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

Table of handwritten notes

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            <s xml:id="echoid-s4958" xml:space="preserve">
              <pb o="202" file="0222" n="222" rhead="GEOMETRIÆ"/>
            lum ſub, DR, & </s>
            <s xml:id="echoid-s4959" xml:space="preserve">ſub compoſita ex, {1/2}, RM, & </s>
            <s xml:id="echoid-s4960" xml:space="preserve">ex, MA, vna cum
              <lb/>
            rectangulo ſub, RM, & </s>
            <s xml:id="echoid-s4961" xml:space="preserve">ſub compoſita ex, {1/6}, RM, &</s>
            <s xml:id="echoid-s4962" xml:space="preserve">, {1/2}, MA. </s>
            <s xml:id="echoid-s4963" xml:space="preserve">Su-
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            matur in, MR, vtcunque punctum, T, per quod agatur ipſi, CF,
              <lb/>
            parallela, TX, fecans curuam, SF, in, V, erit ergo quadratum, R
              <lb/>
            F, vel quadratum, TV, ad quadratum, TX, vt rectangulum, D
              <lb/>
            RA, ad rectangulum, DTA; </s>
            <s xml:id="echoid-s4964" xml:space="preserve">& </s>
            <s xml:id="echoid-s4965" xml:space="preserve">quoniam, MF, eſt parallelogram-
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            mum in eadem baſi, RF, & </s>
            <s xml:id="echoid-s4966" xml:space="preserve">altitudine cum ſemiportione, MRFX
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              <figure xlink:label="fig-0222-01" xlink:href="fig-0222-01a" number="135">
                <image file="0222-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0222-01"/>
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            S, &</s>
            <s xml:id="echoid-s4967" xml:space="preserve">, TX, ducta fuit vtcunque parallela
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            ipſi, RF, repertumque eſt quadratum, T
              <lb/>
            V, ad quadratum, TX, eſſe vt rectangu-
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            lum, DRA, ad rectangulum, DTA, con-
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              <note position="left" xlink:label="note-0222-01" xlink:href="note-0222-01a" xml:space="preserve">Coroll. 3.
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              26. Lib.2.</note>
            ſtructis quatuor magnitudinum ordinibus,
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            vt in antecedente, cocludemus omnia qua-
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            drata parallelogrammi, MF, ad omnia
              <lb/>
            quadrata ſemiportionis, MRFS, eſſe vt
              <lb/>
            rectangula, DRA, tot, quotſunt omnes
              <lb/>
            abſciſſæ ipſius, MR, ad rectangula ſub re-
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            ſiduis omnium abſciſſarum, MR, ad@un-
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            cta, RD, & </s>
            <s xml:id="echoid-s4968" xml:space="preserve">ſub omnibus abſciſſis, MR, adiuncta, MA; </s>
            <s xml:id="echoid-s4969" xml:space="preserve">quia ve-
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              <note position="left" xlink:label="note-0222-02" xlink:href="note-0222-02a" xml:space="preserve">Cor. 32.
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              lib. 2.</note>
            rò, DA, diuiſa eſt vtcumque in duobus punctis, R, M, rectangula
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            ſub, DRA, tot, quot ſunt omnes abſciſſę, RM, ad rectangula ſub
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            refiduis omnium abſciſſarum, MR, adiuncta, RD, & </s>
            <s xml:id="echoid-s4970" xml:space="preserve">ſub omnibus
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              <note position="left" xlink:label="note-0222-03" xlink:href="note-0222-03a" xml:space="preserve">@ Lib. 2.</note>
            abſciſſis, MR, adiuncta, MA, ſunt vt rectangulum, DRA, ad re-
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            ctangulum ſub, DR, & </s>
            <s xml:id="echoid-s4971" xml:space="preserve">ſub compoſita ex, {1/2}, RM, &</s>
            <s xml:id="echoid-s4972" xml:space="preserve">, MA, vna
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            cum rectangulo ſub, RM, & </s>
            <s xml:id="echoid-s4973" xml:space="preserve">ſub compoſita ex, {1/6}, RM, &</s>
            <s xml:id="echoid-s4974" xml:space="preserve">, {1/2}, M
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            A, ergo omnia quadrata parallelogramini, MF, ad omnia quadrata
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            ſemiportionis, MRFS, vel omnia quadrata parallelogrammi, BF,
              <lb/>
            ad omnia quadrata portionis, ICFS, erunt vt rectangulum, DR
              <lb/>
            A, ad rectangulum ſub, DR, & </s>
            <s xml:id="echoid-s4975" xml:space="preserve">ſub compoſita ex, {1/2}, MR, & </s>
            <s xml:id="echoid-s4976" xml:space="preserve">ex,
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            MA, vna cum rectangulo ſub, RM, & </s>
            <s xml:id="echoid-s4977" xml:space="preserve">ſub compoſita ex, {1/6}, RM,
              <lb/>
            &</s>
            <s xml:id="echoid-s4978" xml:space="preserve">, {1/2}, MA.</s>
            <s xml:id="echoid-s4979" xml:space="preserve"/>
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            <s xml:id="echoid-s4980" xml:space="preserve">Iungantur nunc, CM, MF. </s>
            <s xml:id="echoid-s4981" xml:space="preserve">Dico inſuperomnia quadrata por-
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            tionis, ICFS, ad omnia quadrata trianguli, MCF, eſſe vt rectan-
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            gulum ſub compoſita ex, MD, DR, & </s>
            <s xml:id="echoid-s4982" xml:space="preserve">ſub ſexquialtera, MA, vna
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            cum rectangulo ſub compoſita ex, MD, & </s>
            <s xml:id="echoid-s4983" xml:space="preserve">dupla, DR, & </s>
            <s xml:id="echoid-s4984" xml:space="preserve">ſub, {1/2},
              <lb/>
            MR, ad rectangulum, DRA; </s>
            <s xml:id="echoid-s4985" xml:space="preserve">omnia .</s>
            <s xml:id="echoid-s4986" xml:space="preserve">n. </s>
            <s xml:id="echoid-s4987" xml:space="preserve">quadrata parallelogram-
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            mi, BF, ad omnia quadrata portionis, ICFS, oſtenſa ſunt eſſe vt
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            rectangulum, DRA, ad rectangulum ſub, DR, & </s>
            <s xml:id="echoid-s4988" xml:space="preserve">ſub compoſita
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            ex, {1/2}, RM, & </s>
            <s xml:id="echoid-s4989" xml:space="preserve">ex, MA, vna cum rectangulo ſub, RM, & </s>
            <s xml:id="echoid-s4990" xml:space="preserve">ſub com-
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            poſita ex, {1/6}, RM, &</s>
            <s xml:id="echoid-s4991" xml:space="preserve">, {1/2}, MA, ergo eorum tertia pars ad eadem con-
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            ſequentia erunt vt tertia pars rectanguli, DRA, ad eadem conſe-
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            quentia rectangula .</s>
            <s xml:id="echoid-s4992" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4993" xml:space="preserve">vt integrum rectangulum, DRA, ad illa </s>
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