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-s10006" xml:space="preserve">
              <pb o="156" file="0176" n="176" rhead="GNOMONICES"/>
            autem ſupputationis obſignetur notula F: </s>
            <s xml:id="echoid-s10007" xml:space="preserve">& </s>
            <s xml:id="echoid-s10008" xml:space="preserve">à centro A, ad datum ſignum F, recta producatur li-
              <lb/>
            nea A F. </s>
            <s xml:id="echoid-s10009" xml:space="preserve">Dato inſuper arcu B F, æqualis eidem conſtituatur in quadrante B E, ſitq; </s>
            <s xml:id="echoid-s10010" xml:space="preserve">B G: </s>
            <s xml:id="echoid-s10011" xml:space="preserve">& </s>
            <s xml:id="echoid-s10012" xml:space="preserve">à ſi-
              <lb/>
            gno F, ad ſignum G, recta ducatur linea F G. </s>
            <s xml:id="echoid-s10013" xml:space="preserve">Hæc enim à ſemidiametro A B, bifariam diuidetur,
              <lb/>
              <figure xlink:label="fig-0176-01" xlink:href="fig-0176-01a" number="129">
                <image file="0176-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0176-01"/>
              </figure>
              <note position="left" xlink:label="note-0176-01" xlink:href="note-0176-01a" xml:space="preserve">10</note>
            in ſigno quidem H: </s>
            <s xml:id="echoid-s10014" xml:space="preserve">quapropter & </s>
            <s xml:id="echoid-s10015" xml:space="preserve">ad rectos angulos, per 3. </s>
            <s xml:id="echoid-s10016" xml:space="preserve">tertij elementorum Euclidis. </s>
            <s xml:id="echoid-s10017" xml:space="preserve">Erit itaq;
              <lb/>
            </s>
            <s xml:id="echoid-s10018" xml:space="preserve">recta linea F H, perpendicularis ſuper A B: </s>
            <s xml:id="echoid-s10019" xml:space="preserve">& </s>
            <s xml:id="echoid-s10020" xml:space="preserve">triangulum A F H, rectangulum. </s>
            <s xml:id="echoid-s10021" xml:space="preserve">Ergo circulus B C-
              <lb/>
            D E, Meridianum, & </s>
            <s xml:id="echoid-s10022" xml:space="preserve">B C, quadrantem eius ſeptentrionalem, A, vero centrum mundi repreſenta-
              <lb/>
              <note position="left" xlink:label="note-0176-02" xlink:href="note-0176-02a" xml:space="preserve">20</note>
            bit: </s>
            <s xml:id="echoid-s10023" xml:space="preserve">recta porro B D, Horizontem, & </s>
            <s xml:id="echoid-s10024" xml:space="preserve">C E, Verticalem circulum cum ipſo Meridiano ad rectos an
              <lb/>
            gulos incidentem. </s>
            <s xml:id="echoid-s10025" xml:space="preserve">Deinde paulo poſt ita rem proſequitur. </s>
            <s xml:id="echoid-s10026" xml:space="preserve">Data recta linea F H, æqualis eidem con
              <lb/>
            ſtituatur in ſemidiametro A C, ſitq́, illa A I: </s>
            <s xml:id="echoid-s10027" xml:space="preserve">& </s>
            <s xml:id="echoid-s10028" xml:space="preserve">à ſigno H, ad ſignum I, recta linea ducatur H I, di-
              <lb/>
            rimens rectam A F, in ſigno K. </s>
            <s xml:id="echoid-s10029" xml:space="preserve">Erit igitur triangulum A H I, ęqualeatque ſimile triangulo A F H:
              <lb/>
            </s>
            <s xml:id="echoid-s10030" xml:space="preserve">quemadmodum ex 4. </s>
            <s xml:id="echoid-s10031" xml:space="preserve">primi ipſius Euclidis fit manifeſtum. </s>
            <s xml:id="echoid-s10032" xml:space="preserve">Hanc igitur deſcriptionem, generalem
              <lb/>
            protypum Orontius appellat pro horizontalibus, Verticalibus{q́ue}, horologijs conſtruendis: </s>
            <s xml:id="echoid-s10033" xml:space="preserve">ita vt ipſe trian
              <lb/>
            gulo AHK, rtatur in horizontalibus horologijs fabricandis ad datam altitudinem poli B F, non ſecus,
              <lb/>
            atq; </s>
            <s xml:id="echoid-s10034" xml:space="preserve">nos in hac propoſitione vſi ſumus triangulo D H I, in portione Analemmatis contento pro eiſdẽ ho-
              <lb/>
            rologijs componendis ad datam poli altitudinem C E. </s>
            <s xml:id="echoid-s10035" xml:space="preserve">Nam ſtatim in propoſ. </s>
