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

Table of figures

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            <s xml:id="echoid-s32493" xml:space="preserve">
              <pb o="505" file="0521" n="521" rhead="LIBER QVINTVS."/>
            D E F, in quo ducatur diameter D C, ſecans A B, rectam ad angulos rectos, quæ meridiana linea
              <lb/>
            erit, vt propoſ. </s>
            <s xml:id="echoid-s32494" xml:space="preserve">37. </s>
            <s xml:id="echoid-s32495" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s32496" xml:space="preserve">2. </s>
            <s xml:id="echoid-s32497" xml:space="preserve">demonſtrauimus. </s>
            <s xml:id="echoid-s32498" xml:space="preserve">Rurſus aſſumpto gnomone quantocunque, abſcindan-
              <lb/>
            tur ei partes quotlibet æquales ex recta G H, vt in ſuperioribus dictum eſt. </s>
            <s xml:id="echoid-s32499" xml:space="preserve">Itaque ſi latitudines
              <lb/>
            vmbrarum ſupputentur à puncto F, vel E, prout oriẽtales fuerint, aut occidẽtales, ver ſus Boream,
              <lb/>
            vel Auſtrum, prout Boreales fuerint, Auſtralesve, deſcribetur horologiũ polare, vt Meridianum,
              <lb/>
            vt in appoſita figura intueri licet, in qua ex quadruplici latitudine vmbræ F K, grad. </s>
            <s xml:id="echoid-s32500" xml:space="preserve">24. </s>
            <s xml:id="echoid-s32501" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32502" xml:space="preserve">14. </s>
            <s xml:id="echoid-s32503" xml:space="preserve">quę
              <lb/>
            horæ 7. </s>
            <s xml:id="echoid-s32504" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s32505" xml:space="preserve">noc & </s>
            <s xml:id="echoid-s32506" xml:space="preserve">5. </s>
            <s xml:id="echoid-s32507" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s32508" xml:space="preserve">debetur, ſupputata tam à puncto orientali F, quàm ab occidentali
              <lb/>
            E, in Boream, & </s>
            <s xml:id="echoid-s32509" xml:space="preserve">Auſtrum, & </s>
            <s xml:id="echoid-s32510" xml:space="preserve">ex eius longitudine vmbræ P. </s>
            <s xml:id="echoid-s32511" xml:space="preserve">49. </s>
            <s xml:id="echoid-s32512" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32513" xml:space="preserve">6. </s>
            <s xml:id="echoid-s32514" xml:space="preserve">inuentum eſt quadruplex pun
              <lb/>
            ctum L, vna eademq; </s>
            <s xml:id="echoid-s32515" xml:space="preserve">opera, pro hora 7. </s>
            <s xml:id="echoid-s32516" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s32517" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s32518" xml:space="preserve">& </s>
            <s xml:id="echoid-s32519" xml:space="preserve">5. </s>
            <s xml:id="echoid-s32520" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s32521" xml:space="preserve">in tropico ♋, & </s>
            <s xml:id="echoid-s32522" xml:space="preserve">♑. </s>
            <s xml:id="echoid-s32523" xml:space="preserve">Ex vmbræ au-
              <lb/>
            tem longitudine earundem horarum in Aequatore, nempe P. </s>
            <s xml:id="echoid-s32524" xml:space="preserve">44. </s>
            <s xml:id="echoid-s32525" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32526" xml:space="preserve">47. </s>
            <s xml:id="echoid-s32527" xml:space="preserve">inuenta ſunt puncta A, & </s>
            <s xml:id="echoid-s32528" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0521-01" xlink:href="note-0521-01a" xml:space="preserve">10</note>
              <figure xlink:label="fig-0521-01" xlink:href="fig-0521-01a" number="321">
                <image file="0521-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0521-01"/>
              </figure>
              <note position="left" xlink:label="note-0521-02" xlink:href="note-0521-02a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0521-03" xlink:href="note-0521-03a" xml:space="preserve">30</note>
            B, pro eiſdem horis in linea ęquinoctiali, &</s>
            <s xml:id="echoid-s32529" xml:space="preserve">c. </s>
            <s xml:id="echoid-s32530" xml:space="preserve">Rurſus ex latitudine vmbræ E M, occidentali, atque
