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-s43055" xml:space="preserve">
              <pb o="654" file="0670" n="670" rhead="GNOMONICES"/>
            li K P L, ad O M, ſinum rectum arcus P N: </s>
            <s xml:id="echoid-s43056" xml:space="preserve">ac propterea, ex lemmate propoſ. </s>
            <s xml:id="echoid-s43057" xml:space="preserve">1. </s>
            <s xml:id="echoid-s43058" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s43059" xml:space="preserve">1. </s>
            <s xml:id="echoid-s43060" xml:space="preserve">arcus F H,
              <lb/>
            P N, ſimiles erunt. </s>
            <s xml:id="echoid-s43061" xml:space="preserve">Quare quemadmodum arcus F H, complectitur quatuor duodecimas partes
              <lb/>
            quadrantis C F, ita arcus P N, quatuor duodecimas partes, hoc eſt, quatuor ſemihoras, ſiue duas
              <lb/>
            horas, quadrantis L P, complectetur, quandoquidem quadrans in ſex horas, ſiue in 12. </s>
            <s xml:id="echoid-s43062" xml:space="preserve">ſemihoras
              <lb/>
            diſtribuitur; </s>
            <s xml:id="echoid-s43063" xml:space="preserve">ac proinde arcus ſemidiurnus us K P N, continebit octo horas, totusq́ue arcus diur-
              <lb/>
            nus horas 16. </s>
            <s xml:id="echoid-s43064" xml:space="preserve">quod demonſtrandum erat. </s>
            <s xml:id="echoid-s43065" xml:space="preserve">Eadem ratione oſtendemus, arcum, quo arcus ſemi-
              <lb/>
            diurnus paralleli, cuius declinatio per parallelam ductam v. </s>
            <s xml:id="echoid-s43066" xml:space="preserve">g. </s>
            <s xml:id="echoid-s43067" xml:space="preserve">per proximum punctum ipſi F, in
              <lb/>
            quadrante C F, inuenitur, à quadrante differt, continere vnam partem duodecimam, hoc eſt,
              <lb/>
            vnam ſemihoram, quemadmodum & </s>
            <s xml:id="echoid-s43068" xml:space="preserve">arcus inter F, & </s>
            <s xml:id="echoid-s43069" xml:space="preserve">proximum punctum duodecimam partem
              <lb/>
            quadrantis C F, comprehendit; </s>
            <s xml:id="echoid-s43070" xml:space="preserve">atque adeo arcum illum ſemidiurnum continere horas 6 {1/2}. </s>
            <s xml:id="echoid-s43071" xml:space="preserve">& </s>
            <s xml:id="echoid-s43072" xml:space="preserve">to
              <lb/>
              <note position="left" xlink:label="note-0670-01" xlink:href="note-0670-01a" xml:space="preserve">10</note>
              <figure xlink:label="fig-0670-01" xlink:href="fig-0670-01a" number="431">
                <image file="0670-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0670-01"/>
              </figure>
            tum arcum diurnum horas
              <lb/>
            13. </s>
            <s xml:id="echoid-s43073" xml:space="preserve">& </s>
            <s xml:id="echoid-s43074" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s43075" xml:space="preserve">Sed de-
              <lb/>
            monſtremus idem in paral-
              <lb/>
            lelis auſtralibus. </s>
            <s xml:id="echoid-s43076" xml:space="preserve">Quoniam
              <lb/>
            eſt in triangulis ſimilibus
              <lb/>
              <note position="left" xlink:label="note-0670-02" xlink:href="note-0670-02a" xml:space="preserve">4. ſexti.</note>
            D d T, A D q, vt d D, ad
              <lb/>
              <note position="left" xlink:label="note-0670-03" xlink:href="note-0670-03a" xml:space="preserve">2. ſexti.</note>
            d T, ita A d, ad d q; </s>
            <s xml:id="echoid-s43077" xml:space="preserve">& </s>
            <s xml:id="echoid-s43078" xml:space="preserve">per-
              <lb/>
              <note position="left" xlink:label="note-0670-04" xlink:href="note-0670-04a" xml:space="preserve">11. qui@ti.</note>
            mutando, vt D d, ad d A,
              <lb/>
            ita T d, ad d q: </s>
            <s xml:id="echoid-s43079" xml:space="preserve">Eſt autem vt
              <lb/>
            D d, ad d A, ita D T, ad T E;
              <lb/>
            </s>
            <s xml:id="echoid-s43080" xml:space="preserve">
              <note position="left" xlink:label="note-0670-05" xlink:href="note-0670-05a" xml:space="preserve">20</note>
            erit quoque, vt T d, ad d q,
              <lb/>
            ita D T, ad T E. </s>
            <s xml:id="echoid-s43081" xml:space="preserve">Vt autem
              <lb/>
            T d, ad d q, ita eſt, ex ſcho-
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s43082" xml:space="preserve">4. </s>
            <s xml:id="echoid-s43083" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s43084" xml:space="preserve">6. </s>
            <s xml:id="echoid-s43085" xml:space="preserve">Eucl.
