Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s15807" xml:space="preserve">
              <pb o="340" file="368" n="368" rhead="GEOMETR. PRACT."/>
            lis, conficietur eodem pacto rectangulum ex tribus conflatum æquale tribus
              <lb/>
            trapeziis, &</s>
            <s xml:id="echoid-s15808" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15809" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15810" xml:space="preserve">
              <emph style="sc">Vltimo</emph>
            porrò triangulo, ſi quod fuerit, conſtituetur rectangulum
              <note symbol="a" position="left" xlink:label="note-368-01" xlink:href="note-368-01a" xml:space="preserve">ſchol. 41.
                <lb/>
              primi.</note>
            I
              <unsure/>
            e ſupra ſemiſſem baſis, in eadem altitudine cum triangulo.</s>
            <s xml:id="echoid-s15811" xml:space="preserve"/>
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        <div xml:id="echoid-div975" type="section" level="1" n="347">
          <head xml:id="echoid-head374" xml:space="preserve">THEOR. 4. PROPOS. 7.</head>
          <p>
            <s xml:id="echoid-s15812" xml:space="preserve">SI ex duobus punctis ad vnum punctum cuiuſuis lineæ rectæ, quæ
              <lb/>
            communis ſectio ſit plani per duo puncta ducti cum alio quopiam
              <lb/>
            plano, duæ rectæ ducantur, facientes cum illa duos angulos æquales:
              <lb/>
            </s>
            <s xml:id="echoid-s15813" xml:space="preserve">erunt duæ hæ rectæ breuiores quibuſcunque aliis duabus rectis, quæ
              <lb/>
            ex eiſdem duobus punctis ad aliud punctum eiuſdem lineæ rectæ
              <lb/>
            ducuntur.</s>
            <s xml:id="echoid-s15814" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15815" xml:space="preserve">
              <emph style="sc">Ex</emph>
            duobus punctis A, B, ad C, punctum in recta CD, ita vt planum per CD,
              <lb/>
            du ctum tranſeat reuolutum per A, B, ducantur duæ rectæ AC, BC, facientes an-
              <lb/>
            gulos A C F, B C D, æquales: </s>
            <s xml:id="echoid-s15816" xml:space="preserve">& </s>
            <s xml:id="echoid-s15817" xml:space="preserve">ex eiſdem punctis A, B, ducantur primum ad
              <lb/>
            aliud punctum D, ad dextram ipſius C, aliæ duæ rectæ AD, BD. </s>
            <s xml:id="echoid-s15818" xml:space="preserve">Dico AC, BC,
              <lb/>
            eſſe breuiores, quam AD, BD. </s>
            <s xml:id="echoid-s15819" xml:space="preserve">Producta enim AC, verſus C, fiat CE, ipſi CB,
              <lb/>
            æqualis, iungaturque DE. </s>
            <s xml:id="echoid-s15820" xml:space="preserve">Et quia angulus ACF, angulo BCD, ponitur æqua-
              <lb/>
            lis, eſtque angulus ACF, angulo ECD, ad verticem æqualis, erit quoque
              <note symbol="b" position="left" xlink:label="note-368-02" xlink:href="note-368-02a" xml:space="preserve">15. primi.</note>
            gulus BCD, angulo ECD, æqualis. </s>
            <s xml:id="echoid-s15821" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s15822" xml:space="preserve">duo latera BC, CD, duobus
              <lb/>
            lateribus EC, CD, æqualia ſint: </s>
            <s xml:id="echoid-s15823" xml:space="preserve"> erit
              <note symbol="c" position="left" xlink:label="note-368-03" xlink:href="note-368-03a" xml:space="preserve">4. primi.</note>
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                <image file="368-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/368-01"/>
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            D B, baſi D E, æqualis; </s>
            <s xml:id="echoid-s15824" xml:space="preserve">ac proinde A D,
              <lb/>
            D B, ſimul ipſis A D, D E. </s>
            <s xml:id="echoid-s15825" xml:space="preserve">ſimul æquales
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s15826" xml:space="preserve"> Sunt autem A D, D E,
              <note symbol="d" position="left" xlink:label="note-368-04" xlink:href="note-368-04a" xml:space="preserve">@primi.</note>
            quam AE, hoc eſt, quam AC, CB; </s>
            <s xml:id="echoid-s15827" xml:space="preserve">quod
              <lb/>
            CB, CE, poſitæ ſint æquale@. </s>
            <s xml:id="echoid-s15828" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s15829" xml:space="preserve">AD,
              <lb/>
            BD, maiores erunt, quam AC, BC. </s>
            <s xml:id="echoid-s15830" xml:space="preserve">quod
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            eſt propoſitum.</s>
            <s xml:id="echoid-s15831" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15832" xml:space="preserve">
              <emph style="sc">Dvcantvr</emph>
            deinde ex punctis A, B,
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            ad aliud punctum F, ad ſiniſtram ipſius C,
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            aliæ duæ rectæ AF, BF. </s>
            <s xml:id="echoid-s15833" xml:space="preserve">Dico rurſus A C,
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            BC, breuiores eſſe, quam AF, BF. </s>
            <s xml:id="echoid-s15834" xml:space="preserve">Producta enim rurſum AC, ſumptaque CE,
              <lb/>
            ipſi CB, æquali, iungatur EF. </s>
            <s xml:id="echoid-s15835" xml:space="preserve">Et quoniam anguli ACF, BCD, æquales ponun-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s15836" xml:space="preserve"> eſtque ACF, angulo ECD, ad verticem æqualis; </s>
            <s xml:id="echoid-s15837" xml:space="preserve">erunt qu@que
              <note symbol="e" position="left" xlink:label="note-368-05" xlink:href="note-368-05a" xml:space="preserve">15. primi.</note>
            BCD, ECD, æquales: </s>
            <s xml:id="echoid-s15838" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s15839" xml:space="preserve">ex duobus rectis reliqui BCF, ECF, æqua-
              <lb/>
            les erunt. </s>
            <s xml:id="echoid-s15840" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s15841" xml:space="preserve">duo latera BC, CF, duobus lateribus EC, CF, æqualia
              <lb/>
            ſint; </s>
            <s xml:id="echoid-s15842" xml:space="preserve"> erit quo que baſis BF, baſi EF, æqualis: </s>
            <s xml:id="echoid-s15843" xml:space="preserve">Ac proinde AF, FE, ipſis AF,
              <note symbol="f" position="left" xlink:label="note-368-06" xlink:href="note-368-06a" xml:space="preserve">4. primi.</note>
            æquales erunt. </s>
            <s xml:id="echoid-s15844" xml:space="preserve"> Sunt autem AF, FE, maiores, quam AE, hoc eſt, quam AC,
              <note symbol="g" position="left" xlink:label="note-368-07" xlink:href="note-368-07a" xml:space="preserve">20. primi.</note>
            quod BC, CE, poſitæ ſint æquales. </s>
            <s xml:id="echoid-s15845" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s15846" xml:space="preserve">AF, BF, maiores erunt, quam A C,
              <lb/>
            CB. </s>
            <s xml:id="echoid-s15847" xml:space="preserve">quod eſt propoſitum.</s>
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          <head xml:id="echoid-head375" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s15849" xml:space="preserve">
              <emph style="sc">Qvia</emph>
            ergo Natura non impedita agit per lineas breuiſsimas; </s>
            <s xml:id="echoid-s15850" xml:space="preserve">fit, vtradius
              <lb/>
            Solis, vel viſualis cadens ex A, in planum terſum D F, ita vt reflectatur ad </s>
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