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-s6971" xml:space="preserve">
              <pb o="116" file="0136" n="136" rhead="GNOMONICES"/>
            ſinus cõplementi arcus I F, declinationis paralleli propoſiti ad ſinũ totum, ita ſinus cõplementiar-
              <lb/>
            cus BF, latitudinis ortiuæ, occiduęve proximè inuentæ ad ſinũ cõplemẽti arcus B I, hoc eſt, ad ſinũ
              <lb/>
            arcus ſemidiurni I E, in parallelo aultrali, vel arcus ſeminocturni in parallelo boreali. </s>
            <s xml:id="echoid-s6972" xml:space="preserve">Nam arcus
              <lb/>
              <figure xlink:label="fig-0136-01" xlink:href="fig-0136-01a" number="98">
                <image file="0136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0136-01"/>
              </figure>
            Aequatoris inter I, & </s>
            <s xml:id="echoid-s6973" xml:space="preserve">Meridianum ſub Horizonte
              <lb/>
            complementũ eſt arcus B I, in triangulo boreali, cũ
              <lb/>
            arcus Aequatoris ex B, per I, vſque ad Meridianum
              <lb/>
            infra Horizontem porrectus ſit quadrans. </s>
            <s xml:id="echoid-s6974" xml:space="preserve">Igitur
              <lb/>
            ſi fiat, vt ſinus complementi declinationis propoſi-
              <lb/>
            ti paralleli ad ſinum totum, ita ſinus compleinen-
              <lb/>
            ti latitudinis ortiuæ proxime inuentæ in priori di-
              <lb/>
              <note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">10</note>
            ſcurſu, ad aliud, inuenietur ſinus arcus ſemidiur-
              <lb/>
            ni auſtralis, vel ſeminocturni borealis. </s>
            <s xml:id="echoid-s6975" xml:space="preserve">Dempto au-
              <lb/>
            tem arcu ſeminocturno boreali ex ſemicirculo Ae-
              <lb/>
            quatoris, qui inter Meridianum ſupra, & </s>
            <s xml:id="echoid-s6976" xml:space="preserve">infra Ho-
              <lb/>
            rizontem interijcitur, re@iquus erit arcus diurnus
              <lb/>
            borealis I B E.</s>
            <s xml:id="echoid-s6977" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6978" xml:space="preserve">PONATVR exempli gratia inquirendus ar-
              <lb/>
              <note position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">Exemplum.</note>
            cus ſemidiurnus ad latitudinem grad. </s>
            <s xml:id="echoid-s6979" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6980" xml:space="preserve">Sole exi-
              <lb/>
            ſtente in principio ♊, vel ♐, vbi declinationem
              <lb/>
            habet grad. </s>
            <s xml:id="echoid-s6981" xml:space="preserve">20. </s>
            <s xml:id="echoid-s6982" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6983" xml:space="preserve">12. </s>
            <s xml:id="echoid-s6984" xml:space="preserve">Fiat vt 74314. </s>
            <s xml:id="echoid-s6985" xml:space="preserve">ſinus com
              <lb/>
              <note position="left" xlink:label="note-0136-03" xlink:href="note-0136-03a" xml:space="preserve">20</note>
            plementi altitudinis poli, ad 34529. </s>
            <s xml:id="echoid-s6986" xml:space="preserve">ſinũ declinationis paralleli ♊, vel ♐, ita 100000. </s>
            <s xml:id="echoid-s6987" xml:space="preserve">ſinus to-
              <lb/>
            tus ad aliud, inuenieturq́ hic ferè ſinus 46464. </s>
            <s xml:id="echoid-s6988" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s6989" xml:space="preserve">27. </s>
            <s xml:id="echoid-s6990" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6991" xml:space="preserve">41. </s>
            <s xml:id="echoid-s6992" xml:space="preserve">dabit latitudinem
              <lb/>
            ortiuam, occiduamve, borealem quidem paralleli ♊, auſtralem verò paralleli ♐. </s>
            <s xml:id="echoid-s6993" xml:space="preserve">Rurſus fiat, vt
              <lb/>
            93849. </s>
            <s xml:id="echoid-s6994" xml:space="preserve">ſinus complementi declinationis eiuſdem paralleli ♊, vel ♐, ad 100000, ſinum totum,
              <lb/>
            ita 88552. </s>
            <s xml:id="echoid-s6995" xml:space="preserve">ſinus complementi latitudinis ortiuæ proximè inuentæ ad aliud, conſurgetq́; </s>
            <s xml:id="echoid-s6996" xml:space="preserve">quaſi hic
              <lb/>
            ſinus 94355. </s>
