Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s11290" xml:space="preserve">
              <pb o="242" file="272" n="272" rhead="GEOMETR. PRACT."/>
            ad I Y, hoc eſt, ita quadratum G, ad rectangulum I Z: </s>
            <s xml:id="echoid-s11291" xml:space="preserve">Eſt autem
              <note symbol="a" position="left" xlink:label="note-272-01" xlink:href="note-272-01a" xml:space="preserve">1. ſexti.</note>
            B C F, maius quadrato G, ſiue rectilineo A: </s>
            <s xml:id="echoid-s11292" xml:space="preserve">(quando enim ad partes angulo-
              <lb/>
            rum, qui duo bus rectis minores ſunt, conſtruendum eſt trapezium dato recti-
              <lb/>
              <figure xlink:label="fig-272-01" xlink:href="fig-272-01a" number="176">
                <image file="272-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/272-01"/>
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            lineo æquale, debet eſſe triangulum maius rectilineo) erit quo que
              <note symbol="b" position="left" xlink:label="note-272-02" xlink:href="note-272-02a" xml:space="preserve">14. quinti.</note>
            lum V C T, maius rectangulo I Z. </s>
            <s xml:id="echoid-s11293" xml:space="preserve">Igitur vt Num. </s>
            <s xml:id="echoid-s11294" xml:space="preserve">3. </s>
            <s xml:id="echoid-s11295" xml:space="preserve">traditum eſt, conſtruatur
              <lb/>
            trapezium V b, rectangulo I Z, æquale: </s>
            <s xml:id="echoid-s11296" xml:space="preserve">& </s>
            <s xml:id="echoid-s11297" xml:space="preserve">tribus rectis C V, V a, C B, inuen-
              <lb/>
            ta quarta proportionali B D, (tranſibit autem recta ducta C a, per D,
              <note symbol="c" position="left" xlink:label="note-272-03" xlink:href="note-272-03a" xml:space="preserve">ſ@hol. 4.
                <lb/>
              ſexti.</note>
            quarta B D, ritè eſt inuenta, ita vt viciſsim recta C a, ſi ex quiſitè ducatur, ex- hibeat quartam proportionalem quæſitam B D,) demittatur D E, ipſi B C, pa-
              <lb/>
              <note symbol="d" position="left" xlink:label="note-272-04" xlink:href="note-272-04a" xml:space="preserve">4. ſexti.</note>
            rallela. </s>
            <s xml:id="echoid-s11298" xml:space="preserve">Dico trapezium B E, dato rectilineo A, æquale eſſe. </s>
            <s xml:id="echoid-s11299" xml:space="preserve">Quoniam enim
              <lb/>
            trapezium B E, trapezio V b, ſimile eſt, per ea, quæ ad propoſ. </s>
            <s xml:id="echoid-s11300" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11301" xml:space="preserve">libr. </s>
            <s xml:id="echoid-s11302" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11303" xml:space="preserve">Eu-
              <lb/>
            clid. </s>
            <s xml:id="echoid-s11304" xml:space="preserve">demonſtrauimus; </s>
            <s xml:id="echoid-s11305" xml:space="preserve"> erit trapezium B E, ad trapezium V b, vt recta B C,
              <note symbol="e" position="left" xlink:label="note-272-05" xlink:href="note-272-05a" xml:space="preserve">coroll. 20.
                <lb/>
              ſexti.</note>
            rectam X, hoc eſt, vt recta HI, ad IY, hoc eſt, vt quadratum G, ad rectangu- lum I Z. </s>
            <s xml:id="echoid-s11306" xml:space="preserve">Cum ergo trapezium V b, rectangulo I Z, æquale ſit; </s>
            <s xml:id="echoid-s11307" xml:space="preserve"> erit
              <note symbol="f" position="left" xlink:label="note-272-06" xlink:href="note-272-06a" xml:space="preserve">1. ſexti.</note>
            que trapezium BE, quadrato G, hoc eſt, rectilineo A, æquale. </s>
            <s xml:id="echoid-s11308" xml:space="preserve">quod eſt propo-
              <lb/>
              <note symbol="g" position="left" xlink:label="note-272-07" xlink:href="note-272-07a" xml:space="preserve">14. quinti.</note>
            ſitum.</s>
            <s xml:id="echoid-s11309" xml:space="preserve"/>
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            <s xml:id="echoid-s11310" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11311" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter ex alia parte angulorum R B C, S C B, qui duo bus rectis ſunt
              <lb/>
            maiores, etiamſi punctum concurſus F, non habeatur, trapezium conſtituemus
              <lb/>
            rectilineo T, æquale, cuiuſcunque magnitudinis illud ponatur. </s>
            <s xml:id="echoid-s11312" xml:space="preserve">Neque enim in
              <lb/>
            hoc caſu neceſſe eſt, ipſum eſſe minus triangulo B C F, ſi perficeretur. </s>
            <s xml:id="echoid-s11313" xml:space="preserve">Ducta
              <lb/>
            namque ex quolibet puncto T, rectæ C F, ipſi BF, parallella T V, eaque pro-
              <lb/>
            ducta, inueniatur duabus rectis B C, C V, tertia proportionalis X. </s>
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