <lb/>
            metiens facit cum circulo horæ ſextæ à meridie, vel media nocte, grad. </s>
            <s xml:id="echoid-s6356" xml:space="preserve">70. </s>
            <s xml:id="echoid-s6357" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6358" xml:space="preserve">27.</s>
            <s xml:id="echoid-s6359" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <p>
            <s xml:id="echoid-s6360" xml:space="preserve">FIAT rurſus, vt 94234. </s>
            <s xml:id="echoid-s6361" xml:space="preserve">ſinus anguli L, inuenti, ad 86602. </s>
            <s xml:id="echoid-s6362" xml:space="preserve">ſinum complementi declinatio-
              <lb/>
            nis, ita 66913. </s>
            <s xml:id="echoid-s6363" xml:space="preserve">ſinus altitudinis poli ad aliud, habebiturq́; </s>
            <s xml:id="echoid-s6364" xml:space="preserve">hic ferè ſinus 61493. </s>
            <s xml:id="echoid-s6365" xml:space="preserve">cui reſpondent
              <lb/>
            grad. </s>
            <s xml:id="echoid-s6366" xml:space="preserve">37. </s>
            <s xml:id="echoid-s6367" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6368" xml:space="preserve">57. </s>
            <s xml:id="echoid-s6369" xml:space="preserve">pro arcu LH, qui quęritur. </s>
            <s xml:id="echoid-s6370" xml:space="preserve">Dato ergo plano ad Horizontem inclinato &</s>
            <s xml:id="echoid-s6371" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6372" xml:space="preserve">Quod
              <lb/>
            erat faciendum.</s>
            <s xml:id="echoid-s6373" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div373" type="section" level="1" n="131">
          <head xml:id="echoid-head134" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s6374" xml:space="preserve">PROPOSVIMVS proxima ſex Problemata, quoniam eorum mirificus vſus apparebit in ho-
              <lb/>
              <note position="right" xlink:label="note-0125-09" xlink:href="note-0125-09a" xml:space="preserve">Ad quid condu
                <lb/>
              cant ſex antece-
                <lb/>
              dentes propoſi-
                <lb/>
              tiones.</note>
            rologijs, quorum plana, in quibus deſcribuntur, parallela ſunt circulis maximis, qui vel à Verticali decli
              <lb/>
            nant, & </s>
            <s xml:id="echoid-s6375" xml:space="preserve">ad Horizontem ſunt recti; </s>
            <s xml:id="echoid-s6376" xml:space="preserve">vel ab Horizonte declinant, rectiq́, ſunt ad Verticalem; </s>
            <s xml:id="echoid-s6377" xml:space="preserve">vel deniq;
              <lb/>
            </s>
            <s xml:id="echoid-s6378" xml:space="preserve">& </s>
            <s xml:id="echoid-s6379" xml:space="preserve">à Verticali declinant, & </s>
            <s xml:id="echoid-s6380" xml:space="preserve">ad Horizontem ſunt inclinati, vt ex ſequentibus fiet perſpicuum.</s>
            <s xml:id="echoid-s6381" xml:space="preserve"/>
          </p>
        </div>
      </text>
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