Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div948" type="section" level="1" n="334">
          <pb o="331" file="361" n="361" rhead="LIBER OCTAVVS."/>
          <p>
            <s xml:id="echoid-s15449" xml:space="preserve">Si duæ lineæ in plano eoſdem habeant terminos, & </s>
            <s xml:id="echoid-s15450" xml:space="preserve">in eaſdem partes cauæ ſint, compre-
              <lb/>
            hendens comprehenſa maior eſt. </s>
            <s xml:id="echoid-s15451" xml:space="preserve">quod quidem principium eſſe verum, ex eo euidẽ-
              <lb/>
            ter intelligi poteſt quod ex eo, non ſolum Archimedes, verum etiam plurimi a-
              <lb/>
            lij Geometræ tum veteres, tum recentiores, innumera propemodum, atque ad-
              <lb/>
            miranda Theoremata, problemataque demonſtrarint, quæ vt veriſsima, ab o-
              <lb/>
            mnibus recepta ſunt; </s>
            <s xml:id="echoid-s15452" xml:space="preserve">neque vnquam ex illo abſurdi aliquid conſecutum eſt,
              <lb/>
            aut contra id quiſquam hactenus à du obus ferme millibus annorum, noui quid
              <lb/>
            commentus eſt. </s>
            <s xml:id="echoid-s15453" xml:space="preserve">Hoc ergo poſito principio, facilis eſt de-
              <lb/>
              <figure xlink:label="fig-361-01" xlink:href="fig-361-01a" number="251">
                <image file="361-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/361-01"/>
              </figure>
            monſtratio Archimedis. </s>
            <s xml:id="echoid-s15454" xml:space="preserve">Sit namque figura regularis ABC-
              <lb/>
            DEF, deſcripta circa circulũ, cuius centrũ N, tangens eũ in
              <lb/>
            punctis G, H, I, K, L, M. </s>
            <s xml:id="echoid-s15455" xml:space="preserve">Quoniã igitur per præmiſlum prin-
              <lb/>
            cipium rectæ A G, A M, maiores ſunt arcu G M: </s>
            <s xml:id="echoid-s15456" xml:space="preserve">Item B G,
              <lb/>
            B H, maiores arcu G H, & </s>
            <s xml:id="echoid-s15457" xml:space="preserve">ſic de reliquis; </s>
            <s xml:id="echoid-s15458" xml:space="preserve">erunt omnes rectæ
              <lb/>
            ſimul conficientes totum ambitum figuræ, maiores omni-
              <lb/>
            bus arcubus ſimul conficientibus totam circuli perip heriam. </s>
            <s xml:id="echoid-s15459" xml:space="preserve">quod erat demon-
              <lb/>
            ſtrandum.</s>
            <s xml:id="echoid-s15460" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div950" type="section" level="1" n="335">
          <head xml:id="echoid-head362" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s15461" xml:space="preserve">
              <emph style="sc">Cardanvs</emph>
            in libro quinto de proportionibus propoſ. </s>
            <s xml:id="echoid-s15462" xml:space="preserve">201. </s>
            <s xml:id="echoid-s15463" xml:space="preserve">conatur de-
              <lb/>
            monſtrare, duas rectas circulum contingentes, cuiuſmo di ſunt A G, A M, maio-
              <lb/>
            res eſſe arcu intercepto GM, (quod Archimedes ex ſuo aſſumpto principio de-
              <lb/>
            duxit (præmiſsis tribus Lemmatibus, & </s>
            <s xml:id="echoid-s15464" xml:space="preserve">vno principio. </s>
            <s xml:id="echoid-s15465" xml:space="preserve">quorum primum eſt
              <lb/>
            hoc.</s>
            <s xml:id="echoid-s15466" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div951" type="section" level="1" n="336">
          <head xml:id="echoid-head363" xml:space="preserve">LEMMA I.</head>
          <p>
            <s xml:id="echoid-s15467" xml:space="preserve">SI fuerint quatuor quantitates, & </s>
