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

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              <pb o="491" file="0511" n="511" rhead="LIBER VII."/>
            AP, in æqualia parallelogramma, A &</s>
            <s xml:id="echoid-s12556" xml:space="preserve">, &</s>
            <s xml:id="echoid-s12557" xml:space="preserve">Q: </s>
            <s xml:id="echoid-s12558" xml:space="preserve">rurſus autem per
              <lb/>
              <note position="right" xlink:label="note-0511-01" xlink:href="note-0511-01a" xml:space="preserve">Elicit. ex
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              ant. Lem.</note>
            alias ipſi, QY, parallelas diuidantur dictæ altitudinis portiones bi-
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            fariam, & </s>
            <s xml:id="echoid-s12559" xml:space="preserve">ſic ſemper ſiat (ſectis inſimul conſtitutis parallelogram-
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            mi@, quæ idcircò etiam bifariam diuidentur) donec ad parallelo-
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            grammum, vt ad, ℟Q, deueniatur minus ſpatio, +, ſit igitur ſe-
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              <note position="right" xlink:label="note-0511-02" xlink:href="note-0511-02a" xml:space="preserve">1. Deoim@
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              Elem.</note>
            ctum, AP, in parallelogramma, æquè alta, AZ, β&</s>
            <s xml:id="echoid-s12560" xml:space="preserve">, γ℟, Δ Ρ, per
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            ęquidiſtantes lineas, βκ, γV, ΔΧ, quæ ſecent lineas, AQ, in pun-
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            ctis, β, Γ, Δ, CQ, in, E, I, N, DP, in, Z, &</s>
            <s xml:id="echoid-s12561" xml:space="preserve">, ℟, FT, in, ΛΠΣ, HT,
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            in, O, R, S, & </s>
            <s xml:id="echoid-s12562" xml:space="preserve">tandem, LY, in, K, V, X, compleanturq; </s>
            <s xml:id="echoid-s12563" xml:space="preserve">paralle-
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            logramma, BZ, 2&</s>
            <s xml:id="echoid-s12564" xml:space="preserve">, 3℟, ΔΡ, iuxta deſcriptionem ſuperius tradi-
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            tam, erunt enim lineæ, BE.</s>
            <s xml:id="echoid-s12565" xml:space="preserve">, 2I, 3N, ΔQ, extra figuram, CQPD,
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            quod patebit, veluti, AQ, extra, CQPD, fimiliter cadere oſten-
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            ſa eſt, & </s>
            <s xml:id="echoid-s12566" xml:space="preserve">conſequeuter figura ex parallelogrammis, BZ, 2&</s>
            <s xml:id="echoid-s12567" xml:space="preserve">, 3℟, Δ
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            P, compoſita comprehendet ſpatium, CQPD, ſint autem etiam
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            completa parallelogramma, E&</s>
            <s xml:id="echoid-s12568" xml:space="preserve">, Ι℟, NP, quorum deſcriptæ li-
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            neæ, ΕΦ, ΙΩ, NM, intra figuram, CQPD, quidem cadere oſtende-
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            mus ex eadem ratione, quod dictæ parallelæ ipſi, PQ, propinquio-
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            res remotioribus ſint ſemper maiores, & </s>
            <s xml:id="echoid-s12569" xml:space="preserve">ſubinde patebit figuram
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            ex parallelogrammis, E&</s>
            <s xml:id="echoid-s12570" xml:space="preserve">, Ι℟, NP, compoſitam comprehendi à
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            figura, CQPD. </s>
            <s xml:id="echoid-s12571" xml:space="preserve">Tandem compleantur parallelogramma quoque,
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            Gκ, 6V, 9X, ΣΥ, ex quibus compoſitam figuram ſpatium, HTYL,
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            eadem methodo comprehendere demonſtrabimus. </s>
            <s xml:id="echoid-s12572" xml:space="preserve">Cum ergo fi-
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            gura comprehendens ſpatium, CQPD, ſuperet ab eo compreh en-
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            ſam parallelogrammis, BZ, 2Φ, 3Ω, ΔΜ, hoc eſt parallelogram-
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            mo, ΔΡ, quod eſt minus ſpatio, +, dicta comprehendens figura
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            ſuperabit, CQPD, muitò minori ſpatio, quam ſit, +, ſed, HTY
              <lb/>
            L, ſuperat, CQPD, ex hypoteſi ſpatio, +, ergo figura compre-
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            hendens, CQPD, minor eſt, HTYL, & </s>
            <s xml:id="echoid-s12573" xml:space="preserve">multò minor figura ipſum,
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            HTYL, comprehendente, quæ iam deſcripta fuit, hoc autem eſt
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              <note position="right" xlink:label="note-0511-03" xlink:href="note-0511-03a" xml:space="preserve">Ex antec.
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              Lem.</note>
            abſurdum, cum enim paralſelogràmmum, BZ, æquetur ipſi, GK, 2
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            &</s>
            <s xml:id="echoid-s12574" xml:space="preserve">, 6V, 3℟, 9X, &</s>
            <s xml:id="echoid-s12575" xml:space="preserve">, ΔΡ, ΣΥ, tota toti adæquatur contra præde-
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            monſtrata, non ergo figura, HTYL, maior eſt, CQPD.</s>
            <s xml:id="echoid-s12576" xml:space="preserve"/>
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            <s xml:id="echoid-s12577" xml:space="preserve">Sit nunc eadem minor, ſi poſſibile eſt, eodem ſpatio, +, igitur
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            deſcriptis circa, CQPD, eiſdem figuris, ita vt comprehendens, CQ
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            PD, ſuperet ab eo comprehenſam minori ſpatio, quam ſit, +, cõ-
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            pleantur parallelogramma, OV, RX, SY, ex quibus compoſitam
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            figuram, vt ſupra à ſpatio, HTYL, comprehendi oſtendemus. </s>
            <s xml:id="echoid-s12578" xml:space="preserve">Igi-
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            tur ſi comprehendens, CQPD, ſuperat figuram comprehenſam
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            minori ſpatio, quam ſit, +, ipſum ſpatium, CQPD, ſuperabit ab
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            eo comprehenſam figuram multò minori ſpatio, quam ſit, +, idẽ
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            autem ſuperat, HTYL, ſpatio, +, ergo figura comprehenſa </s>
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