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-s1015" xml:space="preserve">
              <pb o="14" file="0034" n="34" rhead="GNOMONICES"/>
            circulorum, eandem habent ſinus tam recti, quàm verſi arcuum ſimilium. </s>
            <s xml:id="echoid-s1016" xml:space="preserve">Et co
              <unsure/>
            n-
              <lb/>
              <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">Sinus toti pro-
                <lb/>
              portionales sũt
                <lb/>
              ſinubus tam re-
                <lb/>
              ctis, quàm uer-
                <lb/>
              ſis arcuum ſi@i
                <lb/>
              lium, & contra.</note>
            tra, arcus, quorum ſinus tam recti, quàm verſi eandem proportionem habent, quam
              <lb/>
            ſinus toti, ſimiles ſunt.</s>
            <s xml:id="echoid-s1017" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1018" xml:space="preserve">SINT arcus A B, C D, circulorum, quorum ſemidiametri A E, C F, ſimiles, & </s>
            <s xml:id="echoid-s1019" xml:space="preserve">
              <lb/>
            eorum ſinus recti B G, D H, verſi autem A G, C H. </s>
            <s xml:id="echoid-s1020" xml:space="preserve">Dico eße, vt A E, ad C F, ita & </s>
            <s xml:id="echoid-s1021" xml:space="preserve">
              <lb/>
            B G, ad D H, & </s>
            <s xml:id="echoid-s1022" xml:space="preserve">A G, ad C H. </s>
            <s xml:id="echoid-s1023" xml:space="preserve">Ductis enim rurſum ſemidiametris B E, D F, erunt ob ſi-
              <lb/>
            militudinem arcuum A B, C D, anguli E, & </s>
            <s xml:id="echoid-s1024" xml:space="preserve">F, æquales, ex ijs, quæ ad propoſ. </s>
            <s xml:id="echoid-s1025" xml:space="preserve">33. </s>
            <s xml:id="echoid-s1026" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s1027" xml:space="preserve">
              <figure xlink:label="fig-0034-01" xlink:href="fig-0034-01a" number="12">
                <image file="0034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0034-01"/>
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            6. </s>
            <s xml:id="echoid-s1028" xml:space="preserve">Euclidis ostendimus; </s>
            <s xml:id="echoid-s1029" xml:space="preserve">at-
              <lb/>
            que adeò, cum & </s>
            <s xml:id="echoid-s1030" xml:space="preserve">anguli ad
              <lb/>
              <note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve">10</note>
            G, H, æquales ſint, nempe
              <lb/>
            recti, æquiangula erunt triã-
              <lb/>
              <note position="left" xlink:label="note-0034-03" xlink:href="note-0034-03a" xml:space="preserve">32. primi.
                <lb/>
              4. ſexti.</note>
            gula B E G, D F H. </s>
            <s xml:id="echoid-s1031" xml:space="preserve">Quare
              <lb/>
            erit, vt B E, ad B G, ita D F,
              <lb/>
            ad D H; </s>
            <s xml:id="echoid-s1032" xml:space="preserve">& </s>
            <s xml:id="echoid-s1033" xml:space="preserve">permutando, vt
              <lb/>
            B E, hoc eſt, A E, ad D F,
              <lb/>
            hoc eſt, ad C F, ita B G,
              <lb/>
            ad D H.</s>
            <s xml:id="echoid-s1034" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1035" xml:space="preserve">RVRSVS, quoniam propter ſimilitudinem arcuum A B, C D, triangula B E G,
              <lb/>
              <note position="left" xlink:label="note-0034-04" xlink:href="note-0034-04a" xml:space="preserve">20</note>
            D F H, eodem modo ſimilia ſunt; </s>
            <s xml:id="echoid-s1036" xml:space="preserve">erit, vt B E, hoc eſt, A E, ad E G, ita D F, hoc eſt, C F,
              <lb/>
              <note position="left" xlink:label="note-0034-05" xlink:href="note-0034-05a" xml:space="preserve">4. ſexti.</note>
            ad F H; </s>
            <s xml:id="echoid-s1037" xml:space="preserve">& </s>
            <s xml:id="echoid-s1038" xml:space="preserve">per conuerſionem rationis, vt A E, ad A G, ita C F, ad C H; </s>
            <s xml:id="echoid-s1039" xml:space="preserve">& </s>
            <s xml:id="echoid-s1040" xml:space="preserve">permutando,
              <lb/>
            vt A E, ad C F, ita A G ad C H. </s>
            <s xml:id="echoid-s1041" xml:space="preserve">quod eſt primum.</s>
