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-s6118" xml:space="preserve">
              <pb o="104" file="0124" n="124" rhead="GNOMONICES"/>
            ex coroll. </s>
            <s xml:id="echoid-s6119" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s6120" xml:space="preserve">16. </s>
            <s xml:id="echoid-s6121" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6122" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6123" xml:space="preserve">Theodoſii, quôd M, polus ſit Horizõtis A B C D, & </s>
            <s xml:id="echoid-s6124" xml:space="preserve">P, polus plani E F;
              <lb/>
            </s>
            <s xml:id="echoid-s6125" xml:space="preserve">ablato communi arcu M Q, erit P M, arcus æqualis arcui Q N, inclinationem plani ad Horizon-
              <lb/>
            tem metienti. </s>
            <s xml:id="echoid-s6126" xml:space="preserve">Quare cum in ſphęrico triangulo H P M, per propoſ. </s>
            <s xml:id="echoid-s6127" xml:space="preserve">17. </s>
            <s xml:id="echoid-s6128" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6129" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6130" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s6131" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s6132" xml:space="preserve">de
              <lb/>
              <figure xlink:label="fig-0124-01" xlink:href="fig-0124-01a" number="90">
                <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0124-01"/>
              </figure>
              <note position="left" xlink:label="note-0124-01" xlink:href="note-0124-01a" xml:space="preserve">10</note>
            triangulis, vel per propoſitionem 13. </s>
            <s xml:id="echoid-s6133" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6134" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6135" xml:space="preserve">Gebri, vel certè per propoſ. </s>
            <s xml:id="echoid-s6136" xml:space="preserve">41. </s>
            <s xml:id="echoid-s6137" xml:space="preserve">noſtrorum triangulorũ
              <lb/>
              <note position="left" xlink:label="note-0124-02" xlink:href="note-0124-02a" xml:space="preserve">20</note>
            ſphæricorum, ſit vt ſinus arcus P M, qui inclinationi plani ad Horizontem æqualis eſt, ad ſinum
              <lb/>
            anguli H, inclinationis Meridiani ipſius plani inclinati ad Meridianum Horizontis, ita ſinus arcus
              <lb/>
            H M, complementi altitudinis poli ſupra Horizontem, ad ſinum anguli P, hoc eſt, ad ſinum ar-
              <lb/>
            cus I Q; </s>
            <s xml:id="echoid-s6138" xml:space="preserve">Si fiat, vt ſinus inclinationis ad Horizontem, ad ſinum inclinationis Meridiani ipſius pla
              <lb/>
            ni inclinati ad Meridianum Horizontis, per propoſ. </s>
            <s xml:id="echoid-s6139" xml:space="preserve">pręcedentem inuentę, ita ſinus complementi
              <lb/>
            altitudinis poli ſupra Horizontem ad aliud, habebitur ſinus arcus primi I Q, quæſiti.</s>
            <s xml:id="echoid-s6140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6141" xml:space="preserve">RVRSVS ducto arcu circuli maximi per puncta G, P, erunt duo arcus G P, G M, trianguli
              <lb/>
              <note position="left" xlink:label="note-0124-03" xlink:href="note-0124-03a" xml:space="preserve">Arcus plani in-
                <lb/>
              clinati inter ma
                <lb/>
              ximum circulũ
                <lb/>
              per eius polos,
                <lb/>
              & per polos Ho
                <lb/>
              @zontis ductũ,
                <lb/>
              & Meridianum
                <lb/>
              Horizontis in-
                <lb/>
              tercep us, quo
                <lb/>
              artificio explo-
                <lb/>
              retur.</note>
            ſphærici G M P, noti; </s>
            <s xml:id="echoid-s6142" xml:space="preserve">quoniam G P, quadrans eſt, per coroll. </s>
            <s xml:id="echoid-s6143" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s6144" xml:space="preserve">16. </s>
            <s xml:id="echoid-s6145" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6146" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6147" xml:space="preserve">Theodoſii, quòd
              <lb/>
            P, polus ſit circuli E F, arcus vero G M, notus eſt, quia interijcitur inter planum inclinatum, & </s>
            <s xml:id="echoid-s6148" xml:space="preserve">
              <lb/>
            verticem M, ac proinde, per coroll. </s>
            <s xml:id="echoid-s6149" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s6150" xml:space="preserve">28. </s>
            <s xml:id="echoid-s6151" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s6152" xml:space="preserve">notus eſt, cum ſit complementum arcus
