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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            <s xml:id="echoid-s15086" xml:space="preserve">
              <pb o="220" file="0240" n="240" rhead="GNOMONICES"/>
            ctam A E, ſupra ſtylum, vel rectam A G, ad ſiniſtram, oſtendemus eadem ratione, rectam F H, ſecare
              <lb/>
            rectam C F, infra ſtylum, & </s>
            <s xml:id="echoid-s15087" xml:space="preserve">rectam C H, ad ſiniſtram quoque, nempe in oppoſitis ſemper partibus; </s>
            <s xml:id="echoid-s15088" xml:space="preserve">re-
              <lb/>
            ctas{q́ue}, quas F H, ex rectis C F, C H, aufert, æquales eſſerectis, quas E G, abſcindit ex rectis
              <lb/>
            A E, A G.</s>
            <s xml:id="echoid-s15089" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15090" xml:space="preserve">DEINDE alius quiſpiam circulus maximus in Auſtrali horologio, inferiorive, per verticem ſty-
              <lb/>
            li B, vel D, ductus, faciat ſectionem L M, quæ non ſecet vtramque A E, A G, ſed alteram tantum, nem-
              <lb/>
              <figure xlink:label="fig-0240-01" xlink:href="fig-0240-01a" number="166">
                <image file="0240-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0240-01"/>
              </figure>
              <note position="left" xlink:label="note-0240-01" xlink:href="note-0240-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0240-02" xlink:href="note-0240-02a" xml:space="preserve">20</note>
            pe A E, in L, ſupra ſtylum, parallela autem ſit alteri, nimirum ipſi A G, Secabit idem hic circulus, cum
              <lb/>
            per ſtyli verticem incedat, boreale horologium, inferiusve, infra ſtylum, hoc eſt, in oppoſita parte, per re-
              <lb/>
            ctam N O, quę rectam C F, ſecet in N: </s>
            <s xml:id="echoid-s15091" xml:space="preserve">eritq́, N O, ipſi C H, parallela. </s>
            <s xml:id="echoid-s15092" xml:space="preserve">Cum enim L M, ponatur paralle-
              <lb/>
              <note position="left" xlink:label="note-0240-03" xlink:href="note-0240-03a" xml:space="preserve">9. vndec.</note>
            la ipſi A G, eidem verò A G, parallela quoque ſit C H, vt ante diximus; </s>
            <s xml:id="echoid-s15093" xml:space="preserve">erunt etiam inter ſe parallelæ
              <lb/>
              <note position="left" xlink:label="note-0240-04" xlink:href="note-0240-04a" xml:space="preserve">16. vndec.</note>
            L M, C H. </s>
            <s xml:id="echoid-s15094" xml:space="preserve">Rurſus quoniam N O, ipſi L M, parallela eſt, (quod L M, N O, ſectiones ſint factæ ab vno,
              <lb/>
              <note position="left" xlink:label="note-0240-05" xlink:href="note-0240-05a" xml:space="preserve">9. vndec.</note>
            eodem{q́ue} plano in planis parallelis) & </s>
            <s xml:id="echoid-s15095" xml:space="preserve">eidem L M, oſtenſa proximè eſt parallela C H; </s>
            <s xml:id="echoid-s15096" xml:space="preserve">erunt quoque N O,
              <lb/>
            C H, inter ſe parallelæ. </s>
            <s xml:id="echoid-s15097" xml:space="preserve">Igitur cum L M, ipſi A G, & </s>
            <s xml:id="echoid-s15098" xml:space="preserve">N O, ipſi C H, parallela ſit; </s>
            <s xml:id="echoid-s15099" xml:space="preserve">erunt anguli L, N,
              <lb/>
              <note position="left" xlink:label="note-0240-06" xlink:href="note-0240-06a" xml:space="preserve">29. primi.</note>
            angulis A, C, æquales, ac propterea recti. </s>
            <s xml:id="echoid-s15100" xml:space="preserve">Quoniam verò A E, C F, parallelæ ſunt, vt ſuperius oſtenſum