            <s xml:id="echoid-s10036" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10037" xml:space="preserve">aſſumit in linea meridia-
              <lb/>
            narectam ęqualem lateri A H, pro linea Horizontis, quemadmodum nos accepimus rectam æqualem la
              <lb/>
              <note position="left" xlink:label="note-0176-03" xlink:href="note-0176-03a" xml:space="preserve">30</note>
            tcri H I, in noſtro triangulo. </s>
            <s xml:id="echoid-s10038" xml:space="preserve">Deinde pro linea Aequatoris ſumit aliam rectam æqualem lateri A K,
              <lb/>
            quemadmodum nos ſumpſimus rectam æqualem rectæ D I, in noſtro triangulo. </s>
            <s xml:id="echoid-s10039" xml:space="preserve">Itaque vult in triangulo
              <lb/>
            A H K, rectam A H, eſſe lineam Horizontis; </s>
            <s xml:id="echoid-s10040" xml:space="preserve">H K, axem mundi; </s>
            <s xml:id="echoid-s10041" xml:space="preserve">& </s>
            <s xml:id="echoid-s10042" xml:space="preserve">A K, lineam Aequatoris, pro
              <lb/>
            horizontalibus horologijs componendis. </s>
            <s xml:id="echoid-s10043" xml:space="preserve">Sic etiam in propoſ. </s>
            <s xml:id="echoid-s10044" xml:space="preserve">3. </s>
            <s xml:id="echoid-s10045" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s10046" xml:space="preserve">pro V erticalibus horologijs
              <lb/>
            conſtruendis accipit in triangulo F H K, rectam F H, pro linea V erticalis circuli; </s>
            <s xml:id="echoid-s10047" xml:space="preserve">H K, pro axe mundi;
              <lb/>
            </s>
            <s xml:id="echoid-s10048" xml:space="preserve">& </s>
            <s xml:id="echoid-s10049" xml:space="preserve">F K, pro Aequatoris linea. </s>
            <s xml:id="echoid-s10050" xml:space="preserve">Qua in re ipſum eſſe mirum in modum hallucinatum, facile demonſtra-
              <lb/>
            bimus hoc modo.</s>
            <s xml:id="echoid-s10051" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10052" xml:space="preserve">QVONIAM latera I A, A H, trianguli I A H, æqualia ſunt lateribus F H, H A, trianguli
              <lb/>
            F H A, angulos{q́ue} continent æquales, vtpote rectos, erunt & </s>
            <s xml:id="echoid-s10053" xml:space="preserve">baſes H I, A F, & </s>
            <s xml:id="echoid-s10054" xml:space="preserve">anguli A H I, H A F,
              <lb/>
              <note position="left" xlink:label="note-0176-04" xlink:href="note-0176-04a" xml:space="preserve">4. primi.</note>
            aquales. </s>
            <s xml:id="echoid-s10055" xml:space="preserve">Quare quemadmodum A F, axis eſt reſpectu Horizontis A H, ita quoque H I, pro axc ſumi
              <lb/>
              <note position="left" xlink:label="note-0176-05" xlink:href="note-0176-05a" xml:space="preserve">40</note>
            potest reſpectu ciuſdem Horizontis A H, quandoquidem tam A F, quàm H I, cum A H, angulum alti-
              <lb/>
            tudinis poli conſtituit. </s>
            <s xml:id="echoid-s10056" xml:space="preserve">Atque hucuſque inter nos & </s>
            <s xml:id="echoid-s10057" xml:space="preserve">Orontium nullum diſcrimen eſt: </s>
            <s xml:id="echoid-s10058" xml:space="preserve">Sed error ipſius cõ-
              <lb/>
            ſiſtit in linea Aequat oris duntaxat, quam nulla ratione eſſe poſſe rectam A K, vt ipſe putat, in regione,
              <lb/>
            cuius latitudo maior ſit, quàm grad. </s>
            <s xml:id="echoid-s10059" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10060" xml:space="preserve">ita perſpicuum faciemus. </s>
            <s xml:id="echoid-s10061" xml:space="preserve">Sit enim primum altitudo poli B F,
              <lb/>
            maior, quàm grad. </s>
            <s xml:id="echoid-s10062" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10063" xml:space="preserve">vt in eius figura. </s>
            <s xml:id="echoid-s10064" xml:space="preserve">Erit igitur angulus F A H, dimidio rectimaior; </s>
            <s xml:id="echoid-s10065" xml:space="preserve">ac proinde cum
              <lb/>
            ei æqualis ſit oſtenſus angulus A H I, erunt duo anguli K A H, K H A, in triangulo A H K, ſimul re-