              <lb/>
            Meridiani inter planum inclinatum, & </s>
            <s xml:id="echoid-s6153" xml:space="preserve">Horizontem. </s>
            <s xml:id="echoid-s6154" xml:space="preserve">Item & </s>
            <s xml:id="echoid-s6155" xml:space="preserve">angulus G M P, notus eſt. </s>
            <s xml:id="echoid-s6156" xml:space="preserve">quoniam
              <lb/>
              <note position="left" xlink:label="note-0124-04" xlink:href="note-0124-04a" xml:space="preserve">30</note>
            enim circulus O N, ductus per polos P, M, circulorum E F, E B F, ſecat arcus E F, E B F, per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s6157" xml:space="preserve">9. </s>
            <s xml:id="echoid-s6158" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6159" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6160" xml:space="preserve">Theodoſii, bifariam; </s>
            <s xml:id="echoid-s6161" xml:space="preserve">eſtq́; </s>
            <s xml:id="echoid-s6162" xml:space="preserve">E B F, per propoſ. </s>
            <s xml:id="echoid-s6163" xml:space="preserve">11. </s>
            <s xml:id="echoid-s6164" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6165" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6166" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s6167" xml:space="preserve">ſemicirculus, erit E N,
              <lb/>
            quadrans, atque adeò quadranti k C, ęqualis. </s>
            <s xml:id="echoid-s6168" xml:space="preserve">ablato ergo communi arcu k N, relinquetur arcus
              <lb/>
            E k, declinationis plani E F, à Verticali, arcui N C, ęqualis, atque adeo arcus N C, notus erit. </s>
            <s xml:id="echoid-s6169" xml:space="preserve">quare
              <lb/>
            & </s>
            <s xml:id="echoid-s6170" xml:space="preserve">angulus N M C, ac proinde & </s>
            <s xml:id="echoid-s6171" xml:space="preserve">reliquus ex duobus rectis G M P, notus erit. </s>
            <s xml:id="echoid-s6172" xml:space="preserve">Quoniam autem
              <lb/>
            eſt in triangulo ſphęrico G P M, per propoſ. </s>
            <s xml:id="echoid-s6173" xml:space="preserve">17. </s>
            <s xml:id="echoid-s6174" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6175" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6176" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s6177" xml:space="preserve">Regiom de triangulis, vel per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s6178" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6179" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6180" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6181" xml:space="preserve">Gebri, vel certè per propoſ. </s>
            <s xml:id="echoid-s6182" xml:space="preserve">41. </s>
            <s xml:id="echoid-s6183" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus arcus
              <lb/>
            G P, nempe ſinus totus, ad ſinum anguli G M P, nempe ad ſinum declinationis plani à Verticali,
              <lb/>
            (habent enim arcus N C, C O, angulorum N M C, C M O, vel G M P, cũ ſemicirculum cõficiant,
              <lb/>
            eundem ſinum) ita ſinus arcus G M, Meridiani, qui inter planum, & </s>
            <s xml:id="echoid-s6184" xml:space="preserve">verticem M, interponitur, ad
              <lb/>
              <note position="left" xlink:label="note-0124-05" xlink:href="note-0124-05a" xml:space="preserve">40</note>
            ſinum anguli G P M, hoc eſt, ad ſinum arcus G Q; </s>
            <s xml:id="echoid-s6185" xml:space="preserve">ſi fiat, vt ſinus totus ad ſinum declinationis, ita
              <lb/>
            ſinus arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s6186" xml:space="preserve">verticem collocati ad aliud, habebitur ſinus arcus ſecun-
              <lb/>
            di G Q, qui quæritur.</s>
            <s xml:id="echoid-s6187" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6188" xml:space="preserve">EXEMPLVM vtriuſque. </s>
            <s xml:id="echoid-s6189" xml:space="preserve">Ponatur inclinatio ad Horizontem grad. </s>
            <s xml:id="echoid-s6190" xml:space="preserve">52. </s>
            <s xml:id="echoid-s6191" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6192" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6193" xml:space="preserve">& </s>
            <s xml:id="echoid-s6194" xml:space="preserve">inclina-
              <lb/>
              <note position="left" xlink:label="note-0124-06" xlink:href="note-0124-06a" xml:space="preserve">Exemplum.</note>
            tio Meridiani B D, ipſius plani inclinati E F, ad Meridianum Horizontis A C, grad. </s>
            <s xml:id="echoid-s6195" xml:space="preserve">90. </s>
