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

Table of handwritten notes

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          <head xml:id="echoid-head214" xml:space="preserve">A. DEMONSTRATIONIS SECTIO I.</head>
          <p>
            <s xml:id="echoid-s2988" xml:space="preserve">SInt duæ quæcunque figuræ planæ ſimiles, ABD, ΦΣΛ. </s>
            <s xml:id="echoid-s2989" xml:space="preserve">Dico
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            eaſdem eſſe in dupla ratione linearum, vel laterum homologo-
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              <note position="left" xlink:label="note-0148-01" xlink:href="note-0148-01a" xml:space="preserve">Coroll. 1.
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              lib. 1.</note>
            rum, earundem. </s>
            <s xml:id="echoid-s2990" xml:space="preserve">Ducantur ipſarum oppoſitę tangentes, AK, FM,
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            figuræ, ABD, &</s>
            <s xml:id="echoid-s2991" xml:space="preserve">, Φ Π, Δ Ω, ſiguræ, Φ Σ Λ, quæ homologis ea-
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            rum lineis æquidiſtent, deinde ſint intradictas oppoſitas tangentes
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            ductæ, KM, Π Ω, taliter, vt illæ ſint incidentes dictarum ſimilium
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              <note position="left" xlink:label="note-0148-02" xlink:href="note-0148-02a" xml:space="preserve">Coroll. 2.
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              9. lib. 1.</note>
            figurarum, & </s>
            <s xml:id="echoid-s2992" xml:space="preserve">tangentium, hoc facto, diuidantur ipſæ incident@s, K
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              <figure xlink:label="fig-0148-01" xlink:href="fig-0148-01a" number="87">
                <image file="0148-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0148-01"/>
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            M, Π Ω, ſimil@ter, & </s>
            <s xml:id="echoid-s2993" xml:space="preserve">ad eandem
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            partem vtcunq; </s>
            <s xml:id="echoid-s2994" xml:space="preserve">in punctis, L, Γ,
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            per quæ puncta ſint ductæ ipſæ, B
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            L, Σ Γ, quarum portiones figuris
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            interceptę ſint, BE, ID, in figu-
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            ra, ABD, &</s>
            <s xml:id="echoid-s2995" xml:space="preserve">, Σ 2, 3 Λ, in figu-
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            ra, Φ Σ Λ, ſumatur autem ex, BL,
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            recta æqualis vtriſque ſimul, BE,
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            ID, ter ninans in, KM, quæ ſit,
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            QL, & </s>
            <s xml:id="echoid-s2996" xml:space="preserve">pariter ipſius, Σ 2, 3 Λ, ſit
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            ſumpta æqualis, Τ Γ, term nans
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            in, Π Ω, & </s>
            <s xml:id="echoid-s2997" xml:space="preserve">in puncto, Γ, ſicq; </s>
            <s xml:id="echoid-s2998" xml:space="preserve">fiat
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            de cæteris, quæ ipſis tangentibus
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            æquidiſtant, & </s>
            <s xml:id="echoid-s2999" xml:space="preserve">manent intra figu-
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            rarum ambitum, quibusn m è in
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            eadem rectitudine ſun antur rectæ
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            æquales in ipſis, KM, ΠΩ, termi-
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            natæ, erunt igitur omnium in@en-
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            tarum linearum reliqui termini in
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            alia quadam inea, quæ inc pi@t in
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            puncto, K, & </s>
            <s xml:id="echoid-s3000" xml:space="preserve">deſinet in, M, pro
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            figura, ABD, & </s>
            <s xml:id="echoid-s3001" xml:space="preserve">quæ incip e in Π, & </s>
            <s xml:id="echoid-s3002" xml:space="preserve">deſinet in, Ω, pro figura,
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            Φ Σ Λ, ſint iſtę lineę, KQM, Π Ω; </s>
            <s xml:id="echoid-s3003" xml:space="preserve">patet igitur figuram, KQM,
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              <note position="left" xlink:label="note-0148-03" xlink:href="note-0148-03a" xml:space="preserve">3. huius.</note>
            eſſe æqualem ipſi, ABD, & </s>
            <s xml:id="echoid-s3004" xml:space="preserve">Π Ω, ipſi, Φ Σ Λ, nam omnes earum
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            lineæ ſumptæ regulis, FM, Δ Ω, ſunt æquales, quod ex ip a con-
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            ſtructione patet; </s>
            <s xml:id="echoid-s3005" xml:space="preserve">dicantur autem iſtæ conſtruct ones, translationes
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            omn um linearum ſ gurarum, ABD, ΦΣΛ, in figuras, KQA, Π
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            Τ Ω, ipſi, KM, ΠΩ adiacentes, effectę regulis dictis tangent bus.
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            </s>
            <s xml:id="echoid-s3006" xml:space="preserve">Patet vlterius figuras, KQM, ΠΤΩ, eſſe ſim les, nam homologę
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            figurarum, ABD, ΦΣΛ, (quia illę ſunt ſimiles) ſunt vt incidentes,
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              <note position="left" xlink:label="note-0148-04" xlink:href="note-0148-04a" xml:space="preserve">Coroll. 1.
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              22. lib. 1.</note>
            KM, ΠΩ, eæden autem in figuras, KQM,ΠΤΩ, modo dicto,
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            translatæ ſunt (ſimui in vnam rectam coniunctis, quæ diuiſæ </s>
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