              <lb/>
            boreali grad. </s>
            <s xml:id="echoid-s32531" xml:space="preserve">72. </s>
            <s xml:id="echoid-s32532" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s32533" xml:space="preserve">16. </s>
            <s xml:id="echoid-s32534" xml:space="preserve">vel eius oppoſita F M, quæ debetur horæ 17. </s>
            <s xml:id="echoid-s32535" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32536" xml:space="preserve">in tropico ♋, eiusq́;
              <lb/>
            </s>
            <s xml:id="echoid-s32537" xml:space="preserve">longitudine vmbræ P. </s>
            <s xml:id="echoid-s32538" xml:space="preserve">5. </s>
            <s xml:id="echoid-s32539" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32540" xml:space="preserve">32. </s>
            <s xml:id="echoid-s32541" xml:space="preserve">inuentum eſt punctum N, pro hora 17. </s>
            <s xml:id="echoid-s32542" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32543" xml:space="preserve">in tropico ♋. </s>
            <s xml:id="echoid-s32544" xml:space="preserve">Item
              <lb/>
              <note position="left" xlink:label="note-0521-04" xlink:href="note-0521-04a" xml:space="preserve">40</note>
            ex latitudine vmbræ F O, orientali, atque auſtrali gr. </s>
            <s xml:id="echoid-s32545" xml:space="preserve">35. </s>
            <s xml:id="echoid-s32546" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32547" xml:space="preserve">14. </s>
            <s xml:id="echoid-s32548" xml:space="preserve">vel eius oppoſita E O, quæ reſpon-
              <lb/>
            det eidem horæ 17. </s>
            <s xml:id="echoid-s32549" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32550" xml:space="preserve">in tropico ♑, eiusq́ue longitudine vmbræ P. </s>
            <s xml:id="echoid-s32551" xml:space="preserve">11. </s>
            <s xml:id="echoid-s32552" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32553" xml:space="preserve">29. </s>
            <s xml:id="echoid-s32554" xml:space="preserve">inuentum eſt
              <lb/>
            punctum P, pro hora 17. </s>
            <s xml:id="echoid-s32555" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32556" xml:space="preserve">in tropico ♑. </s>
            <s xml:id="echoid-s32557" xml:space="preserve">Denique ex longitudine vmbræ occidentali gr. </s>
            <s xml:id="echoid-s32558" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s32559" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32560" xml:space="preserve">13. </s>
            <s xml:id="echoid-s32561" xml:space="preserve">eiuſdem horę 17. </s>
            <s xml:id="echoid-s32562" xml:space="preserve">in Aequatore (cum enim hæc hora in Aequatore ſit orientalis, cadet eius
              <lb/>
            vmbra in partem occidentalem horologii, nempe in oppoſitam) repertũ eſt punctum a, eiuſdem
              <lb/>
            horæ 17. </s>
            <s xml:id="echoid-s32563" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32564" xml:space="preserve">in linea æquinoctiali, &</s>
            <s xml:id="echoid-s32565" xml:space="preserve">c. </s>
            <s xml:id="echoid-s32566" xml:space="preserve">Horæ autem 12. </s>
            <s xml:id="echoid-s32567" xml:space="preserve">& </s>
            <s xml:id="echoid-s32568" xml:space="preserve">24. </s>
            <s xml:id="echoid-s32569" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32570" xml:space="preserve">& </s>
            <s xml:id="echoid-s32571" xml:space="preserve">6. </s>
            <s xml:id="echoid-s32572" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s32573" xml:space="preserve">ducendæ ſunt
              <lb/>
            per puncta in tropicis inuenta lineæ æquinoctiali æquidiſtantes, vt propoſ. </s>
            <s xml:id="echoid-s32574" xml:space="preserve">46. </s>
            <s xml:id="echoid-s32575" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s32576" xml:space="preserve">2. </s>
            <s xml:id="echoid-s32577" xml:space="preserve">oſtenſum eſt. </s>
            <s xml:id="echoid-s32578" xml:space="preserve">
              <lb/>
            Linea porrò horæ 24. </s>
            <s xml:id="echoid-s32579" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32580" xml:space="preserve">producta dabit lineam horizontalem, cum ſit communis ſectio pla-
