Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div951" type="section" level="1" n="336">
          <p>
            <s xml:id="echoid-s15494" xml:space="preserve">
              <pb o="332" file="362" n="362" rhead="GEOMETR. PRACT."/>
            ad B C. </s>
            <s xml:id="echoid-s15495" xml:space="preserve">Et quoniam G C, ipſi A, æqualis, eſt ad G I, vt H F, ipſi D, æqualis, ad
              <lb/>
            HE; </s>
            <s xml:id="echoid-s15496" xml:space="preserve">Erit quo que per conuerſionem rationis GC, hoc eſt, A, ad IC, vt HF, hoc
              <lb/>
            eſt, vt D, ad E F. </s>
            <s xml:id="echoid-s15497" xml:space="preserve">Cum ergo oſtenſum ſit, maiorem eſſe proportionem A, ad
              <lb/>
            IC, quam ad B C; </s>
            <s xml:id="echoid-s15498" xml:space="preserve">erit quo que maior proportio D, ad E F, quam A, ad B C, hoc
              <lb/>
            eſt, A, ad B C, minorem proportionem habebit, quam D, ad E F. </s>
            <s xml:id="echoid-s15499" xml:space="preserve">quod eſt pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s15500" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div953" type="section" level="1" n="337">
          <head xml:id="echoid-head364" xml:space="preserve">LEMMA II.</head>
          <p>
            <s xml:id="echoid-s15501" xml:space="preserve">SI circuli arcum duæ rectæ tangant in vno puncto coeuntes; </s>
            <s xml:id="echoid-s15502" xml:space="preserve">& </s>
            <s xml:id="echoid-s15503" xml:space="preserve">in eo-
              <lb/>
            dem arcu aptentur quotlibet rectæ æquales diuidentes ipſum in par-
              <lb/>
            tes totidem æquales. </s>
            <s xml:id="echoid-s15504" xml:space="preserve">Erunt duæ illæ tangentes omnibus hiſce chor-
              <lb/>
            dis ſimul maiores.</s>
            <s xml:id="echoid-s15505" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15506" xml:space="preserve">
              <emph style="sc">Tangant</emph>
            arcum AB, duæ rectæ AK, BK, coeuntes in K, aptenturq; </s>
            <s xml:id="echoid-s15507" xml:space="preserve">quot-
              <lb/>
            libet rectæ in eo æquales AC, CD, DE, EF, FG, GB, diuidentes arcum in totidem
              <lb/>
            partes æquales. </s>
            <s xml:id="echoid-s15508" xml:space="preserve">Dico rectas AK, BK, ſimul maiores eſſe omnibus illis rectis ſub-
              <lb/>
            tenſis ſimul. </s>
            <s xml:id="echoid-s15509" xml:space="preserve">Productis enim rectis AC, BG, donec coeant in H; </s>
            <s xml:id="echoid-s15510" xml:space="preserve">Item pro-
              <lb/>
            ductis rectis CD, GF, donec concurrantin I, & </s>
            <s xml:id="echoid-s15511" xml:space="preserve">ſic deinceps, ſi plures rectæ fu-
              <lb/>
            erint: </s>
            <s xml:id="echoid-s15512" xml:space="preserve"> Erunt rectæ DI, FI, maiores
              <figure xlink:label="fig-362-01" xlink:href="fig-362-01a" number="253">
                <image file="362-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/362-01"/>
              </figure>
              <note symbol="a" position="left" xlink:label="note-362-01" xlink:href="note-362-01a" xml:space="preserve">21. primi.</note>
            DE, FE. </s>
            <s xml:id="echoid-s15513" xml:space="preserve">Additis ergo æqualibus DC, FG;
              <lb/>
            </s>
            <s xml:id="echoid-s15514" xml:space="preserve">erunt etiam rectæ C I, G I; </s>
            <s xml:id="echoid-s15515" xml:space="preserve">maiores rectis
              <lb/>
              <note symbol="b" position="left" xlink:label="note-362-02" xlink:href="note-362-02a" xml:space="preserve">21. primi.</note>
            CD, DE, EF, FG, ſimul. </s>
            <s xml:id="echoid-s15516" xml:space="preserve"> Sed C H, G H, maiores ſunt rectis C I, G I. </s>
            <s xml:id="echoid-s15517" xml:space="preserve">Igitur multo
              <lb/>
            maiores erunt CH, GH, rectis C D, D E,
              <lb/>
            EF, F G; </s>
            <s xml:id="echoid-s15518" xml:space="preserve">additiſque æqualibus A C, B G,
              <lb/>
            maiores erunt AH, B H, ſimul quam A C,
              <lb/>
            CD, DE, EF, FG, GB, ſimul. </s>
            <s xml:id="echoid-s15519" xml:space="preserve"> Sunt
              <note symbol="c" position="left" xlink:label="note-362-03" xlink:href="note-362-03a" xml:space="preserve">21. primi.</note>
            & </s>
            <s xml:id="echoid-s15520" xml:space="preserve">AK, BK, maiores, quam AH, BH. </s>
            <s xml:id="echoid-s15521" xml:space="preserve">Igi-
              <lb/>
            tur multo maiores erunt A K, B K, ſimul
              <lb/>
            quam AC, CD, DE, EF, FG, GB, ſimul. </s>
            <s xml:id="echoid-s15522" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s15523" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div955" type="section" level="1" n="338">
          <head xml:id="echoid-head365" xml:space="preserve">EEMMA III.</head>
          <p>
            <s xml:id="echoid-s15524" xml:space="preserve">SI circuli arcum tres rectæ tangant in duobus punctis coeuntes, ita vt
              <lb/>
            contactuum punctum medium diuidat arcum bifariam: </s>
            <s xml:id="echoid-s15525" xml:space="preserve">In eodem
              <lb/>
            autem arcu accommodentur quotlibet rectæ numero pares, & </s>
            <s xml:id="echoid-s15526" xml:space="preserve">inter
              <lb/>
            ſe æquales, Erunt tres illæ tangẽtes omnib. </s>
            <s xml:id="echoid-s15527" xml:space="preserve">his ſimul ſumptis maiores.</s>
            <s xml:id="echoid-s15528" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15529" xml:space="preserve">
              <emph style="sc">In</emph>
            antecedente figura arcum AB, tangant tres rectæ AC, CD, DB, conueni-
              <lb/>
            entes in duobus punctis C, D, ſecantes ipſum bifariam in E. </s>
            <s xml:id="echoid-s15530" xml:space="preserve">Accommo den-
              <lb/>
            turque in eo dem arcu quotlibet rectæ æquales, & </s>
            <s xml:id="echoid-s15531" xml:space="preserve">numero pares AF, F E, EG,
              <lb/>
            GB. </s>
            <s xml:id="echoid-s15532" xml:space="preserve">Dico tres AC, CD, DB, ſimul ſumptas eſſe maiores rectis AF, FE, EG, GB,
              <lb/>
            ſimul ſumptis. </s>
            <s xml:id="echoid-s15533" xml:space="preserve">Quoniam enim per Lemma præcedens AC, C E, maiores ſunt,
              <lb/>
            rectis AF, FE: </s>
            <s xml:id="echoid-s15534" xml:space="preserve">Item BD, DE, maiores rectis B G, G E, Erunt quo que A C, C D,
              <lb/>
            D B, ſimul maiores rectis AF, FE, EG, GB, ſimul. </s>
            <s xml:id="echoid-s15535" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s15536" xml:space="preserve"/>
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