            <s xml:id="echoid-s6196" xml:space="preserve">Si igitur
              <lb/>
            fiat vt 78854. </s>
            <s xml:id="echoid-s6197" xml:space="preserve">ſinus inclinationis ad Horizontem ad 100000. </s>
            <s xml:id="echoid-s6198" xml:space="preserve">ſinũ totum, nempe ad ſinum incli-
              <lb/>
            nationis Meridianorũ, ita 74314. </s>
            <s xml:id="echoid-s6199" xml:space="preserve">ſinus complementi altitudinis poli ſupra Horizontẽ ad aliud,
              <lb/>
            inuenietur hic ferè ſinus 94242. </s>
            <s xml:id="echoid-s6200" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s6201" xml:space="preserve">70. </s>
            <s xml:id="echoid-s6202" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6203" xml:space="preserve">28. </s>
            <s xml:id="echoid-s6204" xml:space="preserve">ferè inter Meridianum plani incli-
              <lb/>
            nati, & </s>
            <s xml:id="echoid-s6205" xml:space="preserve">circulum maximum interijcitur, qui inclinationem plani ad Horizontem metitur.</s>
            <s xml:id="echoid-s6206" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6207" xml:space="preserve">RVRSVS ſi fiat, vt 100000. </s>
            <s xml:id="echoid-s6208" xml:space="preserve">ſinus totus ad 50000. </s>
            <s xml:id="echoid-s6209" xml:space="preserve">ſinum declinationis plani à Verticali (po-
              <lb/>
              <note position="left" xlink:label="note-0124-07" xlink:href="note-0124-07a" xml:space="preserve">50</note>
            nimus enim idem planum, de quo proximè egimus, declinare à Verticali à Septentrione in ortũ,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s6210" xml:space="preserve">30. </s>
            <s xml:id="echoid-s6211" xml:space="preserve">ita vt inclinatio cadat in partem auſtralem) ita 66913. </s>
            <s xml:id="echoid-s6212" xml:space="preserve">ſinus arcus Meridiani inter pla-
              <lb/>
            num, & </s>
            <s xml:id="echoid-s6213" xml:space="preserve">verticem intercepti (qui quidem arcus complectitur grad. </s>
            <s xml:id="echoid-s6214" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6215" xml:space="preserve">Nam arcus inter planum,
              <lb/>
            & </s>
            <s xml:id="echoid-s6216" xml:space="preserve">Horizontem continet, per propoſ. </s>
            <s xml:id="echoid-s6217" xml:space="preserve">28. </s>
            <s xml:id="echoid-s6218" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s6219" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s6220" xml:space="preserve">48. </s>
            <s xml:id="echoid-s6221" xml:space="preserve">ſub Horizonte ad partes boreales, qui
              <lb/>
            ablatus ex quadrante relinquit arcum inter planum inclinatum, & </s>
            <s xml:id="echoid-s6222" xml:space="preserve">verticem ad partes auſtrales
              <lb/>
            grad. </s>
            <s xml:id="echoid-s6223" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6224" xml:space="preserve">ex coroll. </s>
            <s xml:id="echoid-s6225" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s6226" xml:space="preserve">28. </s>
            <s xml:id="echoid-s6227" xml:space="preserve">huius lib.) </s>
            <s xml:id="echoid-s6228" xml:space="preserve">ad aliud, reperietur hic propemodum ſinus 33456. </s>
            <s xml:id="echoid-s6229" xml:space="preserve">cui
              <lb/>
            reſpondet arcus ferme grad. </s>
            <s xml:id="echoid-s6230" xml:space="preserve">19. </s>
            <s xml:id="echoid-s6231" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6232" xml:space="preserve">33. </s>
            <s xml:id="echoid-s6233" xml:space="preserve">inter Meridianum Horizontis, & </s>
            <s xml:id="echoid-s6234" xml:space="preserve">circulum maximum in-
              <lb/>
            reriectus, qui inclinationem plani ad Horizontem dimetitur. </s>
            <s xml:id="echoid-s6235" xml:space="preserve">Dato ergo plano ad Meridianum
              <lb/>
            inclinato, quãtus ſit arcus ipſins interceptus inter circulum maximum, qui per polos ipſius, & </s>
            <s xml:id="echoid-s6236" xml:space="preserve">per
              <lb/>
            polos Horizontis tranſit, metiturq́; </s>
            <s xml:id="echoid-s6237" xml:space="preserve">eius inclinationem ad Horizontem, & </s>
            <s xml:id="echoid-s6238" xml:space="preserve">tam Meridianum pro-
              <lb/>
            prium ipſius, &</s>
            <s xml:id="echoid-s6239" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6240" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s6241" xml:space="preserve"/>
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