            <s xml:id="echoid-s6997" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s6998" xml:space="preserve">70. </s>
            <s xml:id="echoid-s6999" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7000" xml:space="preserve">39. </s>
            <s xml:id="echoid-s7001" xml:space="preserve">exhibebit arcum ſemidiurnum paralleli ♐, & </s>
            <s xml:id="echoid-s7002" xml:space="preserve">ſemi-
              <lb/>
            nocturnum paralleli ♊, quo dempto ex ſemicirculo, id eſt, ex grad. </s>
            <s xml:id="echoid-s7003" xml:space="preserve">180. </s>
            <s xml:id="echoid-s7004" xml:space="preserve">reliquus erit arcus ſemi-
              <lb/>
            diurnus paralleli ♊, grad. </s>
            <s xml:id="echoid-s7005" xml:space="preserve">109. </s>
            <s xml:id="echoid-s7006" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7007" xml:space="preserve">21. </s>
            <s xml:id="echoid-s7008" xml:space="preserve">Quòd ſi gradus horum arcuum reducantur ad horas, tri
              <lb/>
            buendo ſingulis horis grad. </s>
            <s xml:id="echoid-s7009" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7010" xml:space="preserve">& </s>
            <s xml:id="echoid-s7011" xml:space="preserve">quaternis minutis horæ ſingulos gradus, continebit arcus ſemi-
              <lb/>
            diurnus paralleli ♐, Hor. </s>
            <s xml:id="echoid-s7012" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7013" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7014" xml:space="preserve">43. </s>
            <s xml:id="echoid-s7015" xml:space="preserve">paralleli autem ♊, Hor. </s>
            <s xml:id="echoid-s7016" xml:space="preserve">7. </s>
            <s xml:id="echoid-s7017" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7018" xml:space="preserve">17. </s>
            <s xml:id="echoid-s7019" xml:space="preserve">paulo amplius. </s>
            <s xml:id="echoid-s7020" xml:space="preserve">Si au-
              <lb/>
              <note position="left" xlink:label="note-0136-04" xlink:href="note-0136-04a" xml:space="preserve">30</note>
            tem eoſdem arcus ſemidiutnos duplicemus, habebimus totos arcus diurnos, nempe arcum diur-
              <lb/>
            num paralleli ♐, grad. </s>
            <s xml:id="echoid-s7021" xml:space="preserve">141. </s>
            <s xml:id="echoid-s7022" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7023" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7024" xml:space="preserve">vel Hor. </s>
            <s xml:id="echoid-s7025" xml:space="preserve">9. </s>
            <s xml:id="echoid-s7026" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7027" xml:space="preserve">26. </s>
            <s xml:id="echoid-s7028" xml:space="preserve">& </s>
            <s xml:id="echoid-s7029" xml:space="preserve">arcum diurnum paralleli ♊, grad.
              <lb/>
            </s>
            <s xml:id="echoid-s7030" xml:space="preserve">21 8, Min. </s>
            <s xml:id="echoid-s7031" xml:space="preserve">42. </s>
            <s xml:id="echoid-s7032" xml:space="preserve">vel Hor. </s>
            <s xml:id="echoid-s7033" xml:space="preserve">14. </s>
            <s xml:id="echoid-s7034" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7035" xml:space="preserve">35. </s>
            <s xml:id="echoid-s7036" xml:space="preserve">paulo minus.</s>
            <s xml:id="echoid-s7037" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Arcus ſemidiur
            <lb/>
          nus, qua ratio-
            <lb/>
          ne aliter inue-
            <lb/>
          ſtigetur per triã
            <lb/>
          gula ſphærica.</note>
          <p>
            <s xml:id="echoid-s7038" xml:space="preserve">POSSVMVS autem arcum ſemidiurnum cuiuſuis paralleli per eadem triangula ſphærica
              <lb/>
            inuenire etiam hoc modo. </s>
            <s xml:id="echoid-s7039" xml:space="preserve">Quoniam in triangulo ſphærico C F H, angulus C, rectus eſt, erit per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s7040" xml:space="preserve">16 lib. </s>
            <s xml:id="echoid-s7041" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7042" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s7043" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s7044" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s7045" xml:space="preserve">13 lib. </s>
            <s xml:id="echoid-s7046" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7047" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s7048" xml:space="preserve">41.
