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

Table of handwritten notes

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            ſunt vt quadratum, VR, ad quadratum, CR, .</s>
            <s xml:id="echoid-s5031" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5032" xml:space="preserve">vt rectangulum,
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              <note position="left" xlink:label="note-0224-01" xlink:href="note-0224-01a" xml:space="preserve">Ex 40. l. 1.
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              & eiuidẽ
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              Scholio.</note>
            AOD, vel quadratum, AO, ad rectangulum, DRA, omnia au-
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            tem quadrata parallelogrammi, BR, ad omnia quadrata ſemipor-
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              <figure xlink:label="fig-0224-01" xlink:href="fig-0224-01a" number="137">
                <image file="0224-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0224-01"/>
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            tionis, ICRM, ſunt vt rectangulum, D
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            RA, ad rectangulum ſub, DR, & </s>
            <s xml:id="echoid-s5033" xml:space="preserve">ſub
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            compoſita ex, {1/2}, RM, & </s>
            <s xml:id="echoid-s5034" xml:space="preserve">ex, MA, vna
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            cum rectangulo ſub, RM, & </s>
            <s xml:id="echoid-s5035" xml:space="preserve">ſub com-
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            poſita ex, {1/6}, RM, &</s>
            <s xml:id="echoid-s5036" xml:space="preserve">, {1/2}, MA, ergo ex
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              <note position="left" xlink:label="note-0224-02" xlink:href="note-0224-02a" xml:space="preserve">Ex anter.</note>
            æquali omnia quadrata parallelogram-
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            mi, GR, ad omnia quadrata ſemiportio-
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            nis, ICRM, vel omnia quadrata paral-
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            lelogrammi, GX, ad omnia quadrata
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            portionis, ICFS, erunt vt quadratum,
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            AO, ad rectangulum ſub, DR, & </s>
            <s xml:id="echoid-s5037" xml:space="preserve">ſub compoſita ex, {1/2}, RM, & </s>
            <s xml:id="echoid-s5038" xml:space="preserve">
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            ex, MA, vna cum rectangulo ſub, RM, & </s>
            <s xml:id="echoid-s5039" xml:space="preserve">ſub compoſita ex, {1/6}, R
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              <note position="left" xlink:label="note-0224-03" xlink:href="note-0224-03a" xml:space="preserve">Ex 9. & B.
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              Cor. 22.
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              lib. 2.</note>
            M, &</s>
            <s xml:id="echoid-s5040" xml:space="preserve">, {1/2}, MA; </s>
            <s xml:id="echoid-s5041" xml:space="preserve">quod etiam pater, ſi parallelogrammum, GX, non
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            ſit circa axim, vel diametrum, MR, quod erat oſtendendum.</s>
            <s xml:id="echoid-s5042" xml:space="preserve"/>
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          <head xml:id="echoid-head322" xml:space="preserve">THEOREMA V. PROPOS. V.</head>
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            <s xml:id="echoid-s5043" xml:space="preserve">SI in circulo, vel ellipſi ducantur coniugati axes, vel dia-
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            metri, in altera autem eorundem ſit tamquam in baſi pa-
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            rallelogrammum circa eundem axim, vel diametrum cum cir-
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            culo, vel ellipſi, circa quæm ſit etiam triangulus, ſed in baſi
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            oppoſita baſi parallelogrammi, ſumatur autem in dicta axi,
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            vel diametro vtcunq; </s>
            <s xml:id="echoid-s5044" xml:space="preserve">punctum, per quod baſibus dictis aga-
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            tur parallela; </s>
            <s xml:id="echoid-s5045" xml:space="preserve">quadratum eiuſdem parallelæ trianguli lateri-
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            bus interceptæ æquabitur reliquo quadrati eius, quæ inter-
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            cipitur lateribus parallelogrammi, dempto quadrato eius,
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            quæ intra circulum, vel ellipſim concludetur.</s>
            <s xml:id="echoid-s5046" xml:space="preserve"/>
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            <s xml:id="echoid-s5047" xml:space="preserve">Sit circulus, vel ellipſis, BDHF, eius coniugati axes, vel diame-
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            tri, BH, DF, in altera autem earum, vtin, DF, tanquam in baſi,
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            & </s>
            <s xml:id="echoid-s5048" xml:space="preserve">circa axim, vel diametrum, BE, ſit parallelogrammum, AF, cir-
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            ca eundem verſo4;</s>
            <s xml:id="echoid-s5049" xml:space="preserve">, ſed in baſi, AC, ſit triangulum, AEC, ſumatur
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            autem in, BE, vtcunque punctum, M, per quodipſi, DF, agatur
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            parallela, VR, ſecans curuam, DBF, in, T, I, & </s>
            <s xml:id="echoid-s5050" xml:space="preserve">latera trianguli,
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            AEC, in, S, N. </s>
            <s xml:id="echoid-s5051" xml:space="preserve">Dico ergo quadratum, SN, æquari reliquo qua-
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            drati, VR, dempto quadrato, TI. </s>
            <s xml:id="echoid-s5052" xml:space="preserve">Nam rectangulum, HEB, ad
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            rectangulum, HMB, eſt vt quadratum, FE, vel quadratum, </s>
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