            <s xml:id="echoid-s15468" xml:space="preserve">minor ſit exceſſus inter primã & </s>
            <s xml:id="echoid-s15469" xml:space="preserve">ſecũ-
              <lb/>
            dã, quam inter tertiã & </s>
            <s xml:id="echoid-s15470" xml:space="preserve">quartam; </s>
            <s xml:id="echoid-s15471" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s15472" xml:space="preserve">prima non minor, quam tertia,
              <lb/>
            maior verò quam ſecunda, Item tertia maior quam quarta: </s>
            <s xml:id="echoid-s15473" xml:space="preserve">Erit mi-
              <lb/>
            nor proportio primæ ad ſecundam, quam tertiæ ad quartam.</s>
            <s xml:id="echoid-s15474" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15475" xml:space="preserve">
              <emph style="sc">Sint</emph>
            quatuor quantitates A, BC, D, EF; </s>
            <s xml:id="echoid-s15476" xml:space="preserve">ſitque GB, exceſſus inter primam
              <lb/>
            A, & </s>
            <s xml:id="echoid-s15477" xml:space="preserve">ſecundam BC, minor exceſſu H E, inter tertiam
              <lb/>
              <figure xlink:label="fig-361-02" xlink:href="fig-361-02a" number="252">
                <image file="361-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/361-02"/>
              </figure>
            D, & </s>
            <s xml:id="echoid-s15478" xml:space="preserve">quartam E F; </s>
            <s xml:id="echoid-s15479" xml:space="preserve">Item prima A, non ſit minor, quã
              <lb/>
            tertia D: </s>
            <s xml:id="echoid-s15480" xml:space="preserve">maior verò quam ſecunda B C: </s>
            <s xml:id="echoid-s15481" xml:space="preserve">Ac deni-
              <lb/>
            que tertia D; </s>
            <s xml:id="echoid-s15482" xml:space="preserve">maiorſit quam quarta E F; </s>
            <s xml:id="echoid-s15483" xml:space="preserve">Dico mino-
              <lb/>
            rem eſſe proportionem primæ A, ad ſecundam B C,
              <lb/>
            quam tertiæ D, ad quartam E F. </s>
            <s xml:id="echoid-s15484" xml:space="preserve">Cum enim A, non
              <lb/>
            minor ſit, ꝗ̃ D: </s>
            <s xml:id="echoid-s15485" xml:space="preserve">at GB, minor, ꝗ̃ HE, erit maior ꝓ
              <note symbol="a" position="right" xlink:label="note-361-01" xlink:href="note-361-01a" xml:space="preserve">8. quinti.</note>
            tio A, ad GB, quam ad HE: </s>
            <s xml:id="echoid-s15486" xml:space="preserve">Eſt autem A, (ſi eſt æqua-
              <lb/>
            lis ip ſi D,) ad H E, vt D, ad H E; </s>
            <s xml:id="echoid-s15487" xml:space="preserve">vel maior eſt proportio A, (ſi maior eſt, quam
              <lb/>
            D,) ad HE. </s>
            <s xml:id="echoid-s15488" xml:space="preserve">quam D, ad HE. </s>
            <s xml:id="echoid-s15489" xml:space="preserve">Igitur maior erit proportio A, ad GB, quam D, ad
              <lb/>
            H E. </s>
            <s xml:id="echoid-s15490" xml:space="preserve">Si igitur fiat vt D, ad HE, ita A, ad G I, habebit quo que A, ad GB, ma-
              <lb/>
            iorem proportionem, quam ad G I; </s>
            <s xml:id="echoid-s15491" xml:space="preserve"> ac proinde erit GI, maior quam G B; </s>
            <s xml:id="echoid-s15492" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-361-02" xlink:href="note-361-02a" xml:space="preserve">10. quinti.</note>
            eo que I C, minor, quam B C. </s>
            <s xml:id="echoid-s15493" xml:space="preserve"> Maior ergo erit proportio A, ad I C. </s>
            <s xml:id="echoid-s15494" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-361-03" xlink:href="note-361-03a" xml:space="preserve">8. quinti.</note>
            </s>
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