              <lb/>
            cto maiores. </s>
            <s xml:id="echoid-s10066" xml:space="preserve">Igitur reliquus A K H, recto minor erit. </s>
            <s xml:id="echoid-s10067" xml:space="preserve">Quare cum linea Aequatoris cum axe in omni
              <lb/>
              <note position="left" xlink:label="note-0176-06" xlink:href="note-0176-06a" xml:space="preserve">32. primi.</note>
            climate rectos faciat angnlos, vt ex portione Analemmatis huius propoſ. </s>
            <s xml:id="echoid-s10068" xml:space="preserve">vel ex ipſomet Analemmate
              <lb/>
            in propoſ. </s>
            <s xml:id="echoid-s10069" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10070" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s10071" xml:space="preserve">conſtat, quis adhuc dubitabit, rectam A K, quæ cum axe H K, angulum acutũ
              <lb/>
            facit A K H, lineam Aequatoris eſſe non poſſe? </s>
            <s xml:id="echoid-s10072" xml:space="preserve">Itaque vt in triangulo A H K, linea Aequatoris ha-
              <lb/>
              <note position="left" xlink:label="note-0176-07" xlink:href="note-0176-07a" xml:space="preserve">50</note>
            beatur, ducenda erit ex A, ad axem H K, perpendicularis A L, quæ neceſſario minor eſt quàm A K.
              <lb/>
            </s>
            <s xml:id="echoid-s10073" xml:space="preserve">
              <note position="left" xlink:label="note-0176-08" xlink:href="note-0176-08a" xml:space="preserve">19. primi.</note>
            Deinde ſit altitudo poli B F, minor, quàm grad. </s>
            <s xml:id="echoid-s10074" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10075" xml:space="preserve">vt in ſecunda figura apparet: </s>
            <s xml:id="echoid-s10076" xml:space="preserve">erit{q́ue} propterea
              <lb/>
            angulus F A H, recto minor. </s>
            <s xml:id="echoid-s10077" xml:space="preserve">Quare cum ei ęqualis ſit oſtenſus angulus A H I, erunt anguli H A F,
              <lb/>
              <note position="left" xlink:label="note-0176-09" xlink:href="note-0176-09a" xml:space="preserve">32. primi.</note>
            A H I, ſimul vno recto minores; </s>
            <s xml:id="echoid-s10078" xml:space="preserve">ac proinde reliquus A K H, in triangulo A K H, rectum ſuperabit.
              <lb/>
            </s>
            <s xml:id="echoid-s10079" xml:space="preserve">Non igitur recta A K, eſſe poteſt linea Aequatoris, cum non faciat cum axe H I, angulos rectos: </s>
            <s xml:id="echoid-s10080" xml:space="preserve">ſed du-
              <lb/>
            cta A L, ad axem H I, perpendicularis lineam Aequatoris dabit. </s>
            <s xml:id="echoid-s10081" xml:space="preserve">Solum in regione, vbi altitudo poli cõ-
              <lb/>
            plectitur grad. </s>
            <s xml:id="echoid-s10082" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10083" xml:space="preserve">recta A K, erit linea Aequatoris, quia ibi ſolum rectos angulos cum axe H I, conſti-
              <lb/>
            tuit. </s>
            <s xml:id="echoid-s10084" xml:space="preserve">Contineat enim altitudo poli B F, grad. </s>
            <s xml:id="echoid-s10085" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10086" xml:space="preserve">vt in tertia figura: </s>
            <s xml:id="echoid-s10087" xml:space="preserve">erit{q́ue} propterea angulus F A H,
              <lb/>
            ſemirectus. </s>
            <s xml:id="echoid-s10088" xml:space="preserve">Cum ergo ei æqualis oſtenſus ſit angulus A H I, erunt duo anguli H A K, A H K, ſimul vni
              <lb/>
            recto ęquales: </s>
            <s xml:id="echoid-s10089" xml:space="preserve">ac propterea reliquus angulus A K H, in triangulo A K H, rectus erit. </s>
            <s xml:id="echoid-s10090" xml:space="preserve">Igitur recta
              <lb/>
              <note position="left" xlink:label="note-0176-10" xlink:href="note-0176-10a" xml:space="preserve">32. primi.</note>
            A K, fungetur munere lineę Aequatoris. </s>
            <s xml:id="echoid-s10091" xml:space="preserve">Manifeſtũ igitur eſt, Orontium pueriliter labi in linea </s>
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