              <lb/>
            </s>
            <s xml:id="echoid-s43086" xml:space="preserve">V Y, ad Y Z; </s>
            <s xml:id="echoid-s43087" xml:space="preserve">quòd in trian-
              <lb/>
            gulo A V Z, in quo recta
              <lb/>
            A Y, ducta eſt, recta T q,
              <lb/>
            baſi V Z, æquidiſtet. </s>
            <s xml:id="echoid-s43088" xml:space="preserve">Igitur
              <lb/>
            erit quoque, vt D T, ad T E,
              <lb/>
            ita V Y, ad Y Z: </s>
            <s xml:id="echoid-s43089" xml:space="preserve">& </s>
            <s xml:id="echoid-s43090" xml:space="preserve">com-
              <lb/>
              <note position="left" xlink:label="note-0670-06" xlink:href="note-0670-06a" xml:space="preserve">30</note>
            ponendo, vt D E, ſinus to-
              <lb/>
            tuscirculi C F D, ad T E, ſi-
              <lb/>
            num rectum arcus F S, ita
              <lb/>
            V Z, ſinus totus paralleli
              <lb/>
            V a X, ad Y Z, ſinum rectũ
              <lb/>
            arcus a b. </s>
            <s xml:id="echoid-s43091" xml:space="preserve">Quare ex lemmate propoſ. </s>
            <s xml:id="echoid-s43092" xml:space="preserve">1. </s>
            <s xml:id="echoid-s43093" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s43094" xml:space="preserve">1. </s>
            <s xml:id="echoid-s43095" xml:space="preserve">arcus F S, a b, ſimiles ſunt: </s>
            <s xml:id="echoid-s43096" xml:space="preserve">atque idcirco quem-
              <lb/>
            admodum arcus F S, complectitur quatuor duodecimas partes quadrantis D F, ita arcus a b, qua-
              <lb/>
            tuor duodecimas partes, hoc eſt, quatuor ſemihoras, ſiue duas horas, quadrantis a V, complecte-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s43097" xml:space="preserve">hoc eſt, arcus ſemidiurnus V b, quatuor cõtinebit horas, totusq́; </s>
            <s xml:id="echoid-s43098" xml:space="preserve">arcus diurnus horas 8. </s>
            <s xml:id="echoid-s43099" xml:space="preserve">quod
              <lb/>
            erat oſtendendum. </s>
            <s xml:id="echoid-s43100" xml:space="preserve">Non aliter demonſtrabimus, arcum, quo arcus ſemidiurnus paralleli, cuius
              <lb/>
              <note position="left" xlink:label="note-0670-07" xlink:href="note-0670-07a" xml:space="preserve">40</note>
            declinatio per parallelam ductam v. </s>
            <s xml:id="echoid-s43101" xml:space="preserve">g. </s>
            <s xml:id="echoid-s43102" xml:space="preserve">per punctum tertio loco à puncto F, poſitum in quadran-
              <lb/>
            te D F, inuenitur, à quadrante differt, continere tres partes duodecimas, hoc eſt, hor 1 {1/2}. </s>
            <s xml:id="echoid-s43103" xml:space="preserve">quem-
              <lb/>
            admodum & </s>
            <s xml:id="echoid-s43104" xml:space="preserve">arcus inter F, & </s>
            <s xml:id="echoid-s43105" xml:space="preserve">tertium punctum verſus D, tres partes duodecimas quadrantis D F,
              <lb/>
            complectitur; </s>
            <s xml:id="echoid-s43106" xml:space="preserve">atque adeo arcnm illum ſemidiurnum comprehendere horas 7 {1/2}. </s>
            <s xml:id="echoid-s43107" xml:space="preserve">& </s>
            <s xml:id="echoid-s43108" xml:space="preserve">totum arcum
              <lb/>
            diurnum horas 15. </s>
            <s xml:id="echoid-s43109" xml:space="preserve">Eademq́ue de c
              <unsure/>
            æteris ratio eſt. </s>
            <s xml:id="echoid-s43110" xml:space="preserve">Recte igitur praxi illa declinationes, & </s>
            <s xml:id="echoid-s43111" xml:space="preserve">radij
              <lb/>
            arcuum diurnorum inueſtigantur. </s>
            <s xml:id="echoid-s43112" xml:space="preserve">Atque hic finem noſtræ Gnomonicæ imponamus. </s>
            <s xml:id="echoid-s43113" xml:space="preserve">Con-
              <lb/>
            ſtructiones enim aliorum horologiorum, quæ viatoria dici ſolent, & </s>
            <s xml:id="echoid-s43114" xml:space="preserve">minus inſignia
              <lb/>
            ſunt, (ſi enim omnia perſequi vellemus, in immenſum propemodum excreſce-
              <lb/>
            ret volumen) ex alijs ſcriptoribus peti poſſunt. </s>
            <s xml:id="echoid-s43115" xml:space="preserve">De quibus fortaſſis alias
              <lb/>
            copioſius diſſeremus, præſertim cum deſcriptio horologij in for
              <lb/>
              <note position="left" xlink:label="note-0670-08" xlink:href="note-0670-08a" xml:space="preserve">50</note>
            ma annuli ab Orontio tradita, & </s>
            <s xml:id="echoid-s43116" xml:space="preserve">aliorum quorundam,
              <lb/>
            errore non careat. </s>
            <s xml:id="echoid-s43117" xml:space="preserve">Hæcinterim vt ſtudioſus
              <lb/>
            lector boni conſulat, vehe-
              <lb/>
            menter oro.</s>
            <s xml:id="echoid-s43118" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div2111" type="section" level="1" n="533">
          <head xml:id="echoid-head562" xml:space="preserve">FINIS OCTAVI LIBRI.</head>
        </div>
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