Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s11107" xml:space="preserve">
              <pb o="238" file="268" n="268" rhead="GEOMETR. PRACT."/>
            totidem partes GI, IK, KL, LM, MH, illis ordine proportionales. </s>
            <s xml:id="echoid-s11108" xml:space="preserve">Dico ita eſ-
              <lb/>
            ſe, verbi gratia, duas partes AC, CD, ſimul ad reliquastres DE, EF, FB, ſimul, vt
              <lb/>
            ſunt duæ GI, IK, ſimulad reliquas tres KL, LM, MH, ſimul, &</s>
            <s xml:id="echoid-s11109" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11110" xml:space="preserve">Quoniam enim
              <lb/>
            eſt, vt AC, ad CD, ita GI, ad IK, erit componendo etiam, vt AD, ad CD, ita GK,
              <lb/>
            ad IK: </s>
            <s xml:id="echoid-s11111" xml:space="preserve">Vtautem CD, ad DE, ita eſt IK, ad KL. </s>
            <s xml:id="echoid-s11112" xml:space="preserve">Igitur ex æqualitate erit, vt AD,
              <lb/>
            ad DE, ita GK, ad KL.</s>
            <s xml:id="echoid-s11113" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11114" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            quia conuertendo eſt, vt BF, ad F E, ita HM, ad ML; </s>
            <s xml:id="echoid-s11115" xml:space="preserve">erit quo-
              <lb/>
            que componendo, vt BE, ad FE, ita HL, ad ML: </s>
            <s xml:id="echoid-s11116" xml:space="preserve">Vtautem FE, ad ED, ita eſt
              <lb/>
            ML; </s>
            <s xml:id="echoid-s11117" xml:space="preserve">ad LK. </s>
            <s xml:id="echoid-s11118" xml:space="preserve">Igitur ex æqualitate erit, vt B E, ad ED, ita HL, ad L K; </s>
            <s xml:id="echoid-s11119" xml:space="preserve">& </s>
            <s xml:id="echoid-s11120" xml:space="preserve">com-
              <lb/>
              <figure xlink:label="fig-268-01" xlink:href="fig-268-01a" number="172">
                <image file="268-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/268-01"/>
              </figure>
            ponendo, vt B D, ad E D, ita H K, ad L K; </s>
            <s xml:id="echoid-s11121" xml:space="preserve">& </s>
            <s xml:id="echoid-s11122" xml:space="preserve">conuertendo, vt D E, ad D B, ita
              <lb/>
            KL, ad KH. </s>
            <s xml:id="echoid-s11123" xml:space="preserve">Itaque cumoſtenſum ſit, eſſe vt AD, ad DE, ita vt GK, ad KL, & </s>
            <s xml:id="echoid-s11124" xml:space="preserve">vt
              <lb/>
            D E, ad D B, ita K L, ad K H; </s>
            <s xml:id="echoid-s11125" xml:space="preserve">erit ex æqualitate, vt A D, ad D B, ita G K,
              <lb/>
            ad K H.</s>
            <s xml:id="echoid-s11126" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11127" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter oſtendemus eſſe, vt AC, ad CB, ita GI, ad IH. </s>
            <s xml:id="echoid-s11128" xml:space="preserve">Nam rurſus con-
              <lb/>
            uertendo, componendo, & </s>
            <s xml:id="echoid-s11129" xml:space="preserve">ex æqualitate erit vt B C, ad D C, ita HI, ad K I; </s>
            <s xml:id="echoid-s11130" xml:space="preserve">& </s>
            <s xml:id="echoid-s11131" xml:space="preserve">
              <lb/>
            conuertendo, vt CD, ad CB, ita IK, ad IH. </s>
            <s xml:id="echoid-s11132" xml:space="preserve">Cum ergo ſit, vt AC, ad CD, ita GI,
              <lb/>
            ad IK, & </s>
            <s xml:id="echoid-s11133" xml:space="preserve">vt CD, ad CB, ita IK, ad I H; </s>
            <s xml:id="echoid-s11134" xml:space="preserve">erit ex æqualitate, vt AC, ad CB, ita GI,
              <lb/>
            ad I H.</s>
