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

Table of Notes

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            in, O, ideò, vt vna ad vnam, ſic omnes ad omnes. </s>
            <s xml:id="echoid-s3334" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3335" xml:space="preserve">vt, LE, ad, E
              <lb/>
              <note position="right" xlink:label="note-0161-01" xlink:href="note-0161-01a" xml:space="preserve">Coroll. 4.
                <lb/>
              huius.</note>
            O, ſic omnes lineæ figuræ, LEF, erunt ad omnes lineas figuræ, O
              <lb/>
            EF, regula, LE, .</s>
            <s xml:id="echoid-s3336" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3337" xml:space="preserve">vt, LE, ad, EO, ita figura, LEF, ad figu-
              <lb/>
            ram, OEF; </s>
            <s xml:id="echoid-s3338" xml:space="preserve">eodem modo oſtendemus, vt, QY, ad, YT, ſic eſſe
              <lb/>
              <note position="right" xlink:label="note-0161-02" xlink:href="note-0161-02a" xml:space="preserve">4. huius.</note>
            figuram, QYM, ad figuram, TYM, eſt autem vt, QY, ad, YT,
              <lb/>
            ita, LE, ad, EO, ergo figura, LEF, ad, OEF, erit vt, QYM,
              <lb/>
            ad, TYM, & </s>
            <s xml:id="echoid-s3339" xml:space="preserve">ſic erit quælibet alia figura in ſolido, LEDF, ipſi,
              <lb/>
              <note position="right" xlink:label="note-0161-03" xlink:href="note-0161-03a" xml:space="preserve">4. huius.</note>
            LEF, æquidiſtans, ad eius portionem in ſolido, OEDF, manen-
              <lb/>
            tem, ergo vt vna ad vnam, ſic omnes ad omnes .</s>
            <s xml:id="echoid-s3340" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3341" xml:space="preserve">vt figura, LEF,
              <lb/>
            ad figuram, OEF, ſic omnia plana ſolidi, LEDF, ad omnia pla-
              <lb/>
              <note position="right" xlink:label="note-0161-04" xlink:href="note-0161-04a" xml:space="preserve">3. huius.</note>
            na ſolidi, OEDF, regula plano, LEF, & </s>
            <s xml:id="echoid-s3342" xml:space="preserve">ita ſolidum, LEDF,
              <lb/>
            ad ſolidum, OEDF, eſt autem figura, LEF, ad figuram, OEF,
              <lb/>
            vt, LE, ad, EO, vel ad, 34, ergo ſolidum, LEDF, ad ſolidum,
              <lb/>
            OEDF, erit vt, LE, ad, 34, quod pariterſerua.</s>
            <s xml:id="echoid-s3343" xml:space="preserve"/>
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          <head xml:id="echoid-head227" xml:space="preserve">E. SECTIO V.</head>
          <p>
            <s xml:id="echoid-s3344" xml:space="preserve">DVcatur nunc intra ſolidum, OEDF, planum ipſi, DEF, æ-
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            quidiſtans, quod in eo producat figuram, CNX, quæ ſecet
              <lb/>
            figuram, ODE, in recta, CN, &</s>
            <s xml:id="echoid-s3345" xml:space="preserve">, OFE. </s>
            <s xml:id="echoid-s3346" xml:space="preserve">in recta, NX, & </s>
            <s xml:id="echoid-s3347" xml:space="preserve">ſuper-
              <lb/>
            ficiem, ODF, in linea, CX, ſecet autem & </s>
            <s xml:id="echoid-s3348" xml:space="preserve">lineas, DO, in, C, O
              <lb/>
            E, in, N, &</s>
            <s xml:id="echoid-s3349" xml:space="preserve">, OF, in, X, ſimiliter in ſolido, 3467, ducatur pla-
              <lb/>
            num ipſi, 647, æquidiſtans, quod abipſa, 34, abſcindat, 35, æqua-
              <lb/>
            lem ipſi, ON, & </s>
            <s xml:id="echoid-s3350" xml:space="preserve">producat in eo figuram, RSP; </s>
            <s xml:id="echoid-s3351" xml:space="preserve">vlterius per pun-
              <lb/>
            cta, C, X, ducantur, BH, G Ω, parallele ipſi, LE, & </s>
            <s xml:id="echoid-s3352" xml:space="preserve">occurrentes
              <lb/>
            lineis, DL, LF, in, B, G, & </s>
            <s xml:id="echoid-s3353" xml:space="preserve">rectis, DE, EF, in, H, Ω, deinde
              <lb/>
            à puncto, B, ducatur, BV, parallela ipſi, DE, ſiue, CN, (nam,
              <lb/>
            DE, CN, ſunt communes ſectiones planorum æquidiſtantium, C
              <lb/>
            NX, DEF, & </s>
            <s xml:id="echoid-s3354" xml:space="preserve">plani, ODE, eadem ſecantis, vnde, CN, DE, ſunt
              <lb/>
            parallelæ, veluti patebit etiam, NX, æquidiſtare ipſi, EF,) & </s>
            <s xml:id="echoid-s3355" xml:space="preserve">iun-
              <lb/>
            gatur, VG, quia ergo, NX, eſt parallela ipſi, Ε Ω, &</s>
            <s xml:id="echoid-s3356" xml:space="preserve">, Χ Ω, ipſi,
              <lb/>
            NE, erit, Χ Ω, æqualis ipſi, NE, & </s>
            <s xml:id="echoid-s3357" xml:space="preserve">quia, LE, ad, EO, eſt vt, B
              <lb/>
            H, ad, HC, .</s>
            <s xml:id="echoid-s3358" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3359" xml:space="preserve">vt, VE, ad, EN, eſt autem, G Ω, ad, Ω Χ, vt,
              <lb/>
            LE, ad, EO, quia eſt illi parallela, & </s>
            <s xml:id="echoid-s3360" xml:space="preserve">ſecatur à linea, OF, in, X,
              <lb/>
            ergo, G Ω, ad, Ω Χ, erit vt, VE, ad, EN, ſunt autem, Ω Χ, EN,
              <lb/>
            inter ſe æquales, ergo &</s>
            <s xml:id="echoid-s3361" xml:space="preserve">, G Ω, VE, erunt æquales, & </s>
            <s xml:id="echoid-s3362" xml:space="preserve">ſunt paralle-
              <lb/>
            læ, ergo etiam eas iungentes, VG, Ε Ω, erunt æquales, & </s>
            <s xml:id="echoid-s3363" xml:space="preserve">paralle-
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            læ. </s>
            <s xml:id="echoid-s3364" xml:space="preserve">Sumatur nunc intra lineam, CX, vtcunq; </s>
            <s xml:id="echoid-s3365" xml:space="preserve">punctum, I, per quod
              <lb/>
            ipſi, LE, parallela ducatur, AK, quæ ſuperficiei, LDF, occurrat
              <lb/>
            in, A, & </s>
            <s xml:id="echoid-s3366" xml:space="preserve">plano, DEF, in, K, quia ergo, AK, æquidiſtat ipſi, L
              <lb/>
              <note position="right" xlink:label="note-0161-05" xlink:href="note-0161-05a" xml:space="preserve">Exis: @@
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              Elem.</note>
            E, poterit per, AK, planum duci æquidiſtans plano, LEF, ſit du-
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            ctum idem, quod prius, quod adhuc ſecet figura, LDE, in </s>
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