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

Table of handwritten notes

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              <pb o="379" file="0399" n="399" rhead="LIBER V."/>
            & </s>
            <s xml:id="echoid-s9771" xml:space="preserve">baſi quadrato, AC, ad parallelepipedum ſub altitudine hyper
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            bolæ, OVX, baſi autem quadrato, OX. </s>
            <s xml:id="echoid-s9772" xml:space="preserve">Nam omnia quadrata
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            hyperbolæ, ADC, regula, AC, ad omnia quadrata hyperbolæ,
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            OVX, regula, OX, (iunctis, AD, DC, OV, VX,) ſumptis medijs
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              <note position="right" xlink:label="note-0399-01" xlink:href="note-0399-01a" xml:space="preserve">Defin. 12.
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              1. 1.</note>
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                <image file="0399-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0399-01"/>
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            omnibus quadratis triangulorum, AD
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            C, OVX, habent rationem compoſitã
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            ex ratione omnium quadratorum hy-
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            perbolæ, ADC, ad omnia quadrata
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              <note position="right" xlink:label="note-0399-02" xlink:href="note-0399-02a" xml:space="preserve">1. huius.</note>
            trianguli, ADC, .</s>
            <s xml:id="echoid-s9773" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9774" xml:space="preserve">ex ratione, MB, ad,
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            BF, & </s>
            <s xml:id="echoid-s9775" xml:space="preserve">ex ratione omnium quadratorũ
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            trianguli, ADC, ad omnia quadrata
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              <note position="right" xlink:label="note-0399-03" xlink:href="note-0399-03a" xml:space="preserve">C. Col. 22.
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              1. 2.</note>
            trianguli, OVX, quæ eſt compoſita ex
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            ratione altitudinis trianguli, ADC, vel
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            hyperbolæ, ADC, ad altitudinem triã-
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            guli, OVX, vel hyperbolæ, OVX, & </s>
            <s xml:id="echoid-s9776" xml:space="preserve">ex
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            ratione quadrati, AC, ad quadratum,
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            OX, & </s>
            <s xml:id="echoid-s9777" xml:space="preserve">tandem eſt compoſita ex ratio-
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              <note position="right" xlink:label="note-0399-04" xlink:href="note-0399-04a" xml:space="preserve">1. huius.</note>
            ne omnium quadratorum trianguli, O
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            VX, ad omnia quadrata hyperbolæ, O
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            VX, .</s>
            <s xml:id="echoid-s9778" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9779" xml:space="preserve">ex ea, quam habet, HI, ad, IR, harum autem rationum
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              <note position="right" xlink:label="note-0399-05" xlink:href="note-0399-05a" xml:space="preserve">6, 1. 2.</note>
            componentium iſtæ duæ .</s>
            <s xml:id="echoid-s9780" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9781" xml:space="preserve">quam habet, MB, ad, BF, &</s>
            <s xml:id="echoid-s9782" xml:space="preserve">, HI, ad,
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            IR, componunt rationem rectanguli ſub, MB, HI, ad rectangulũ
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            ſub, RI, FB; </s>
            <s xml:id="echoid-s9783" xml:space="preserve">aliæ autem duæ rationes componentes .</s>
            <s xml:id="echoid-s9784" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9785" xml:space="preserve">quam ha-
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            bet altitudo hyperbolæ, ADC, ad altitudinem hyperbolæ, OVX,
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            & </s>
            <s xml:id="echoid-s9786" xml:space="preserve">quam habet quadratum, AC, ad quadratum, OX, componunt
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            rationem parallelepipedi ſub altitudine hyperbolæ, ADC, baſi
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            quadrato, AC, ad parallelepipedum ſub altitudine hyperbolæ, O
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            VX, baſi quadrato, OX, ergo omnia quadrata hyperbolæ, ADC,
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            regula, AC, ad omnia quadrata hyperbolæ, OVX, regula, OX,
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            habent rationem compoſitam ex ratione rectanguli ſub, MB, HI,
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            ad rectangulum ſub, RI, FB, & </s>
            <s xml:id="echoid-s9787" xml:space="preserve">ex ratione parallelepipedi ſub al-
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            titudine hyperbolę, ADC, baſi quadrato, AC, ad parallelepipe-
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            dum ſub altitudine hyperbolæ, OVX, baſi verò quadrato, OX,
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            quod oſtendere opus erat.</s>
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          <head xml:id="echoid-head568" xml:space="preserve">THEOREMA X. PROPOS. XI.</head>
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            <s xml:id="echoid-s9789" xml:space="preserve">IN eadem antec. </s>
            <s xml:id="echoid-s9790" xml:space="preserve">figura, iuncta, DV, & </s>
            <s xml:id="echoid-s9791" xml:space="preserve">à puncto, X, ducta,
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            XP, parallela ipſi, DV, indefinitè producta, à puncto
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            autem, O, ipſa, OP, parallela ei, quæ tangeret </s>
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