              <lb/>
              <note position="left" xlink:label="note-0240-07" xlink:href="note-0240-07a" xml:space="preserve">29. primi.</note>
              <note position="left" xlink:label="note-0240-08" xlink:href="note-0240-08a" xml:space="preserve">30</note>
            eſt, erunt inter ſe æquales anguli alterni in punctis L, & </s>
            <s xml:id="echoid-s15101" xml:space="preserve">N, rectarum A E, C F, facti à communi ſectione
              <lb/>
            circulorum maximorum ſectiones A E, C F, & </s>
            <s xml:id="echoid-s15102" xml:space="preserve">L M, N O, facientium, quæ quidem communis ſectio per
              <lb/>
            puncta L, B, D, N, tranſit, cum per hæc eadem circuli ipſi maximi tranſeant. </s>
            <s xml:id="echoid-s15103" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s15104" xml:space="preserve">anguli re-
              <lb/>
            cti A, C, quos ſtyli cum rectis A L, C N, constituunt, æquales: </s>
            <s xml:id="echoid-s15105" xml:space="preserve">Item & </s>
            <s xml:id="echoid-s15106" xml:space="preserve">ſtyli A B, C D, æquales, qui
              <lb/>
            æqualibus angulis L, N, ſubtenduntur in triangulis A B L, C D N, quorum baſes ſunt partes communis
              <lb/>
            ſectionis maximorum circulorum ſectiones A E, C F, & </s>
            <s xml:id="echoid-s15107" xml:space="preserve">L M, N O, in vtroque horologio facientium.
              <lb/>
            </s>
            <s xml:id="echoid-s15108" xml:space="preserve">
              <note position="left" xlink:label="note-0240-09" xlink:href="note-0240-09a" xml:space="preserve">26. primi.</note>
            Igitur latera quoque A L, C N, æqualia erunt. </s>
            <s xml:id="echoid-s15109" xml:space="preserve">Tanto ergo interuallo in recta A E, remouetur ſectio
              <lb/>
            L M, à ſtylo ſurſum verſus, quanto in recta C F, ſectio N O, à ſtylo deorſum verſus abeſt. </s>
            <s xml:id="echoid-s15110" xml:space="preserve">Quòd ſi recta
              <lb/>
            L M, ſecet rectam A E, infra ſtylum, ostendemus eadem ratione, rectam N O, ſecare rectam C F, ſupra
              <lb/>
            ſtylum, parallelam{q́ue} eſſe N O, ipſi L M, & </s>
            <s xml:id="echoid-s15111" xml:space="preserve">rectam, quam N O, ex C F, abſcindit, ęqualem eſſe rectæ, quam
              <lb/>
            L M, ex A E, aufert.</s>
            <s xml:id="echoid-s15112" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p style="it">
            <s xml:id="echoid-s15113" xml:space="preserve">POSTREMO alius quiſpiam maximus circulus in horologio Auſtrali, ſiue ſuperiori, faciat ſe-
              <lb/>
            ctionem M P, quæ rurſus non ſecet vtramque A E, C F, ſed ipſam A G, duntaxat in P, ad ſiniſtram, pa-
              <lb/>
            rallela autem ſit ipſi A E. </s>
            <s xml:id="echoid-s15114" xml:space="preserve">Secabit hic idem circulus, cum per verticem ſtyli ducatur, horologium borea-
              <lb/>
            le, ſeu inferius in oppoſita parte, hoc eſt, ad ſiniſtram quoque, per rectam O Q, quæ rectam C H, ſecet
              <lb/>
            in Q: </s>
            <s xml:id="echoid-s15115" xml:space="preserve">erit{q́ue} O Q, ipſi C F, parallela. </s>
            <s xml:id="echoid-s15116" xml:space="preserve">Cum enim M P, parallela ponatur ipſi A E, eidem verò A E,
              <lb/>
              <note position="left" xlink:label="note-0240-11" xlink:href="note-0240-11a" xml:space="preserve">9. vndec.</note>
            parallela quoque oſtenſa ſit antea C F; </s>
            <s xml:id="echoid-s15117" xml:space="preserve">erunt inter ſe quoque parallelæ M P, C F. </s>