            <s xml:id="echoid-s1042" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1043" xml:space="preserve">SED iam ſit, vt A E, ad C F, ita tam B G, ad D H, quàm A G, ad C H. </s>
            <s xml:id="echoid-s1044" xml:space="preserve">Dicoarcus
              <lb/>
            A B, C D, ſimiles eſſe. </s>
            <s xml:id="echoid-s1045" xml:space="preserve">Ductis enim rurſus rectis B E, D F; </s>
            <s xml:id="echoid-s1046" xml:space="preserve">quoniam eſt, vt A E, ad C F,
              <lb/>
            ita B G, ad D H; </s>
            <s xml:id="echoid-s1047" xml:space="preserve">& </s>
            <s xml:id="echoid-s1048" xml:space="preserve">permutando, vt A E, hoc est, B E, ad B G, ita C F, hoc eſt, D F, ad
              <lb/>
            D H; </s>
            <s xml:id="echoid-s1049" xml:space="preserve">ſunt{q́ue} anguli ad G, H, æquales, nemperecti, habebunt triangula B E G, D F H, an-
              <lb/>
            gulos G, H, æquales, & </s>
            <s xml:id="echoid-s1050" xml:space="preserve">latera B E, BG, circa angulum B, lateribus D F, D H, circa an-
              <lb/>
              <note position="left" xlink:label="note-0034-06" xlink:href="note-0034-06a" xml:space="preserve">30</note>
            gulum D, proportionalia. </s>
            <s xml:id="echoid-s1051" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s1052" xml:space="preserve">@trumque reliquorum angulorum E, F, minc
              <unsure/>
            rem
              <lb/>
              <note position="left" xlink:label="note-0034-07" xlink:href="note-0034-07a" xml:space="preserve">17. primi.
                <lb/>
              7. ſexti.</note>
            habeant recto, quod anguli G, H, recti ſint, erunt ipſa triangula B E G, D F H, æquian-
              <lb/>
            gula, æquales{q́ue} habebunt angulos B, D, circum quos proportionalia ſunt latera, atq; </s>
            <s xml:id="echoid-s1053" xml:space="preserve">adeo
              <lb/>
            & </s>
            <s xml:id="echoid-s1054" xml:space="preserve">reliquos E, F. </s>
            <s xml:id="echoid-s1055" xml:space="preserve">Quocirca, ex ijs, quæ ad propoſ. </s>
            <s xml:id="echoid-s1056" xml:space="preserve">33. </s>
            <s xml:id="echoid-s1057" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1058" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1059" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1060" xml:space="preserve">oſtendimus, arcus A B,
              <lb/>
            C D, ſimiles erunt. </s>
            <s xml:id="echoid-s1061" xml:space="preserve">Quare conſtat, arcus, quorum ſinus recti proportionales ſunt ſinubus
              <lb/>
            totis, ſimiles eße.</s>
            <s xml:id="echoid-s1062" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1063" xml:space="preserve">DEINDE quia eſt, vt A E, ad C F, ita A G, ad C H; </s>
            <s xml:id="echoid-s1064" xml:space="preserve">erit permutando, vt A E, ad
              <lb/>
            A G, ita C F, ad C H; </s>
            <s xml:id="echoid-s1065" xml:space="preserve">& </s>
            <s xml:id="echoid-s1066" xml:space="preserve">per conuerſionem rationis, vt A E, hoc eſt, B E, ad E G, ta C F,
              <lb/>
            hoc est, D F, ad F H. </s>
            <s xml:id="echoid-s1067" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s1068" xml:space="preserve">anguli ad G, H, æquales ſint, nimirum recti, habebunt
              <lb/>
              <note position="left" xlink:label="note-0034-08" xlink:href="note-0034-08a" xml:space="preserve">40</note>
            triangula B E G, D F H, angulos G, H, æquales, & </s>
            <s xml:id="echoid-s1069" xml:space="preserve">latera B E, E G, circa angulum E, la-
              <lb/>
            teribus D F, F H, circa angulum F, proportionalia. </s>
            <s xml:id="echoid-s1070" xml:space="preserve">Habent autem & </s>
            <s xml:id="echoid-s1071" xml:space="preserve">vtrumque reliquo
              <unsure/>
            -
              <lb/>
            rum angulorũ B, D, rect
              <unsure/>
            o minorem, quod anguli
              <unsure/>
            G, H, ſint recti. </s>
            <s xml:id="echoid-s1072" xml:space="preserve">Igitur æquiangula erunt
              <lb/>
              <note position="left" xlink:label="note-0034-09" xlink:href="note-0034-09a" xml:space="preserve">17. Primi.
