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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              <pb o="306" file="0322" n="322" rhead="GNOMONICES"/>
            moueatur, donec rectum ſit ad planum horologij, & </s>
            <s xml:id="echoid-s20632" xml:space="preserve">ſtyl{us} I K, ad idem rect{us}, congruet punctum I,
              <lb/>
            puncto F, atque adeo & </s>
            <s xml:id="echoid-s20633" xml:space="preserve">puncto β. </s>
            <s xml:id="echoid-s20634" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s20635" xml:space="preserve">recta C I, axi C β, congruet. </s>
            <s xml:id="echoid-s20636" xml:space="preserve">Hinc fit, rectam G I, in eo
              <lb/>
            ſitu eſſe ſectionem communem Aequatoris, & </s>
            <s xml:id="echoid-s20637" xml:space="preserve">Meridiani proprii ipſius plani declinantis, cum vterque
              <lb/>
            circulus per G, & </s>
            <s xml:id="echoid-s20638" xml:space="preserve">per I, centrum mundi ducatur, Quare angul{us} C I G, rect{us} erit, cum dicta commu-
              <lb/>
            nis ſectio ſemper ſit ad axem perpendicularis, vt ex ſuperiorib{us} manifeſtum eſt. </s>
            <s xml:id="echoid-s20639" xml:space="preserve">Cætera ex demonſtra-
              <lb/>
            tis in prima conſtructione hui{us} propoſ. </s>
            <s xml:id="echoid-s20640" xml:space="preserve">perſpicua ſunt.</s>
            <s xml:id="echoid-s20641" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20642" xml:space="preserve">BENEFICIO Ellipſis deſcribem{us} quoque idem horologium declinans à Verticali, quemadmo-
              <lb/>
              <note position="left" xlink:label="note-0322-01" xlink:href="note-0322-01a" xml:space="preserve">Deſcriptio eiuſ
                <lb/>
              dem horologii
                <lb/>
              beneficio Elli-
                <lb/>
              pſis.</note>
            dum & </s>
            <s xml:id="echoid-s20643" xml:space="preserve">Horizontale, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s20644" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20645" xml:space="preserve">ſuperioris lib, oſtendim{us}, pancis mutatis. </s>
            <s xml:id="echoid-s20646" xml:space="preserve">Sit enim rurſ{us}
              <lb/>
            longitudo styli data K F, eius{q́ue} loc{us} punctum K. </s>
            <s xml:id="echoid-s20647" xml:space="preserve">Inuenta igitur, vt in proxima deſcriptione præcepi-
              <lb/>
            m{us}, linea meridiana C E; </s>
            <s xml:id="echoid-s20648" xml:space="preserve">centro horologii C; </s>
            <s xml:id="echoid-s20649" xml:space="preserve">linea æquinoctiali α G; </s>
            <s xml:id="echoid-s20650" xml:space="preserve">axe mundi C I, & </s>
            <s xml:id="echoid-s20651" xml:space="preserve">linea ſtyli C G:
              <lb/>
            </s>
            <s xml:id="echoid-s20652" xml:space="preserve">
              <note position="left" xlink:label="note-0322-02" xlink:href="note-0322-02a" xml:space="preserve">10</note>
            ſumatur in axe producto punctum H, remoti{us}, quàm I, vt accurati{us} horologium deſcribatur, à quo ad
              <lb/>
              <figure xlink:label="fig-0322-01" xlink:href="fig-0322-01a" number="219">
                <image file="0322-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0322-01"/>
              </figure>
              <note position="left" xlink:label="note-0322-03" xlink:href="note-0322-03a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0322-04" xlink:href="note-0322-04a" xml:space="preserve">30</note>
              <note position="left" xlink:label="note-0322-05" xlink:href="note-0322-05a" xml:space="preserve">40</note>
            axem perpendicularis ducatur H N, ſecans lineam ſtyli in N, vt H N, ſit noua quædam ſectio commu-
              <lb/>
            nis Acquatoris, & </s>
            <s xml:id="echoid-s20653" xml:space="preserve">Meridiani proprii plani declinantis, punctum{q́ue} N, illud, per quod noua linea æquino-
              <lb/>
            ctialis ducenda eſſet ad lineam ſtyli perpendicularis. </s>