              <lb/>
            </s>
            <s xml:id="echoid-s7049" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus arcus F H, complementi declinationis paralleli
              <lb/>
            propoſiti (Nam F H, in parallelo boreali complementum eſt declinationis F I, in auſtrali verò
              <lb/>
            arcus F H, eundem ſinum habet, quem complementum arcus F I, declinationis cum eo ſemicir-
              <lb/>
            culum conſtituens, quod quidem complementum interijcitur inter F, & </s>
            <s xml:id="echoid-s7050" xml:space="preserve">alterum polum, cum ar-
              <lb/>
              <note position="left" xlink:label="note-0136-06" xlink:href="note-0136-06a" xml:space="preserve">40</note>
            cus ex I, per F, vſque ad alterum polum tendens ſit quadrans) ad ſinum anguli recti C, id eſt, ad ſi-
              <lb/>
            num totum, ita ſinus arcus C H, altitudinis poli, ad ſinum anguli F. </s>
            <s xml:id="echoid-s7051" xml:space="preserve">Ex tribus ergo prioribus co-
              <lb/>
            gnitis cognoſcetur & </s>
            <s xml:id="echoid-s7052" xml:space="preserve">angulus F. </s>
            <s xml:id="echoid-s7053" xml:space="preserve">Rurſus quia in triangulo ſphærico B I F, angulus I, rectus eſt, erit
              <lb/>
            per eaſdem propoſitiones, vt ſinus anguli B, complementi altitudinis poli, quem Aequator facit
              <lb/>
            cum Horizonte, ad ſinum arcus F I, declinationis dati paralleli, ita ſinus anguli F, proxime co-
              <lb/>
            gniti ad ſinum arcus B I. </s>
            <s xml:id="echoid-s7054" xml:space="preserve">Igitur ex tribus notis cognitus fiet arcus B I, qui in ſignis borealibus ad-
              <lb/>
            ditus quadranti conficit arcum ſemidiurnum E I, in ſignis autem auſtralibus ex quadrante ſub-
              <lb/>
            latus relinquit arcum ſemidiurnum E I. </s>
            <s xml:id="echoid-s7055" xml:space="preserve">Itaque ſi fiat, vt ſinus complementi declinationis paral-
              <lb/>
            leli propoſiti ad ſinum totum, ita ſinus altitudinis poli ad aliud, habebitur ſinus quidam, quem
              <lb/>
            Primum Inuentum licebit appellare. </s>
            <s xml:id="echoid-s7056" xml:space="preserve">Deinde ſi fiat, vt ſinus complementi altitudinis poli ad ſi-
              <lb/>
              <note position="left" xlink:label="note-0136-07" xlink:href="note-0136-07a" xml:space="preserve">50</note>
            num declinationis, ita ſinus, quem diximus Primum Inuentum, ad aliud, inuenietur ſinus, cuius
              <lb/>
            arcus, Sole exiſtente boreali, additus quadranti, vel Sole auſtrali exiſtente, ex quadrante demptus,
              <lb/>
            dabit arcum ſemidiurnum.</s>
            <s xml:id="echoid-s7057" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7058" xml:space="preserve">COMMODISSIME etiam ſine triangulis ſphæricis latitudines ortiuas, occiduasue, atq;
              <lb/>
            </s>
            <s xml:id="echoid-s7059" xml:space="preserve">
              <note position="left" xlink:label="note-0136-08" xlink:href="note-0136-08a" xml:space="preserve">Amplitudo or.
                <lb/>
              tiua uel occi-
                <lb/>
              dua, quo modo
                <lb/>
              ſuppu@etur pe@
                <lb/>
              ſinus ex Ana-
                <lb/>
              @emmate.</note>
            arcus ſemidiurnos reperiemus hac ratione. </s>
            <s xml:id="echoid-s7060" xml:space="preserve">Repetatur Analemma, hoc eſt, figura ſecunda præ-
              <lb/>
            cedentis propoſ. </s>
            <s xml:id="echoid-s7061" xml:space="preserve">vbi H N, tam in parallelo boreali, quàm in auſtrali oſtenſus eſt eſſe arcus ſemi-
              <lb/>
            diurnus; </s>
            <s xml:id="echoid-s7062" xml:space="preserve">Item E L, ſinus rectus eſt amplitudinis ortiuæ, occiduæue: </s>
            <s xml:id="echoid-s7063" xml:space="preserve">Nam vt in ſcholio propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s7064" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7065" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s7066" xml:space="preserve">demonſtrauimus recta, ex L, ducta ad B D, perpendicularis, cum ſit commu-
              <lb/>
            nis ſectio Horizontis & </s>
            <s xml:id="echoid-s7067" xml:space="preserve">paralleli, aufert ex circulo A B C D, arcum latitudinis ortiuæ, ſiue occi-
              <lb/>
            duæ, cuius quidem ſinus eſt E L. </s>
            <s xml:id="echoid-s7068" xml:space="preserve">Quoniam igitur in triangulo rectangulo E k L, ſi E L, ponatur
              <lb/>
            ſinus totus, recta E K, eſt ſinus anguli E L
              <emph style="sc">K</emph>
            , complementi altitudinis poli, vt in tractatione </s>
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