                <lb/>
              7. ſexti.</note>
            triangula B E G, D F H, æquales{q́ue} habebunt angulos E, F, circum quos proportionalia
              <lb/>
            ſunt latera. </s>
            <s xml:id="echoid-s1073" xml:space="preserve">Quam ob rem, per ea, quæ ad propoſ. </s>
            <s xml:id="echoid-s1074" xml:space="preserve">33. </s>
            <s xml:id="echoid-s1075" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1076" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1077" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s1078" xml:space="preserve">ſcripſimus, arcus A B, C D,
              <lb/>
            ſimiles erunt. </s>
            <s xml:id="echoid-s1079" xml:space="preserve">Ex quibus liquet, arcus, quorum ſinus verſi ſunt ſinubus totis proportiona-
              <lb/>
            les, ſimiles eſſe: </s>
            <s xml:id="echoid-s1080" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1081" xml:space="preserve">idem de ſinubus rectis proxime oſtenſum eſt. </s>
            <s xml:id="echoid-s1082" xml:space="preserve">@uam ergo proportio-
              <lb/>
            nem habent ſinus toti, &</s>
            <s xml:id="echoid-s1083" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1084" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s1085" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1086" xml:space="preserve">CONSTAT igitur ex his, arcus A D, Q X, in figura præcedentis demonſtrationis
              <lb/>
              <note position="left" xlink:label="note-0034-10" xlink:href="note-0034-10a" xml:space="preserve">50</note>
            ſimiles eſſe, vt in demonſtratione huius propoſ. </s>
            <s xml:id="echoid-s1087" xml:space="preserve">aſſumebatur; </s>
            <s xml:id="echoid-s1088" xml:space="preserve">quandoquidem eorum ſinus
              <lb/>
            recti eandem proportionem habent, quam ſemidiametri circulorum, quorum ſunt arcus.
              <lb/>
            </s>
            <s xml:id="echoid-s1089" xml:space="preserve">Item ita eſſe ſinum totum Zodiaci ad M O, ſinum totum circuli M P N Q, vt eſt ſinus
              <lb/>
            arcus Zodiaci grad. </s>
            <s xml:id="echoid-s1090" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1091" xml:space="preserve">ad O φ, ſinum arcus Q X, continentis etiam 30. </s>
            <s xml:id="echoid-s1092" xml:space="preserve">gradus; </s>
            <s xml:id="echoid-s1093" xml:space="preserve">propterc
              <unsure/>
            a
              <lb/>
            quòd eiuſm
              <unsure/>
            odi arcus ſimiles ſint. </s>
            <s xml:id="echoid-s1094" xml:space="preserve">Id quod in ſequenti corollario vſui nobis futurum eſt.</s>
            <s xml:id="echoid-s1095" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div53" type="section" level="1" n="17">
          <head xml:id="echoid-head20" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s1096" xml:space="preserve">Ex demonſtratione huius propoſitionis manifeſtum eſt, vt eſt M E, ſinus totus ad M O, ſinum maxi-
              <lb/>
              <note position="left" xlink:label="note-0034-11" xlink:href="note-0034-11a" xml:space="preserve">Eadem eſt pro-
                <lb/>
              poruo ſinus to-
                <lb/>
              tius ad ſinũ ma</note>
            mæ declinationis Solis, i@a eſie C E, ſinum arcus Eclipticæ A D, ab æquinoctio A, computati ad φ O, </s>
          </p>
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