            <s xml:id="echoid-s20654" xml:space="preserve">Abſciſſa autem recta C O, ipſi H N, æquali, deſcri
              <lb/>
            bantur ex centro horologii C, ad interualla C N, C O, duo circuli, & </s>
            <s xml:id="echoid-s20655" xml:space="preserve">in minori ducatur diameter S T,
              <lb/>
            ad N R, diametrũ maioris perpendicularis: </s>
            <s xml:id="echoid-s20656" xml:space="preserve">erit{q́ue}, N R, maior diameter Ellipſis, & </s>
            <s xml:id="echoid-s20657" xml:space="preserve">S T, minor; </s>
            <s xml:id="echoid-s20658" xml:space="preserve">quemad-
              <lb/>
            modũ in horizontali horologio maior diameter eſt B V, & </s>
            <s xml:id="echoid-s20659" xml:space="preserve">minor R X. </s>
            <s xml:id="echoid-s20660" xml:space="preserve">Iam verò puncta Ellipſis, per quæ
              <lb/>
            horæ ducendæ ſunt, inuenientur, vt in horologio horizontali dictum est, ſi dicti duo circuli in 24. </s>
            <s xml:id="echoid-s20661" xml:space="preserve">partes
              <lb/>
            æquales ſecentur, initio facto non à linea meridiana propria plani declinantis, hoc eſt, à linea styli R N,
              <lb/>
              <note position="left" xlink:label="note-0322-06" xlink:href="note-0322-06a" xml:space="preserve">50</note>
            ſed ab alia quadam recta, quam ita reperiemus. </s>
            <s xml:id="echoid-s20662" xml:space="preserve">Ex L, centro circuli, beneficio cuius in pręcedenti de-
              <lb/>
            ſcriptione in linea æquinoctiali α G, puncta horaria inuestigauimus (quod quidem centrum diſtat à pun-
              <lb/>
            cto G, interuallo G I) ducatur per punctum M, vbi æquinoctialis linea & </s>
            <s xml:id="echoid-s20663" xml:space="preserve">meridiana ſe mutuo ſecant, re-
              <lb/>
            cta L M, & </s>
            <s xml:id="echoid-s20664" xml:space="preserve">angulo C L M, conſtituatur ad rectam C L, in centro C, ęqualis L C P, ex eadem parte, ex
              <lb/>
            qua punctum M, exiſtit. </s>
            <s xml:id="echoid-s20665" xml:space="preserve">Nam à recta P Q, inchoanda eſt diuiſio circulorum. </s>
            <s xml:id="echoid-s20666" xml:space="preserve">Idem punctum P, à quo
              <lb/>
            diniſio incipit, reperiemus, ſi ex N, verſus meridianam lineam C M, ſupputem{us} arcum Aequatoris in-
              <lb/>
            teriectum inter Meridianum proprium plani declinantis, & </s>
            <s xml:id="echoid-s20667" xml:space="preserve">Meridianum Horizontis, vſque ad P: </s>
            <s xml:id="echoid-s20668" xml:space="preserve">qui
              <lb/>
            arcus in noſtro exemplo continet grad. </s>
            <s xml:id="echoid-s20669" xml:space="preserve">40. </s>
            <s xml:id="echoid-s20670" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s20671" xml:space="preserve">48. </s>
            <s xml:id="echoid-s20672" xml:space="preserve">fere. </s>
            <s xml:id="echoid-s20673" xml:space="preserve">Tanta enim eſt fere inclinatio dictorum Meri-
              <lb/>
            dianorum inuenta ex propoſ. </s>
            <s xml:id="echoid-s20674" xml:space="preserve">30. </s>
            <s xml:id="echoid-s20675" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20676" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20677" xml:space="preserve">vt ſupra dixim{us}. </s>
            <s xml:id="echoid-s20678" xml:space="preserve">Itaque ſit inueniendum punctum Ellipſis, per
              <lb/>
            quod hora 12. </s>
            <s xml:id="echoid-s20679" xml:space="preserve">ducenda ſit. </s>
            <s xml:id="echoid-s20680" xml:space="preserve">Per P, punctum horę 12. </s>
            <s xml:id="echoid-s20681" xml:space="preserve">in maiori circulo ducatur minori Ellipſis diametro
              <lb/>
            S T, parallela P Z; </s>
            <s xml:id="echoid-s20682" xml:space="preserve">(quæ facile ducetur, ſi arcui P N, ſumatur æqualis N V. </s>
            <s xml:id="echoid-s20683" xml:space="preserve">Recta enim P V, </s>
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