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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        <div xml:id="echoid-div97" type="section" level="1" n="31">
          <pb o="29" file="0049" n="49" rhead="LIBER PRIMVS."/>
        </div>
        <div xml:id="echoid-div103" type="section" level="1" n="32">
          <head xml:id="echoid-head35" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1986" xml:space="preserve">HAEC ratio deſcribendæ conicæ ſectionis, vna cum demonſtratione, non differt ab ea, quam Fede-
              <lb/>
            ricus Commandinus adducit in libro de horologiorum deſcriptione, niſi quòd ipſe de cono recto ſolum lo-
              <lb/>
            quitur, nos autem problema omni cono tam recto, quàm ſcaleno accommodauimus, & </s>
            <s xml:id="echoid-s1987" xml:space="preserve">praxes, quæ ad
              <lb/>
            deſcriptionem ſectionum conorum rectorum requiruntur, ſimul complexi ſumus. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">Præcipit enim ipſe, vt
              <lb/>
            ſumantur in primis figuris, in diametro D E, quotcunque puncta K, L, atque per ipſa baſi B C, paralle-
              <lb/>
            læ agantur. </s>
            <s xml:id="echoid-s1989" xml:space="preserve">Sed facilius eſt in cono recto, beneficio circini in vtroque latere A B, A C, puncta ſumere F,
              <lb/>
            G, H, I. </s>
            <s xml:id="echoid-s1990" xml:space="preserve">Rectæ enim hæc puncta connectentes parallelæ ſunt, vt oſtendimus. </s>
            <s xml:id="echoid-s1991" xml:space="preserve">Deinde iubet in primis figu-
              <lb/>
            ris, inter K F, k H, & </s>
            <s xml:id="echoid-s1992" xml:space="preserve">L G, L I, inuenire medias proportionales: </s>
            <s xml:id="echoid-s1993" xml:space="preserve">quod quidem nos præstitimus ſemi-
              <lb/>
              <note position="left" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve">10</note>
            circulis deſcriptis in ſecundis figuris. </s>
            <s xml:id="echoid-s1994" xml:space="preserve">Poſtremo, diuiſa diametro D E, in plano ſeorſum, nimirum in
              <lb/>
            tertijs figuris, vt diuiſa eſt in cono primarum figurarum, iubet ex punctis diuiſionum in tertijs figuris
              <lb/>
            perpendiculares vtrinque educere ad diametrum: </s>
            <s xml:id="echoid-s1995" xml:space="preserve">quod & </s>
            <s xml:id="echoid-s1996" xml:space="preserve">nos in tertijs figuris fecimus praxi perfacili
              <lb/>
            & </s>
            <s xml:id="echoid-s1997" xml:space="preserve">breui, præſertim vbi multa eſſent puncta. </s>
            <s xml:id="echoid-s1998" xml:space="preserve">In has perpendiculares transfert medias proportionales
              <lb/>
            inuentas, vt nos, & </s>
            <s xml:id="echoid-s1999" xml:space="preserve">per extrema puncta mediarum proportionalium translatarum ducit ſectionem coni-
              <lb/>
            cam, quemadmodum & </s>
            <s xml:id="echoid-s2000" xml:space="preserve">à nobis factum eſt.</s>
            <s xml:id="echoid-s2001" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2002" xml:space="preserve">FRANCISCVS Maurolycus abbas libro tertio de lineis horarijs vtitur alijs deſcriptionibus
              <lb/>
            particularibus trium conicarum ſectionum: </s>
            <s xml:id="echoid-s2003" xml:space="preserve">ſed ratio deſcriptionis à nobis tradita ſimplicior est, & </s>
            <s xml:id="echoid-s2004" xml:space="preserve">fa-
              <lb/>
            cilior, conuenit{q́ue} in omnes ſectiones, vt conſtat. </s>
            <s xml:id="echoid-s2005" xml:space="preserve">Nihil autem diximus de conica illa ſectione deſcriben-
              <lb/>
            da, quæ circulus eſt, quia perfacilis eſt eius deſcriptio, cognita diametro.</s>
            <s xml:id="echoid-s2006" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s2007" xml:space="preserve">PLACET autem hoc loco tradere aliam rationem non iniucundam, & </s>
            <s xml:id="echoid-s2008" xml:space="preserve">fortaſſis ea, quam expli-
              <lb/>
            cauimus, faciliorem, deſcribendi parabolam, duas hyperbolas oppoſitas, & </s>
            <s xml:id="echoid-s2009" xml:space="preserve">Ellipſim, quarum axes dati
              <lb/>
            ſint, quæ quidem ratio (quod vehementer miror) à nemine hactenus, quod ſciam, obſeruata eſt. </s>
            <s xml:id="echoid-s2010" xml:space="preserve">Hanc au-
              <lb/>
            tem conis rectis duntaxat accommodabimus, propterea quòd ijs ſolum in horologiorum deſcriptionibus
