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

Table of handwritten notes

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            lam, ADC, in puncto, D, quæ indefinitè quoq; </s>
            <s xml:id="echoid-s9792" xml:space="preserve">producta
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            occurrat ipſi, XP, in puncto, P, ſuppoſitoque, BD, eſſe
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            axim, oſtendemus omnia quadrata hyperbolæ, ADC, ad
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            rectangula omnia hyperbolæ, OVX, ſimilia rectangulo
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            ſub, XO, OP, habere rationem compoſit am ex ratione re-
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            ctanguli ſub, MB, HI, ad rectangulum ſub, RI, FB, & </s>
            <s xml:id="echoid-s9793" xml:space="preserve">ex
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            tatione parallelepipedi ſub altitudine hyperbolæ, ADC,
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            & </s>
            <s xml:id="echoid-s9794" xml:space="preserve">baſi quadrato, AC, ad parallelepipedum ſub altitudine
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            hyperbolæ, OVX, baſi aute m rectangulo ſub, XO, OP.</s>
            <s xml:id="echoid-s9795" xml:space="preserve"/>
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            <s xml:id="echoid-s9796" xml:space="preserve">Nam omnia quadrata hyperbolæ, ADC, regula eadẽ, AC, ad oĩa
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            quadrata hyperbolę, OVX, regula, OX, oſtenſa ſunt habere ratio-
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            nẽ cõpoſitam ex ratione rectang. </s>
            <s xml:id="echoid-s9797" xml:space="preserve">ſub, MB, HI, ad rectang. </s>
            <s xml:id="echoid-s9798" xml:space="preserve">ſub, RI,
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            FB, & </s>
            <s xml:id="echoid-s9799" xml:space="preserve">parallelepipedi ſub altitudine hyperbolę, ADC, baſi quadr.
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            </s>
            <s xml:id="echoid-s9800" xml:space="preserve">
              <note position="left" xlink:label="note-0400-01" xlink:href="note-0400-01a" xml:space="preserve">Iu antec.</note>
            AC, ad parallelepipedũ ſub altitudine hyperbolę, OVX, baſi autẽ
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              <figure xlink:label="fig-0400-01" xlink:href="fig-0400-01a" number="273">
                <image file="0400-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0400-01"/>
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            quadrato, OX; </s>
            <s xml:id="echoid-s9801" xml:space="preserve">inſuper omnia quadra-
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            ta hyperbolę, OVX, ad rectangula
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            omnia eiuſdem hyperbolę ſimilia re-
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            ctangulo, XOP, regula, XO, ſunt vt
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            vnum ad vnum, ſcilicet vt quadratũ,
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            XO, ad rectangulum, XOP, .</s>
            <s xml:id="echoid-s9802" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9803" xml:space="preserve">ſumpta
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            communi altitudine eiuſdem hyperbo-
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            læ, OVX, altitudine, vt parallelepi-
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            pedum ſub altitudine hyperbolæ, O
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            VX, baſi quadrato, OX, ad parallele-
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            pipedum ſub eadem altitudine, baſi
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            autem rectangulo, XOP, ergo omnia
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            quadrata hyperbolę, ADC, regula,
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            AC, ad omnia rectangula hyperbolę,
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            OVX, ſimilia rectangulo, XOP, regu-
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            la, OX, erunt in ratione compoſita ex ratione rectanguli ſub, MB,
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            HI, ad rectangulum ſub, RI, FB, & </s>
            <s xml:id="echoid-s9804" xml:space="preserve">parallelepipedi ſub altitudine
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            hyperbolę, ADC, & </s>
            <s xml:id="echoid-s9805" xml:space="preserve">ſub quadrato, AC, ad parallelepipedum ſub
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            altitudine hyperbolę, OVX, baſi quadrato, OX, & </s>
            <s xml:id="echoid-s9806" xml:space="preserve">ex ratione hui-
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            us parallelepipedi ad parallelepipedum ſub eiuſdem hyperbolę, O
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            VX, altitudine baſi rectangulo, XOP, quę duę vltimò dictę racio-
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            nes componunt rationem parallelepipedi ſub altitudine hyperbo-
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            lę, ADC, baſi quadrato, AC, ad parallelepipedum ſub altitudine
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            hyperbolę, OVX, baſi rectangulo, XOP, ergo omnia quadrata
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            hyperbolę, ADC, regula, AC, ad omnia rectangula </s>
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