              <lb/>
            ni horologij, & </s>
            <s xml:id="echoid-s32581" xml:space="preserve">circuli horæ 24. </s>
            <s xml:id="echoid-s32582" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32583" xml:space="preserve">hoc eſt, Horizontis. </s>
            <s xml:id="echoid-s32584" xml:space="preserve">Quam ita quoque ducemus. </s>
            <s xml:id="echoid-s32585" xml:space="preserve">Ex ta-
              <lb/>
              <note position="right" xlink:label="note-0521-05" xlink:href="note-0521-05a" xml:space="preserve">Linea horizon-
                <lb/>
              talis, atque hora
                <lb/>
              12. ab or. uel
                <lb/>
              occ. quomodo
                <lb/>
              ducenda.</note>
            bula longitudinum vmbrarum propoſ. </s>
            <s xml:id="echoid-s32586" xml:space="preserve">2. </s>
            <s xml:id="echoid-s32587" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s32588" xml:space="preserve">ſumatur longitudo vmbræ reſpondens altitu-
              <lb/>
              <note position="left" xlink:label="note-0521-06" xlink:href="note-0521-06a" xml:space="preserve">50</note>
            dini poli ſupra Horizontem, vt in noſtro exemplo reſpondens grad. </s>
            <s xml:id="echoid-s32589" xml:space="preserve">42. </s>
            <s xml:id="echoid-s32590" xml:space="preserve">quæ comprehendit P. </s>
            <s xml:id="echoid-s32591" xml:space="preserve">13.
              <lb/>
            </s>
            <s xml:id="echoid-s32592" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32593" xml:space="preserve">20. </s>
            <s xml:id="echoid-s32594" xml:space="preserve">eaq́ue transferatur beneficio circini ex C, in lineam meridianam verſus Boream, vſque ad
              <lb/>
            punctum Q. </s>
            <s xml:id="echoid-s32595" xml:space="preserve">Per hoc enim ducenda eſt linea horizontalis, vel horæ 24. </s>
            <s xml:id="echoid-s32596" xml:space="preserve">lineæ æquinoctiali paral-
              <lb/>
            lela, vel ad C D, perpendicularis. </s>
            <s xml:id="echoid-s32597" xml:space="preserve">Quoniam enim arcus Meridiani inter circulum horæ 6. </s>
            <s xml:id="echoid-s32598" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s32599" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s32600" xml:space="preserve">med. </s>
            <s xml:id="echoid-s32601" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s32602" xml:space="preserve">cui horologium æquidiſtat, atque Horizontem interpoſitus ex parte auſtrali metitur
              <lb/>
            altitudinem poli ſupra Horizontem, hoc eſt, in noſtro exemplo complectitur gr. </s>
            <s xml:id="echoid-s32603" xml:space="preserve">42. </s>
            <s xml:id="echoid-s32604" xml:space="preserve">ſi Sol ponere-
              <lb/>
            tur in eo puncto Horizontis ex parte auſtrali, vbi à Meridiano ſecatur, haberet ſupra circulum ho-
              <lb/>
            rę 6. </s>
            <s xml:id="echoid-s32605" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s32606" xml:space="preserve">& </s>
            <s xml:id="echoid-s32607" xml:space="preserve">med. </s>
            <s xml:id="echoid-s32608" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s32609" xml:space="preserve">altitudinem grad. </s>
            <s xml:id="echoid-s32610" xml:space="preserve">42. </s>
            <s xml:id="echoid-s32611" xml:space="preserve">quanta nimirum eſt poli altitudo ſupra Horizontẽ. </s>
            <s xml:id="echoid-s32612" xml:space="preserve">
              <lb/>
            Igitur eius vmbra à ſtylo proiecta caderet in punctum Q, verſus Boreales partes, quæ Soli oppo-
              <lb/>
            nuntur, cum vmbra C Q, debeatur gradibus 42. </s>
            <s xml:id="echoid-s32613" xml:space="preserve">ſiue altitudini poli. </s>
            <s xml:id="echoid-s32614" xml:space="preserve">Et quoniam tantum ex alte-
              <lb/>
            ra parte diſtat linea horæ 12. </s>
            <s xml:id="echoid-s32615" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s32616" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s32617" xml:space="preserve">ab æquinoctiali linea, quantum horizontalis abeſt, </s>
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