              <lb/>
            vſuri ſumus. </s>
            <s xml:id="echoid-s2011" xml:space="preserve">Pro Parabola igitur præmittendum eſt huiuſmodi lemma conueniens tam cono recto
              <lb/>
            quàm Scaleno.</s>
            <s xml:id="echoid-s2012" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div105" type="section" level="1" n="33">
          <head xml:id="echoid-head36" xml:space="preserve">LEMMA.</head>
          <p>
            <s xml:id="echoid-s2013" xml:space="preserve">DATO cono & </s>
            <s xml:id="echoid-s2014" xml:space="preserve">diametro parabolæ, inuenire latus rectum parabolæ.</s>
            <s xml:id="echoid-s2015" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <note position="right" xml:space="preserve">Inuentio late-
            <lb/>
          ris recti Parabo
            <lb/>
          les, cuius diam@
            <lb/>
          ter in cono da-
            <lb/>
          ta ſit.</note>
          <figure number="31">
            <image file="0049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0049-01"/>
          </figure>
          <note position="left" xml:space="preserve">40</note>
          <p style="it">
            <s xml:id="echoid-s2016" xml:space="preserve">SIT datus conus A B C, in quo triangulum per axem A B C: </s>
            <s xml:id="echoid-s2017" xml:space="preserve">ſecetur autem conus
              <lb/>
            plano faciente parabolam E F G, iuxta ea, quæ ab Apollonio demonstrata ſunt propoſ. </s>
            <s xml:id="echoid-s2018" xml:space="preserve">11.
              <lb/>
            </s>
            <s xml:id="echoid-s2019" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2020" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2021" xml:space="preserve">ita vt eius axis E H, æquidiſtans ſit lateri A C, trianguli per axem. </s>
            <s xml:id="echoid-s2022" xml:space="preserve">Huius igitur
              <lb/>
            paraboles rectum latus inueniemus hoc modo. </s>
            <s xml:id="echoid-s2023" xml:space="preserve">Fiat vt alterum latus trianguli per axem,
              <lb/>
              <note position="left" xlink:label="note-0049-06" xlink:href="note-0049-06a" xml:space="preserve">50</note>
            nempe A B, ad baſim B C, ita B C, ad A I. </s>
            <s xml:id="echoid-s2024" xml:space="preserve">Deinde vt alterum latus A C, ad A I, inuen-
              <lb/>
              <note position="right" xlink:label="note-0049-07" xlink:href="note-0049-07a" xml:space="preserve">11. ſexti.</note>
            tam, ita A E, ad E K. </s>
            <s xml:id="echoid-s2025" xml:space="preserve">Dico E K, eſſe rectum latus paraboles E F G, hoc eſt, illam eſſere-
              <lb/>
              <note position="right" xlink:label="note-0049-08" xlink:href="note-0049-08a" xml:space="preserve">12. ſexti.</note>
            ctam, iuxta quam poſſunt or dinatim applicatæ ad diametrum E H. </s>
            <s xml:id="echoid-s2026" xml:space="preserve">Sit enim rectangulũ
              <lb/>
            C B, contentum ſub lateribus trianguli per axem A B, A C; </s>
            <s xml:id="echoid-s2027" xml:space="preserve">& </s>
            <s xml:id="echoid-s2028" xml:space="preserve">ad A B, applicetur rectan-
              <lb/>
            gulum B I, contentum ſub A B, A I, quod æquale erit quadrato baſis B C, propterea quòd
              <lb/>
              <note position="right" xlink:label="note-0049-09" xlink:href="note-0049-09a" xml:space="preserve">17. ſexti.</note>
            tres rectæ A B, B C, A I, continuè proportionales ſunt, ex conſt
              <unsure/>
            ructione; </s>
            <s xml:id="echoid-s2029" xml:space="preserve">erit{q́ue} C A I,
              <lb/>
            vna linea recta, quòd duo anguli ad A, recti ſint. </s>
            <s xml:id="echoid-s2030" xml:space="preserve">Quoniam igitur eſt, vt C A, ad A I,
              <lb/>
              <note position="right" xlink:label="note-0049-10" xlink:href="note-0049-10a" xml:space="preserve">14. primi.</note>
            ita A E, ad E K, per conſtructionem; </s>
            <s xml:id="echoid-s2031" xml:space="preserve">& </s>
            <s xml:id="echoid-s2032" xml:space="preserve">conuertendo, vt A I, ad A C, ita E K, ad A E;
              <lb/>
            </s>
            <s xml:id="echoid-s2033" xml:space="preserve">Vt autem A I, ad A C, ita eſt rectangulum B I, hoc eſt, quadr atum baſis B C, ad rectan-
              <lb/>
              <note position="right" xlink:label="note-0049-11" xlink:href="note-0049-11a" xml:space="preserve">1. ſexti.</note>
            </s>
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