Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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            poſitas, ex quibus ſumantur quotcunque partes æquales, AI, IH,
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            nempè æquales ipſi, CA, &</s>
            <s xml:id="echoid-s2867" xml:space="preserve">, BP, æqualis ipſi, BC, & </s>
            <s xml:id="echoid-s2868" xml:space="preserve">complean-
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            tur parallelogramma, AM, IK, BQ; </s>
            <s xml:id="echoid-s2869" xml:space="preserve">ſunt igitur parallelogramma,
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            CF, AM, IK, in æqualibus altitudinibus, ac baſibus, & </s>
            <s xml:id="echoid-s2870" xml:space="preserve">ideò ſin-
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            gulorum omnia quadrata regulis eiſdem baſibus, erunt æqualia, & </s>
            <s xml:id="echoid-s2871" xml:space="preserve">
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              <note position="left" xlink:label="note-0142-01" xlink:href="note-0142-01a" xml:space="preserve">9. Huius</note>
            pari ratione omnia quadrata parallelogrammorum, BQ, CQ, e-
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            runt ęqualia, regula, CD, altitudines autem parallelogrammorum,
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            CF, AM, IK, ſunt æquales ipſi, AO, & </s>
            <s xml:id="echoid-s2872" xml:space="preserve">altitudines parallelogram-
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            morum, CE, BQ, ſunt æquales, nempè ipſi, CN, habemus ergo
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            æquèmultiplices primę, & </s>
            <s xml:id="echoid-s2873" xml:space="preserve">tertiæ .</s>
            <s xml:id="echoid-s2874" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2875" xml:space="preserve">compoſitum ex altitudinibus pa-
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            rallelogrammorum, CF, AM, IK, quod tam multiplex eſt altitu-
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              <figure xlink:label="fig-0142-01" xlink:href="fig-0142-01a" number="82">
                <image file="0142-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0142-01"/>
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            dinis, AO, quam compoſitum ex omnibus qua-
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            dratis, CF, AM, IK, multiplex eſt omnium
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            quadratorum parallelogrammi, CF, & </s>
            <s xml:id="echoid-s2876" xml:space="preserve">ſic com-
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            poſitum ex altitudinibus parallelogrammorum,
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            CE, BQ, tam multiplex eſt altitudinis, CN,
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            ac compoſitum ex omnibus quadratis parallelo.
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            </s>
            <s xml:id="echoid-s2877" xml:space="preserve">grammorum, BQ, CE, multiplex eſt omnium
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            quadratorum, CE; </s>
            <s xml:id="echoid-s2878" xml:space="preserve">ideſt quam multiplicia ſunt
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            omnia quadrata parallelogrammi, HD, omnium quadratorum pa-
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            rallelogrammi, AD, tam altitudo parallelogrammi, HD, multi-
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            plex eſt altitudinis parallelogrammi, AD, ſiue tam ipſa, CH, mul-
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            tiplex eſt ipfius, CA, dum ſunt æquiangula, & </s>
            <s xml:id="echoid-s2879" xml:space="preserve">quam omnia qua-
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            drata parallelogrammi, PD, multiplicia ſunt omnium quadratorum
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            parallelogrammi, BD, tam altitudo parallelogrammi, PD, mul-
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            tiplex eſt altitudinis, CN, vel tam, PC, multiplex eſt ipſius, CB: </s>
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            Si autem multiplex primæ fuerit æquale multiplici ſecundæ, etiam
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            multiplex tertiæ erit æquale multiplici quartæ, ſi maius maius, & </s>
            <s xml:id="echoid-s2881" xml:space="preserve">ſi
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            minus minus, nam ſi altitudo parallelogrammi, HD, fuerit æqua-
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            lis altitudini parallelogrammi, DP, omnia quadrata, HD, erunt
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            æqualia omnibus quadratis, DP, nam parallelogramma, HD, D
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            P, ſunt in eadem baſi, CD, ſi illa maior, & </s>
            <s xml:id="echoid-s2882" xml:space="preserve">hæc maiora, & </s>
            <s xml:id="echoid-s2883" xml:space="preserve">ſi mi-
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              <note position="left" xlink:label="note-0142-02" xlink:href="note-0142-02a" xml:space="preserve">Exautec.</note>
            nor minora, ergo prima ad ſecundam erit, vt tertia ad quartam,
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              <note position="left" xlink:label="note-0142-03" xlink:href="note-0142-03a" xml:space="preserve">5. Quinti
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              Elem.</note>
            nempè vt altitudo parallelogrammi, AD, ad altitudinem paralle-
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            logrammi, DB, .</s>
            <s xml:id="echoid-s2884" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2885" xml:space="preserve">AO, ad, CN, vel, AC, ad, CB, dum ſunt
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            æquiangula, ita erunt omnia quadrata, AD, ad omnia quadrata,
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            DB, ſunt ergo, vt altitudines ipſorum parallelogrammorum, vel
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            vt latera ęqualiter baſi inclinata, cum nempè parallelogramma ſunt
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            æquiangula: </s>
            <s xml:id="echoid-s2886" xml:space="preserve">hæc autem etiam verificarentur ſi parallelogramma
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            eſſent in æqualibus baſibus, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s2887" xml:space="preserve"/>
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