            <s xml:id="echoid-s15118" xml:space="preserve">Rurſus quoniam O Q,
              <lb/>
              <note position="left" xlink:label="note-0240-12" xlink:href="note-0240-12a" xml:space="preserve">16. vndec.</note>
            ipſi M P, parallela eſt, (quod M P, O Q, ſectiones ſint factæ ab vno, eodem{q́ue} plano in planis paralle-
              <lb/>
              <note position="left" xlink:label="note-0240-13" xlink:href="note-0240-13a" xml:space="preserve">9. vndec.</note>
            lis) & </s>
            <s xml:id="echoid-s15119" xml:space="preserve">eidem M P, oſtenſa eſt proximè parallela C F; </s>
            <s xml:id="echoid-s15120" xml:space="preserve">erunt etiam inter ſe parallelæ O Q, C F. </s>
            <s xml:id="echoid-s15121" xml:space="preserve">Igitur
              <lb/>
              <note position="left" xlink:label="note-0240-14" xlink:href="note-0240-14a" xml:space="preserve">29. primi.</note>
            cum M P, ipſi A E, parallela ſit, & </s>
            <s xml:id="echoid-s15122" xml:space="preserve">O Q, ipſi C F; </s>
            <s xml:id="echoid-s15123" xml:space="preserve">erunt anguli P, Q, angulis A, C, æquales, ac pro-
              <lb/>
              <note position="left" xlink:label="note-0240-15" xlink:href="note-0240-15a" xml:space="preserve">29. primi.</note>
              <note position="left" xlink:label="note-0240-16" xlink:href="note-0240-16a" xml:space="preserve">50</note>
            inderecti. </s>
            <s xml:id="echoid-s15124" xml:space="preserve">Quia verò, vt ſuperius oſtendimus, A G, C H, parallelæ ſunt, erunt inter ſe æquales anguli
              <lb/>
            alterni in punctis P, Q, rectarum A G, C H, facti à communi ſectione circulorum maximorum ſectio-
              <lb/>
            ctiones A G, C H, & </s>
            <s xml:id="echoid-s15125" xml:space="preserve">M P, O Q, facientium, quæ quidem ſectio communis per puncta P, B, D, Q,
              <lb/>
            tranſit, quòd per hæc eadem circuli ipſi maximi tranſeant quoque. </s>
            <s xml:id="echoid-s15126" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s15127" xml:space="preserve">anguli recti A, C,
              <lb/>
            quos ſtyli cum rectis A P, C Q, faciunt, æquales: </s>
            <s xml:id="echoid-s15128" xml:space="preserve">Item & </s>
            <s xml:id="echoid-s15129" xml:space="preserve">ſtyli A B, C D, æquales, qui æqualibus an-
              <lb/>
            gulis P, Q, ſubtenduntur in triangulis A B P, C D Q, quorum baſes ſunt ſegmenta communis ſectio-
              <lb/>
            nis maximorum circulorum ſectiones A G, C H, & </s>
            <s xml:id="echoid-s15130" xml:space="preserve">M P, O Q, in vtroque horologio facientium. </s>
            <s xml:id="echoid-s15131" xml:space="preserve">Igi-
              <lb/>
              <note position="left" xlink:label="note-0240-17" xlink:href="note-0240-17a" xml:space="preserve">26. primi.</note>
            tur latera quoque A P, C Q, æqualia erunt. </s>
            <s xml:id="echoid-s15132" xml:space="preserve">Spatijs ergo æqualibus rectæ M P, O Q, in rectis A G,
              <lb/>
            C H, abſunt à ſtylis ſiniſtram verſus. </s>
            <s xml:id="echoid-s15133" xml:space="preserve">Quòd ſi recta M P, ſecet rectam A G, ad dextram, demonſtra-
              <lb/>
            bimus eadem argumentatione, rectam O Q, ſecare rectam C H, ad dextram quoque, & </s>
            <s xml:id="echoid-s15134" xml:space="preserve">parallelam
              <lb/>
            eſſe O Q, ipſi M P, rectas, quas M P, O Q, ex A G, C H, amputant, eſſe æquales.</s>
            <s xml:id="echoid-s15135" xml:space="preserve"/>
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