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

Table of handwritten notes

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            <s xml:id="echoid-s5088" xml:space="preserve">
              <pb o="207" file="0227" n="227" rhead="LIBER III."/>
            quadrata trianguli, BAD, ad omnia quadrata portionis, BAD,
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              <note position="right" xlink:label="note-0227-01" xlink:href="note-0227-01a" xml:space="preserve">1. Huius.</note>
            ſunt vt, EC, ad compoſitam ex, EC, CO; </s>
            <s xml:id="echoid-s5089" xml:space="preserve">harum autem trium ra-
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            tionum componentium rationem ſupradictam illa, quam habet, C
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              <note position="right" xlink:label="note-0227-02" xlink:href="note-0227-02a" xml:space="preserve">6. Lib. 2.</note>
            E, ad, EA, &</s>
            <s xml:id="echoid-s5090" xml:space="preserve">, CE, ad, ECO, componit rationem quadrati, C
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            E, ad rectangulum ſub, AE, & </s>
            <s xml:id="echoid-s5091" xml:space="preserve">fub, ECO, habemus ergo illas tres
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            rationes in has duas reſolutas .</s>
            <s xml:id="echoid-s5092" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5093" xml:space="preserve">in eam, quam habet quadratum, E
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            C, ad rectangulum ſub, AE, &</s>
            <s xml:id="echoid-s5094" xml:space="preserve">, ECO, & </s>
            <s xml:id="echoid-s5095" xml:space="preserve">in eam, quam habet com-
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            poſita ex, OA, AE, ad, AE; </s>
            <s xml:id="echoid-s5096" xml:space="preserve">ratio autem quadrati, EC, ad rectan-
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            gulum ſub, AE, &</s>
            <s xml:id="echoid-s5097" xml:space="preserve">, ECO, & </s>
            <s xml:id="echoid-s5098" xml:space="preserve">ratio ipſius, OAE, ſumptę pro al-
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            titudine ad, AE, pariter pro altitudine ſumptam, componunt ratio-
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            nem parallelepipedi ſub baſi quadrato, CE, altitudine autem, EA
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              <note position="right" xlink:label="note-0227-03" xlink:href="note-0227-03a" xml:space="preserve">Per D. Co
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              rollar. 4.
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              Gen. 34.
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              lib. 2.</note>
            O, ad parallepipedum ſub baſi quadrato, AE, altitudine autem, E
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            CO, quod ſerua.</s>
            <s xml:id="echoid-s5099" xml:space="preserve"/>
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            <s xml:id="echoid-s5100" xml:space="preserve">Duplicentur nunchorum parallelepipedorum altitudines, omnia
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            ergo quadrata portionis, BCD, ad omnia quadrata portionis, BA
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            D, erunt vt parallelepipedum ſub quadrato, EC, altitudine verò
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            dupla, EA, & </s>
            <s xml:id="echoid-s5101" xml:space="preserve">dupla, AO, quæ eſt, AC, ad parallelepipedum ſub
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            baſi quadrato, AE, altitudine dupla, EC, & </s>
            <s xml:id="echoid-s5102" xml:space="preserve">dupla, CO, quę eſt,
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            AC; </s>
            <s xml:id="echoid-s5103" xml:space="preserve">parallelepipedum autem ſub quadrato, CE, & </s>
            <s xml:id="echoid-s5104" xml:space="preserve">ſub compoſita
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              <note position="right" xlink:label="note-0227-04" xlink:href="note-0227-04a" xml:space="preserve">35. Lib. 2.</note>
            ex dupla, AE, &</s>
            <s xml:id="echoid-s5105" xml:space="preserve">, AC, æquatur parallelepipedis ſub quadrato, C
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            E, & </s>
            <s xml:id="echoid-s5106" xml:space="preserve">ſub, AE, bis, vna cum parallelepipedo ſub, AC, & </s>
            <s xml:id="echoid-s5107" xml:space="preserve">ſub qua-
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            drato, CE, ideſt vna cum parallelepipedo ſub, AE, adhuc ſemel,
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              <note position="right" xlink:label="note-0227-05" xlink:href="note-0227-05a" xml:space="preserve">36. Lib. 2.</note>
            & </s>
            <s xml:id="echoid-s5108" xml:space="preserve">ſub quadrato, EC, cum cubo, EC, quę ſimul cum prædictis con-
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            ficiunt parallelepipedum ter ſub, AE, & </s>
            <s xml:id="echoid-s5109" xml:space="preserve">ſub quadrato, EC, cum
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            cubo ipſius, EC. </s>
            <s xml:id="echoid-s5110" xml:space="preserve">Similiter oſtendemus parallelepipedum ſub qua-
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            drato, AE, & </s>
            <s xml:id="echoid-s5111" xml:space="preserve">ſub compoſita ex, CA, & </s>
            <s xml:id="echoid-s5112" xml:space="preserve">dupla, CE, æquari paral-
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            lelepipedis ter ſub, CE, & </s>
            <s xml:id="echoid-s5113" xml:space="preserve">ſub quadrato, EA, cumcubo, EA, er-
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            go omnia quadrata portionis, BCD, ad omnia quadrata portionis,
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            BAD, erunt vt parallelepipedum ter ſub quadra@o, CE, altitudi-
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            ne, EA, cum cubo, CE, ad parallelepipedum ter ſub quadrato, A
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            E, altitudine, EC, cum cubo, AE, ergo, componendo, omnia qua-
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            drata circuli, vel ellipſis, ABCD, ad omnia quadrata portionis, B
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            AD, erunt vt parallelepipedum ter ſub altitudine, AE, & </s>
            <s xml:id="echoid-s5114" xml:space="preserve">quadra-
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            to, EC, cum cubo, EC, ſimul cum parallelepipedo ter ſub altitu-
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            dine, CE, & </s>
            <s xml:id="echoid-s5115" xml:space="preserve">ſub quadrato, EA, cum cubo, EA, ad parallelepipe-
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            dum ter ſub quadrato, AE, altitudine, EC, cum cubo, AE, illa
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              <note position="right" xlink:label="note-0227-06" xlink:href="note-0227-06a" xml:space="preserve">38. Lib. 2.</note>
            autem ſimul ſumpta conficiunt cubum, AC, ergo omnia quadrata
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            circuli, vel ellipſis, ABCD, ad omnia quadrata portionis, BAD,
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            erunt vt cubus, AC, ad parallelepipedum ſub baſi quadrato, AE,
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            altitudine linea compoſita ex dupla, EC, & </s>
            <s xml:id="echoid-s5116" xml:space="preserve">ex, AC, ergo (dimi-
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            diatis huius rationis terminis) omnia quadrata circuli, vel ellipſis, A
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            BCD, ad omnia quadrata portionis, BAD, erunt vt </s>
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