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

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            <s xml:id="echoid-s5987" xml:space="preserve">
              <pb o="243" file="0263" n="263" rhead="LIBER III."/>
            F M, ad omnia quadrata eiuſdem parallelogrammi; </s>
            <s xml:id="echoid-s5988" xml:space="preserve">Δ V, regula,
              <lb/>
              <note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">29. Lib. 2.</note>
            R V, ſunt vt, FM, ad, RV, ergo ex æquali omnia quadrata por-
              <lb/>
            tionis, RFV, regula, FM, ad omnia quadrata, Δ V, regula, R
              <lb/>
            V, erunt vt, {2/3}, ω M, ad, RV, vel vt, {1/3}, ω M, ad, RM, .</s>
            <s xml:id="echoid-s5989" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5990" xml:space="preserve">ſum-
              <lb/>
            pta, RM, communi altitudine, vt rectangulum ſub, {1/3}, ω M, & </s>
            <s xml:id="echoid-s5991" xml:space="preserve">
              <lb/>
            ſub, RM, ad quadratum, RM, vel ad rectangulum, FMH;
              <lb/>
            </s>
            <s xml:id="echoid-s5992" xml:space="preserve">omnia vero quadrata, Δ V, regula, RV, ad omnia quadrata por-
              <lb/>
              <note position="right" xlink:label="note-0263-02" xlink:href="note-0263-02a" xml:space="preserve">Vlt. 2. El.</note>
            tionis, RFV, regula eadem, runt vt, HM, ad compoſitam ex,
              <lb/>
              <note position="right" xlink:label="note-0263-03" xlink:href="note-0263-03a" xml:space="preserve">1. Huius.</note>
            {1/2}, HM, &</s>
            <s xml:id="echoid-s5993" xml:space="preserve">, {1/6}, MF, .</s>
            <s xml:id="echoid-s5994" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5995" xml:space="preserve">ſumpta, MF, communi altitudine, vt re-
              <lb/>
              <note position="right" xlink:label="note-0263-04" xlink:href="note-0263-04a" xml:space="preserve">5. Lib. @</note>
            ctangulum, FMH, ad rectangulum ſub, FM, & </s>
            <s xml:id="echoid-s5996" xml:space="preserve">ſub compoſita ex,
              <lb/>
            {1/2}, HM, &</s>
            <s xml:id="echoid-s5997" xml:space="preserve">, {1/6}, MF, erant autem omnia quadrata portionis, RFV,
              <lb/>
            regula, FM, ad omnia quadrata, Δ V, regula, RV, vt rectangulum
              <lb/>
            ſub, {1/3}, M ω, & </s>
            <s xml:id="echoid-s5998" xml:space="preserve">ſub, RM, ad rectangulum, FMH, ergo ex æquali
              <lb/>
            omnia quadrata portionis, RFV, regula, FM, ad omnia quadrata
              <lb/>
            eiuſdem, regula, RV, erunt vt rectangulum ſub, {1/3}, M ω, & </s>
            <s xml:id="echoid-s5999" xml:space="preserve">ſub, R
              <lb/>
            M, ad rectangulum ſub, FM, & </s>
            <s xml:id="echoid-s6000" xml:space="preserve">ſub compoſita ex, {1/2}, HM, &</s>
            <s xml:id="echoid-s6001" xml:space="preserve">, {1/6},
              <lb/>
            M F, .</s>
            <s xml:id="echoid-s6002" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6003" xml:space="preserve">vt rectangulum ſub tota, M ω, & </s>
            <s xml:id="echoid-s6004" xml:space="preserve">ſub, RM, ad rectangu-
              <lb/>
            lum ſub, FM, & </s>
            <s xml:id="echoid-s6005" xml:space="preserve">ſub compoſita ex, {1/2}, FM, & </s>
            <s xml:id="echoid-s6006" xml:space="preserve">ſexquialtera, MH,
              <lb/>
            .</s>
            <s xml:id="echoid-s6007" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6008" xml:space="preserve">& </s>
