Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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        <div xml:id="echoid-div327" type="section" level="1" n="201">
          <p>
            <s xml:id="echoid-s3047" xml:space="preserve">
              <pb o="130" file="0150" n="150" rhead="GEOMETRIÆ"/>
            MZP, adomnes lineas figuræ, OZP, regula, MP, & </s>
            <s xml:id="echoid-s3048" xml:space="preserve">ideò vt, M
              <lb/>
              <note position="left" xlink:label="note-0150-01" xlink:href="note-0150-01a" xml:space="preserve">Goroll. 4.
                <lb/>
              huius.</note>
            P, ad, PO, vel ad, Ω &</s>
            <s xml:id="echoid-s3049" xml:space="preserve">, ita figura, MZP, ad figuram, OZP,
              <lb/>
              <note position="left" xlink:label="note-0150-02" xlink:href="note-0150-02a" xml:space="preserve">4. huius.</note>
            quod etiam ſerua.</s>
            <s xml:id="echoid-s3050" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div329" type="section" level="1" n="202">
          <head xml:id="echoid-head217" xml:space="preserve">D. SECTIO IV.</head>
          <p>
            <s xml:id="echoid-s3051" xml:space="preserve">VLterius ab ipſis, OP, Ω &</s>
            <s xml:id="echoid-s3052" xml:space="preserve">, abſcindantur partes æquales, O
              <lb/>
            R, ΩΥ, & </s>
            <s xml:id="echoid-s3053" xml:space="preserve">per puncta, R, Y, ducantur ipſis, ZP, ℟ &</s>
            <s xml:id="echoid-s3054" xml:space="preserve">, æ-
              <lb/>
            quidiſtantes, SR, VY, & </s>
            <s xml:id="echoid-s3055" xml:space="preserve">per, S, vbi, RS, ſecat lineam, ZO, du-
              <lb/>
              <figure xlink:label="fig-0150-01" xlink:href="fig-0150-01a" number="88">
                <image file="0150-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0150-01"/>
              </figure>
            catur, HC, æquidiſtans ipſi, M
              <lb/>
            P, & </s>
            <s xml:id="echoid-s3056" xml:space="preserve">per, C, vbi, HC, ſecat li-
              <lb/>
            neain, ZM, ducatur, CN, pa-
              <lb/>
            rallelaipſi, ZP, ſecans, MP, in,
              <lb/>
            N; </s>
            <s xml:id="echoid-s3057" xml:space="preserve">eſt igitur vt, MP, ad, PO,
              <lb/>
            ita, CH, ad, HS, per conſtru-
              <lb/>
            ctionem .</s>
            <s xml:id="echoid-s3058" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3059" xml:space="preserve">ita, NP, ad, PR, & </s>
            <s xml:id="echoid-s3060" xml:space="preserve">
              <lb/>
            permutando, vt, MP, ad, PN,
              <lb/>
            ita, OP, ad, PR, diuidendo, vt,
              <lb/>
            MN, ad, NP, ita, OR, ad, R
              <lb/>
            P, .</s>
            <s xml:id="echoid-s3061" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3062" xml:space="preserve">ita, ΩΥ, ad, Y &</s>
            <s xml:id="echoid-s3063" xml:space="preserve">, igitur ip-
              <lb/>
            ſæ, CN, VY, æquidiſtant regu-
              <lb/>
            lis homologarum, quę ſunt, ZP,
              <lb/>
            ℟ &</s>
            <s xml:id="echoid-s3064" xml:space="preserve">, & </s>
            <s xml:id="echoid-s3065" xml:space="preserve">diuidunt ad eandem par-
              <lb/>
            tem ſimiliter ipſas incidentes, M
              <lb/>
            P, Ω &</s>
            <s xml:id="echoid-s3066" xml:space="preserve">, (ſi .</s>
            <s xml:id="echoid-s3067" xml:space="preserve">n. </s>
            <s xml:id="echoid-s3068" xml:space="preserve">ZP, ℟ &</s>
            <s xml:id="echoid-s3069" xml:space="preserve">, ſtatue-
              <lb/>
              <note position="left" xlink:label="note-0150-03" xlink:href="note-0150-03a" xml:space="preserve">Corollar.
                <lb/>
              123. lib. 1.</note>
            ris regulas homologarum ipſę, M
              <lb/>
            P, Ω &</s>
            <s xml:id="echoid-s3070" xml:space="preserve">, ſunt incidentes, ſi verò
              <lb/>
            has ſtatueris regulas, illæ erunt in-
              <lb/>
            cidentes, ambę .</s>
            <s xml:id="echoid-s3071" xml:space="preserve">n. </s>
            <s xml:id="echoid-s3072" xml:space="preserve">terminant in
              <lb/>
            oppoſitas tangentes, quæ ſunt re-
              <lb/>
            gulæ homologarum earundem) ergo, CN, ad, VY, erit vt, MP,
              <lb/>
            ad, Ω &</s>
            <s xml:id="echoid-s3073" xml:space="preserve">, .</s>
            <s xml:id="echoid-s3074" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3075" xml:space="preserve">vt, ZP, ad, ℟ &</s>
            <s xml:id="echoid-s3076" xml:space="preserve">, & </s>
            <s xml:id="echoid-s3077" xml:space="preserve">ſunt, CN, SR, æquales, &</s>
            <s xml:id="echoid-s3078" xml:space="preserve">, S
              <lb/>
            R, VY, vtcunque ductæ ipſis, ZP, ℟ &</s>
            <s xml:id="echoid-s3079" xml:space="preserve">, æquidiſtantes, ergo ve,
              <lb/>
            ZP, ad, ℟ &</s>
            <s xml:id="echoid-s3080" xml:space="preserve">, ita, SR, ad, VY, ergo vt, ZP, ad, ℟ &</s>
            <s xml:id="echoid-s3081" xml:space="preserve">, ita erit
              <lb/>
              <note position="left" xlink:label="note-0150-04" xlink:href="note-0150-04a" xml:space="preserve">4. huius.</note>
            figura, OZP, ad figuram, Ω ℟ &</s>
            <s xml:id="echoid-s3082" xml:space="preserve">, quod pariter ſerua.</s>
            <s xml:id="echoid-s3083" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div331" type="section" level="1" n="203">
          <head xml:id="echoid-head218" xml:space="preserve">E. SECTIO V. ET VLTIMA.</head>
          <p>
            <s xml:id="echoid-s3084" xml:space="preserve">QVoniam verò figura, MZP, ad figuram, Ω ℟ &</s>
            <s xml:id="echoid-s3085" xml:space="preserve">, habet ratio-
              <lb/>
              <note position="left" xlink:label="note-0150-05" xlink:href="note-0150-05a" xml:space="preserve">Defin. 12.
                <lb/>
              lib. 1.</note>
            nem compoſitam ex ratione figuræ, MZP, ad figuram, O
              <lb/>
            ZP, .</s>
            <s xml:id="echoid-s3086" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3087" xml:space="preserve">ex ratione, MP, ad, Ω &</s>
            <s xml:id="echoid-s3088" xml:space="preserve">, & </s>
            <s xml:id="echoid-s3089" xml:space="preserve">ex ratione figuræ, OZ
              <lb/>
            P, ad figuram, Ω ℟ &</s>
            <s xml:id="echoid-s3090" xml:space="preserve">, .</s>
            <s xml:id="echoid-s3091" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3092" xml:space="preserve">ex ratione ipſius, ZP, ad, ℟ & </s>
            <s xml:id="echoid-s3093" xml:space="preserve">a .</s>
            <s xml:id="echoid-s3094" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3095" xml:space="preserve">ex </s>
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