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

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              <pb o="137" file="0157" n="157" rhead="LIBER II."/>
            planorum, necnon planorum earundem figurarum incidentium,
              <lb/>
            nempè, HL, 3 Σ, quod ſerua.</s>
            <s xml:id="echoid-s3248" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div342" type="section" level="1" n="210">
          <head xml:id="echoid-head225" xml:space="preserve">B. SECTIO II.</head>
          <p>
            <s xml:id="echoid-s3249" xml:space="preserve">NVnc quia figuræ iam dictæ adiacentes homologis lineis figura-
              <lb/>
            rum, H {00/ }, Σ 2, plurificari poſſunt, quę ſunt in eodem plano,
              <lb/>
            vti apparet in figuris, S, Y, β, Γ, quę cum ſint in eodem plano ſunt
              <lb/>
            tamen duæ figuræ, ideò vt ex duobus fiat vna tantum, adhuc om-
              <lb/>
            nium linearum harum adiacentium figurarum aliam translationem
              <lb/>
            regulis, HL, Σ 3, faciemus; </s>
            <s xml:id="echoid-s3250" xml:space="preserve">ducantur ergo per ipſas, LG, 38, duo
              <lb/>
            plana, quorum & </s>
            <s xml:id="echoid-s3251" xml:space="preserve">oppoſitorum planorum tangentium communes
              <lb/>
            ſectiones ſint ipſæ, 3 {12/ }, 8 {13/ }, LQ, GT, cum ipſis, 3 Σ, 82, LH,
              <lb/>
            G {00/ }, angulos æquales continentes, & </s>
            <s xml:id="echoid-s3252" xml:space="preserve">agantur duę ex oppoſito tan-
              <lb/>
            gentes figuras, OZX, Φ Γ Λ, parallelę ipſis, OX, Φ Λ, quę ſint ip-
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            iæ, ZF, Γ 7, productæ cum reliquis tangentibus oppoſitis, OX, Φ
              <lb/>
            Λ, donec occurrant planis, LT, 3 {13/ }, vt in punctis, E, F; </s>
            <s xml:id="echoid-s3253" xml:space="preserve">4, 7, iun-
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            ctis rectis lineis, EF, 47. </s>
            <s xml:id="echoid-s3254" xml:space="preserve">Quia ergo, DE, ęquidiſtat ipſi, {00/ }G, &</s>
            <s xml:id="echoid-s3255" xml:space="preserve">,
              <lb/>
              <note position="right" xlink:label="note-0157-01" xlink:href="note-0157-01a" xml:space="preserve">16. Vnd@
                <lb/>
              Elem.</note>
            EF, ipſi, GT, angulus, DEF, æquatur angulo, {00/ } GT, & </s>
            <s xml:id="echoid-s3256" xml:space="preserve">eadem
              <lb/>
            ratione angulus, 647, probabitur æqualis ipſi, 28 {13/ }, vnde, quia,
              <lb/>
            {00/ }GT, æquatur ipſi, 28 {13/ }, angulus, FED, erit æqualis angulo,
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            746, & </s>
            <s xml:id="echoid-s3257" xml:space="preserve">cum ſit, vt, OX, ad, Φ Λ, vel vt, OE, ad, Φ 4, quia, L
              <lb/>
            G, 38, ſunt lineæ incidentes ſimilium planarum figurarum, H {00/ },
              <lb/>
              <note position="right" xlink:label="note-0157-02" xlink:href="note-0157-02a" xml:space="preserve">Corollat.
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              24. lib. 1.</note>
            Σ 2, vel vt, XE, ad, Λ 4, ita, EF, ad, 47, ſint autem, XE, Λ 4,
              <lb/>
            comprehenſæ inter eaidem extremitates rectarum, EF, 47, & </s>
            <s xml:id="echoid-s3258" xml:space="preserve">peri-
              <lb/>
            metrum figurarum, OZX, Φ Γ Λ, eaſdem tangentes, ergo, EF, 4
              <lb/>
            7, erunt incidentes ſimilium figurarum, OZX, Φ Γ Λ, & </s>
            <s xml:id="echoid-s3259" xml:space="preserve">oppoſita-
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            rum tangentium, OE, ZF; </s>
            <s xml:id="echoid-s3260" xml:space="preserve">Φ 4, Γ 7. </s>
            <s xml:id="echoid-s3261" xml:space="preserve">Similiter ſi ſic producantur
              <lb/>
              <note position="right" xlink:label="note-0157-03" xlink:href="note-0157-03a" xml:space="preserve">24. lib. 1.</note>
            oppoſitæ tangentes figurarum, S, Y; </s>
            <s xml:id="echoid-s3262" xml:space="preserve">β Δ, quarum duæ incidant ip-
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            ſis, LG, 38, vt in, K, {10/ }, reliquæ vero in punctis, {11/ } {14/ }, planis, L
              <lb/>
            T, 3 {13/ }, occurrant, iunctis, K {14/ }, {10/ } {11/ }, oſtendemus pariter ipſas, K
              <lb/>
            {14/ }, {10/ } {11/ }, eſſe incidentes ſimilium figurarum, Y, Δ, vel ſimilium, S,
              <lb/>
            β, & </s>
            <s xml:id="echoid-s3263" xml:space="preserve">oppoſitarum tangentium extremarum, quæ ad puncta, K 14,
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            &</s>
            <s xml:id="echoid-s3264" xml:space="preserve">, {10/ }, {11/ }, terminantur. </s>
            <s xml:id="echoid-s3265" xml:space="preserve">Si igitur transferamus omnes lineas tum fi-
              <lb/>
              <note position="right" xlink:label="note-0157-04" xlink:href="note-0157-04a" xml:space="preserve">Vide ad
                <lb/>
              finem A.
                <lb/>
              p. 15. hu-
                <lb/>
              ius.</note>
            gurarum, S, Y, tum, β, Δ, regulis eiſdem tangentibus, vel ſemper
              <lb/>
            regulis ipſis, OE, Φ 4, prius compoſitis illis, quę ſibi in directum e-
              <lb/>
            runt, tum in figuris, S, Y, tum, β Δ, vt ex illis fiat vnica compoſita
              <lb/>
            recta linea, prędictis in directum poſita in figura adiacente, qualis ſit,
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            9 {10/ }, æqualis .</s>
            <s xml:id="echoid-s3266" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3267" xml:space="preserve">compoſitæ ex his, quibus adiacent figuræ, β Δ, &</s>
            <s xml:id="echoid-s3268" xml:space="preserve">,
              <lb/>
            MK, æqualis compoſitæ ex his, quibus adiacent figuræ, S, Y; </s>
            <s xml:id="echoid-s3269" xml:space="preserve">tan-
              <lb/>
            dem habebimus figuras adiacentes ipſis incidentibus .</s>
            <s xml:id="echoid-s3270" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s3271" xml:space="preserve">MK {14/ }, 9 {10/ }
              <lb/>
            {11/ }, in quibus plures figuræ, S, Y, in vnam, MK {14/ }, & </s>
            <s xml:id="echoid-s3272" xml:space="preserve">β, Δ, in </s>
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