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-s10284" xml:space="preserve">
              <pb o="160" file="0180" n="180" rhead="GNOMONICES"/>
            ræ quintæ poſt meridiem, & </s>
            <s xml:id="echoid-s10285" xml:space="preserve">ſeptimæ poſt mediam noctem; </s>
            <s xml:id="echoid-s10286" xml:space="preserve">H T, horæ quartę poſt meridiem, & </s>
            <s xml:id="echoid-s10287" xml:space="preserve">
              <lb/>
            @ctauę poſt mediam noctem, &</s>
            <s xml:id="echoid-s10288" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10289" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10290" xml:space="preserve">EASDEM has lineas horarias ex H, per puncta lineę D C, emiſſas in hac figura obtinebimus
              <lb/>
            quoque, ſi interualla horarum in horologio inter centrum H, & </s>
            <s xml:id="echoid-s10291" xml:space="preserve">ęquinoctialem lineam poſita
              <lb/>
            transferamus ex puncto H, huius figurę in rectam D C, beneficio circini, notando puncta in re-
              <lb/>
            cta D C, (quod quidem fiet, ſi ad dicta interualla horologij deſcribantur ex H, huius figurę arcus
              <lb/>
            quidam occulti ſecã-
              <lb/>
              <figure xlink:label="fig-0180-01" xlink:href="fig-0180-01a" number="133">
                <image file="0180-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0180-01"/>
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            tes rectã D C, in pun
              <lb/>
            ctis, quę notãda ſunt)
              <lb/>
            & </s>
            <s xml:id="echoid-s10292" xml:space="preserve">per puncta in re-
              <lb/>
              <note position="left" xlink:label="note-0180-01" xlink:href="note-0180-01a" xml:space="preserve">10</note>
            cta D C, hac ratione
              <lb/>
            inuenta rectas ex H,
              <lb/>
            emittamus. </s>
            <s xml:id="echoid-s10293" xml:space="preserve">Si enim
              <lb/>
            in horologio intelli-
              <lb/>
            gatur centrum E, in
              <lb/>
            propria poſitione cõ-
              <lb/>
            iunctum cum centro
              <lb/>
            mundi D, (vt in prę-
              <lb/>
            cedenti propoſ. </s>
            <s xml:id="echoid-s10294" xml:space="preserve">dixi-
              <lb/>
            mus, quando triangu
              <lb/>
              <note position="left" xlink:label="note-0180-02" xlink:href="note-0180-02a" xml:space="preserve">20</note>
            lum DHI, rectũ ad
              <lb/>
            horologij planũ ſta-
              <lb/>
            tuebamus, & </s>
            <s xml:id="echoid-s10295" xml:space="preserve">circulũ
              <lb/>
            ex E, deſcriptum ani-
              <lb/>
            mo concipiebamus
              <lb/>
            moueri circa lineam
              <lb/>
            ęquinoctialẽ F k, do-
              <lb/>
            nec eius centrum E,
              <lb/>
            cum D, centro mundi coniungeretur) intelligemus duo triangula, nempe H D F, vel H E F,
              <lb/>
            in horologio, & </s>
            <s xml:id="echoid-s10296" xml:space="preserve">H D C, in hac propoſita figura. </s>
            <s xml:id="echoid-s10297" xml:space="preserve">Et quoniam latera illius H D, D F, ęqualia ſunt
              <lb/>
              <note position="left" xlink:label="note-0180-03" xlink:href="note-0180-03a" xml:space="preserve">30</note>
            lateribus huius H D, D C; </s>
            <s xml:id="echoid-s10298" xml:space="preserve">(ſumpta enim eſt ipſi D F, vel E F, ęqualis D C, in priori con-
              <lb/>
            ſtructione huius figurę, & </s>
            <s xml:id="echoid-s10299" xml:space="preserve">axis H D, hic idem eſt, qui ibi) ſuntq́; </s>
            <s xml:id="echoid-s10300" xml:space="preserve">anguli dictis lateribus contenti
              <lb/>
            æquales, nempe recti; </s>
            <s xml:id="echoid-s10301" xml:space="preserve">(Nam angulus H D C, in hac figura rectus eſt, ex conſtructione; </s>
            <s xml:id="echoid-s10302" xml:space="preserve">at verò
              <lb/>
            H D F, in horologio rectus eſt, eò quòd axis H D, ad planum Aequatoris rectus exiſtens, perpendi
              <lb/>
            cularis etiam eſt, per definitionem 3. </s>
            <s xml:id="echoid-s10303" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10304" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10305" xml:space="preserve">Euclidis, ad rectam D F, in plano Aequatoris exiſten-
              <lb/>
            tem) erunt & </s>
            <s xml:id="echoid-s10306" xml:space="preserve">baſes HF, H C, ęquales. </s>
            <s xml:id="echoid-s10307" xml:space="preserve">Quare ſi rectam H F, in horologio ſumptam transferamus
              <lb/>
              <note position="left" xlink:label="note-0180-04" xlink:href="note-0180-04a" xml:space="preserve">4. primi.</note>
            in hac figura ex puncto H, in rectam D C, vt dictum eſt in hac poſteriori conſtructione propoſitę
              <lb/>
            ſigurę, offendemus omnino punctum C, quod ante ex priori conſtructione eiuſdem figure inueni-
              <lb/>
            mus pro hora quinta, ac ſeptima. </s>
            <s xml:id="echoid-s10308" xml:space="preserve">Aliàs ſi recta H F, in horologio translata ex puncto H, huius fi-
              <lb/>
            gurę in rectam D C, caderet in aliud punctum, quàm in C, oſtenderemus, vt proximè, ductam re-