            <s xml:id="echoid-s6009" xml:space="preserve">ſub compoſita ex, {1/2}, FM, & </s>
            <s xml:id="echoid-s6010" xml:space="preserve">ſexquialtera, MI, & </s>
            <s xml:id="echoid-s6011" xml:space="preserve">ſexquial-
              <lb/>
            tera, IH, porrò ſexquialtera, IH, cum, {1/2}, FM, efficit duas, FM,
              <lb/>
            I H, quibus ſi iunxeris, MI, detractam de ſexquialtera ipſius, MI,
              <lb/>
            fiet tota, FH, cum, MN, æqualis dimidio, FM, & </s>
            <s xml:id="echoid-s6012" xml:space="preserve">ſexquialteræ,
              <lb/>
            M H: </s>
            <s xml:id="echoid-s6013" xml:space="preserve">Omnia ergo quadrata portionis, RFV, regula, FM, ad om-
              <lb/>
            nia quadrata eiuſdem portionis, regula, RV, erunt vt rectangulum
              <lb/>
            ſub, M ω, & </s>
            <s xml:id="echoid-s6014" xml:space="preserve">ſub, RM, ad rectangulum ſub, FM, & </s>
            <s xml:id="echoid-s6015" xml:space="preserve">ſub compoſi-
              <lb/>
            ta ex, FH, MN, .</s>
            <s xml:id="echoid-s6016" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6017" xml:space="preserve">ad rectangulum ſub, FM, & </s>
            <s xml:id="echoid-s6018" xml:space="preserve">ſub, MN, ſub,
              <lb/>
              <note position="right" xlink:label="note-0263-05" xlink:href="note-0263-05a" xml:space="preserve">Ex vlt. 2.
                <lb/>
              Elem.</note>
            F M, & </s>
            <s xml:id="echoid-s6019" xml:space="preserve">ſub, MH, & </s>
            <s xml:id="echoid-s6020" xml:space="preserve">ad quadratum, FM: </s>
            <s xml:id="echoid-s6021" xml:space="preserve">quia verò rectangulum,
              <lb/>
            F MH, æquatur quadrato, RM, erunt omnia illa quadrata, vt re-
              <lb/>
            ctangulum ſub, ω M, & </s>
            <s xml:id="echoid-s6022" xml:space="preserve">ſub, RM, ad quadratum, RM, quadra-
              <lb/>
            tum, MF, & </s>
            <s xml:id="echoid-s6023" xml:space="preserve">rectangulum ſub, FM, MN, vel vt iſtorum dupla. </s>
            <s xml:id="echoid-s6024" xml:space="preserve">ſ.
              <lb/>
            </s>
            <s xml:id="echoid-s6025" xml:space="preserve">vt rectangulum ſub, ω M, & </s>
            <s xml:id="echoid-s6026" xml:space="preserve">ſub, RV, ad quadratum, RM, qua-
              <lb/>
            dratum, MV, duo quadrata, FM, & </s>
            <s xml:id="echoid-s6027" xml:space="preserve">duo rectangula ſub, FM, M
              <lb/>
            N, .</s>
            <s xml:id="echoid-s6028" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6029" xml:space="preserve">vnum ſub, FM, MI, cui ſi iunxeris vnum de duobus quadra-
              <lb/>
              <note position="right" xlink:label="note-0263-06" xlink:href="note-0263-06a" xml:space="preserve">12. Elem.</note>
            tis ipſius, FM, componetur rectangulum, FMH, quod eſt æqua-
              <lb/>
            le quadrato, RM. </s>
            <s xml:id="echoid-s6030" xml:space="preserve">Sunt ergo omnia quadrata portionis, RFV, re-
              <lb/>
              <note position="right" xlink:label="note-0263-07" xlink:href="note-0263-07a" xml:space="preserve">Vlt. 2. El.</note>
            gula, FM, ad omnia quadrata eiuſdem portionis, regula, RV, vt
              <lb/>
            rectangulum ſub, ω M, & </s>
            <s xml:id="echoid-s6031" xml:space="preserve">ſub, RV, ad tria quadrata, R, M cum
              <lb/>
            vno quadrato, FM, quod oſtendere oportebat.</s>
            <s xml:id="echoid-s6032" xml:space="preserve"/>
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