            <s xml:id="echoid-s11135" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11136" xml:space="preserve">
              <emph style="sc">Pari</emph>
            ratione erit, vt AF, ad FB, ita GM, ad MH. </s>
            <s xml:id="echoid-s11137" xml:space="preserve">Erit namquerurſus com-
              <lb/>
            ponendo, & </s>
            <s xml:id="echoid-s11138" xml:space="preserve">ex æqualitate, vt AF, ad EF, ita GM, ad LM. </s>
            <s xml:id="echoid-s11139" xml:space="preserve">Cum ergo ſit quo-
              <lb/>
            que, vt EF, ad FB, ita LM, ad MH: </s>
            <s xml:id="echoid-s11140" xml:space="preserve">erit ex æqualitate, vt AF, ad FB, ita GM, ad
              <lb/>
            MH; </s>
            <s xml:id="echoid-s11141" xml:space="preserve">& </s>
            <s xml:id="echoid-s11142" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s11143" xml:space="preserve">Conſtatigitur primum.</s>
            <s xml:id="echoid-s11144" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11145" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            pars v. </s>
            <s xml:id="echoid-s11146" xml:space="preserve">g. </s>
            <s xml:id="echoid-s11147" xml:space="preserve">tertia DE, ſecta ſit vtcunque in partes duas D N, N E;
              <lb/>
            </s>
            <s xml:id="echoid-s11148" xml:space="preserve">& </s>
            <s xml:id="echoid-s11149" xml:space="preserve">tertia quo que pars KL, in duas KO, OL, illis proportionales. </s>
            <s xml:id="echoid-s11150" xml:space="preserve">Dico eſſe quo-
              <lb/>
            que vt AN, ad NB, ita GO, ad OH. </s>
            <s xml:id="echoid-s11151" xml:space="preserve">Erit enim conuertendo, vt EN, ad N D, ita
              <lb/>
            L O, ad O K: </s>
            <s xml:id="echoid-s11152" xml:space="preserve">& </s>
            <s xml:id="echoid-s11153" xml:space="preserve">componendo, vt ED, ad DN, ita LK, ad K O. </s>
            <s xml:id="echoid-s11154" xml:space="preserve">Quare cum ſit,
              <lb/>
            vt CD, ad DE, ita IK, ad KL, & </s>
            <s xml:id="echoid-s11155" xml:space="preserve">vt DE, ad DN, ita KL, ad KO: </s>
            <s xml:id="echoid-s11156" xml:space="preserve">erit ex æqualita-
              <lb/>
            te, vt CD, ad DN, ita IK, ad KO, atque ita partes AC, CD, DN, partibus GI, IK,
              <lb/>
            KO, proportionales ſunt.</s>
            <s xml:id="echoid-s11157" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11158" xml:space="preserve">
              <emph style="sc">Rvrsvs</emph>
            quia eſt conuertendo, vt FE, ad E D, ita ML, ad LK; </s>
            <s xml:id="echoid-s11159" xml:space="preserve">& </s>
            <s xml:id="echoid-s11160" xml:space="preserve">compo-
              <lb/>
            nendo, vt DE, ad NE, ita KL, ad OL; </s>
            <s xml:id="echoid-s11161" xml:space="preserve">erit exæqualitate, vt FE, ad E N, ita ML,
              <lb/>
            ad LO; </s>
            <s xml:id="echoid-s11162" xml:space="preserve">& </s>
            <s xml:id="echoid-s11163" xml:space="preserve">conuertendo, vt NE, ad EF, ita OL, ad LM; </s>
            <s xml:id="echoid-s11164" xml:space="preserve">ac proinde omnes par-
              <lb/>
            tes AC, CD, DN, NE, EF, FB, omnibus partibus GI, IK, KO, OL, LM,
              <lb/>
            M H, proportionales ſunt. </s>
            <s xml:id="echoid-s11165" xml:space="preserve">Igitur vt in prima parte demonſtra-
              <lb/>
            tumeſt, erit vt AN, ad NB, ita GO, ad OH. </s>
            <s xml:id="echoid-s11166" xml:space="preserve">Conſtat
              <lb/>
            ergo etiam ſecundum.</s>
            <s xml:id="echoid-s11167" xml:space="preserve"/>
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