              <lb/>
              <note position="left" xlink:label="note-0180-05" xlink:href="note-0180-05a" xml:space="preserve">40</note>
            ctam H C, fore ęqualem ipſi H F, in horologio, atque adeò & </s>
            <s xml:id="echoid-s10309" xml:space="preserve">ipſi rectę ex H, in rectam
              <lb/>
            D C, quę ponitur cadere in aliud punctum, quàm in C; </s>
            <s xml:id="echoid-s10310" xml:space="preserve">cum hęc translata ſit ęqualis ſumpta eidẽ
              <lb/>
            H F, ex conſtructione. </s>
            <s xml:id="echoid-s10311" xml:space="preserve">Quare due rectæ æquales ducentur ex H, ad rectam D C, infra rectum an-
              <lb/>
            gulum D, quod eſt abſurdum. </s>
            <s xml:id="echoid-s10312" xml:space="preserve">Nam vt propoſ. </s>
            <s xml:id="echoid-s10313" xml:space="preserve">16. </s>
            <s xml:id="echoid-s10314" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10315" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10316" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s10317" xml:space="preserve">ex Proclo demonſtrauimus, ex H, ad
              <lb/>
            rectam D C, ſolum duæ rectæ inter ſe æquales duci poſſunt, vna infra punctum D, & </s>
            <s xml:id="echoid-s10318" xml:space="preserve">ſupra idem
              <lb/>
            punctum altera; </s>
            <s xml:id="echoid-s10319" xml:space="preserve">non autem ambæ inſra punctum D, vt hic contingeret. </s>
            <s xml:id="echoid-s10320" xml:space="preserve">Cadet ergo recta H F,
              <lb/>
            translata ex H, in rectam D C, in punctum C. </s>
            <s xml:id="echoid-s10321" xml:space="preserve">Eadem ratione alia interualla horarum in horolo-
              <lb/>
            gio inter H, & </s>
            <s xml:id="echoid-s10322" xml:space="preserve">lineam æquinoctialem tran slata ex puncto H, huius figurę in rectam D C, demon-
              <lb/>
            ſtrabimus cadere in puncta, quæ prius inuenta ſunt. </s>
            <s xml:id="echoid-s10323" xml:space="preserve">Atque hactenus in hac figura ductę ſunt ex
              <lb/>
            H, per puncta rectę D C, lineę horarię à duodecima hora meridiei vſq; </s>
            <s xml:id="echoid-s10324" xml:space="preserve">ad horam quintam à mer.
              <lb/>
            </s>
            <s xml:id="echoid-s10325" xml:space="preserve">
              <note position="left" xlink:label="note-0180-06" xlink:href="note-0180-06a" xml:space="preserve">50</note>
            & </s>
            <s xml:id="echoid-s10326" xml:space="preserve">ab hora ſeptima à med. </s>
            <s xml:id="echoid-s10327" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s10328" xml:space="preserve">vſque ad horam duodecimam meridiei, vt ex ipſa conſtructione
              <lb/>
            conſtat. </s>
            <s xml:id="echoid-s10329" xml:space="preserve">Dictę enim horę duntaxat ſecant ęquinoctialem lineam in horologio, quarum quidem
              <lb/>
            interualla translata ſunt. </s>
            <s xml:id="echoid-s10330" xml:space="preserve">Vnde aliarum horarum lineas ita ducemus.</s>
            <s xml:id="echoid-s10331" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10332" xml:space="preserve">PRO hora ſexta à mer. </s>
            <s xml:id="echoid-s10333" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s10334" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s10335" xml:space="preserve">ducatur ex H, ipſi D C, patallela H V; </s>
            <s xml:id="echoid-s10336" xml:space="preserve">Et pro hora ſe-
              <lb/>
            ptima à mer. </s>
            <s xml:id="echoid-s10337" xml:space="preserve">& </s>
            <s xml:id="echoid-s10338" xml:space="preserve">quinta à med. </s>
            <s xml:id="echoid-s10339" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s10340" xml:space="preserve">ducatur H X, angulum V H X, ęqualem faciens angulo V H C.
              <lb/>
            </s>
            <s xml:id="echoid-s10341" xml:space="preserve">Similiter pro hora octaua à mer. </s>
            <s xml:id="echoid-s10342" xml:space="preserve">& </s>
            <s xml:id="echoid-s10343" xml:space="preserve">quarta à med. </s>
            <s xml:id="echoid-s10344" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s10345" xml:space="preserve">ducatur H Y, angulũ V H Y, angulo VHT,
              <lb/>
            faciens ęqualem, & </s>
            <s xml:id="echoid-s10346" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s10347" xml:space="preserve">Quod facile fiet, ſi ex H, arcus circuli deſcribatur. </s>
            <s xml:id="echoid-s10348" xml:space="preserve">Nam ſi cir-
              <lb/>
            eumferentiæ huius arcus interceptæ inter H V, & </s>
            <s xml:id="echoid-s10349" xml:space="preserve">rectas ex H, ad dexterã ipſius H V, eductas, (quę
              <lb/>
            nimirum rectam D C, ſecant) transferantur ad ſiniſtram partem eiuſdem H V, in dictum arcum,
              <lb/>
            facient rectę ex H, per illas circumferentias translatas ad ſiniſtram ipſius H V, emiſſę cum H V,
              <lb/>
            angulos ęquales illis, qui ex parte dextra cum eadem H V, fiunt; </s>
            <s xml:id="echoid-s10350" xml:space="preserve">propterea quòd arcus, quibus illi
              <lb/>
              <note position="left" xlink:label="note-0180-07" xlink:href="note-0180-07a" xml:space="preserve">27. tertij.</note>
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