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

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            <s xml:id="echoid-s3366" xml:space="preserve">
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            QY, DEF, in recta, YM, ſuperſiciem, LDF, in linea, QM, ſu-
              <lb/>
            perficiem, ODF, in linea, TM, & </s>
            <s xml:id="echoid-s3367" xml:space="preserve">figuram, CNX, in recta, ZI,
              <lb/>
            ſecet autem, QY, ipſam, BV, in puncto, ℟, & </s>
            <s xml:id="echoid-s3368" xml:space="preserve">iungatur, A ℟, erit
              <lb/>
            ergo, ZI, ipſi, YK, æquidiſtans, eſt autem etiam, AK, æquidiſtans
              <lb/>
            ipſi, QY, ergo, YI, erit parallelogrammum, & </s>
            <s xml:id="echoid-s3369" xml:space="preserve">ideò, IK, erit æ.
              <lb/>
            </s>
            <s xml:id="echoid-s3370" xml:space="preserve">
              <note position="left" xlink:label="note-0162-01" xlink:href="note-0162-01a" xml:space="preserve">Percõſtru
                <lb/>
              ctionem.</note>
            qualis ipſi, ZY, & </s>
            <s xml:id="echoid-s3371" xml:space="preserve">quia, AK, ad, KI, eſt vt, QY, ad, YT, .</s>
            <s xml:id="echoid-s3372" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3373" xml:space="preserve">vt,
              <lb/>
            BH, ad, HC, .</s>
            <s xml:id="echoid-s3374" xml:space="preserve">i vt, ℟ Y, ad, YZ, erit, AK, ad, KI, vt, ℟ Y, ad,
              <lb/>
            YZ, ſunt verò, IK, ZY, æquales, ergo &</s>
            <s xml:id="echoid-s3375" xml:space="preserve">, AK, ℟ Y, erunt æqua-
              <lb/>
            les, & </s>
            <s xml:id="echoid-s3376" xml:space="preserve">ſunt parallelæ, quia ambo ſunt parallelæ eidem, LE, ergo
              <lb/>
            eas iungentes, quæ ſunt, ℟ A, YK, erunt æquales, & </s>
            <s xml:id="echoid-s3377" xml:space="preserve">parallelę, eſt
              <lb/>
              <figure xlink:label="fig-0162-01" xlink:href="fig-0162-01a" number="94">
                <image file="0162-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0162-01"/>
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            autem, YK, pa-
              <lb/>
            rallela ipſi, Ε Ω,
              <lb/>
            &</s>
            <s xml:id="echoid-s3378" xml:space="preserve">, Ε Ω, ipſi, VG,
              <lb/>
            ergo, ℟ A, erit pa-
              <lb/>
            rallela ipſi, VG.
              <lb/>
            </s>
            <s xml:id="echoid-s3379" xml:space="preserve">Similiterautẽ pro-
              <lb/>
            cedemus in reli-
              <lb/>
            quis, quę per pun-
              <lb/>
            cta lineę, CX, ipſi,
              <lb/>
            LE, ducuntur æ-
              <lb/>
            quidiſtantes, do-
              <lb/>
            nec occurrant ſu-
              <lb/>
            perſiciei, LDF,
              <lb/>
            & </s>
            <s xml:id="echoid-s3380" xml:space="preserve">plano, DEF,
              <lb/>
            harum autem patet nihil extra ſuperficiem, LDF, manere, ex iam
              <lb/>
            dictis, ſint ergo omnium earum termini ex vna parte in linea, BAG,
              <lb/>
            ex alia in linea, Η Κ Ω, veluti ergo oſtenſum eſt, A ℟, eſſe paralle-
              <lb/>
            lam ipſi, GV, ſic oſtendemus reliquas, quę iungunt puncta, quibus
              <lb/>
            iam ductæ occurrunt lineæ, BG, cum punctis, in quibus plana per
              <lb/>
            dictas lineas ducta, ipſi, LEF, æquidiſtantia, ſecant ipſam, BV, eſſe
              <lb/>
            ipſi, VG, paralſelas ergo omnes erunt in eodem plano, in eo ſcili-
              <lb/>
            cet quod tranſit per, BV, VG, omnes .</s>
            <s xml:id="echoid-s3381" xml:space="preserve">n. </s>
            <s xml:id="echoid-s3382" xml:space="preserve">dictæ parallelæ tranſeunt
              <lb/>
            per puncta rectæ lineæ, BV, ſunt igiturd cta occurſuum puncta, & </s>
            <s xml:id="echoid-s3383" xml:space="preserve">
              <lb/>
            in ſuperficie, LDF, & </s>
            <s xml:id="echoid-s3384" xml:space="preserve">in plano, BVG, erunt ergo in eorum com-
              <lb/>
            muni ſectione, linea ergo, BAG, eſt communis ſectio plani per, B
              <lb/>
            V, VG, tranſeuntis, & </s>
            <s xml:id="echoid-s3385" xml:space="preserve">ſuperficiei, LDF; </s>
            <s xml:id="echoid-s3386" xml:space="preserve">habemus ergo ſolidum,
              <lb/>
            Β Ω, in cuius ambiente ſuperficie ſunt duæ figuræ planæ inuicem pa-
              <lb/>
            rallelæ, BVG, Η Ε Ω, in quarum circuitu ſumptis vtcunque duo-
              <lb/>
            bus punctis, V, E, & </s>
            <s xml:id="echoid-s3387" xml:space="preserve">iuncta, VE, cæteræ iungentes quælibet aliæ
              <lb/>
              <note position="left" xlink:label="note-0162-02" xlink:href="note-0162-02a" xml:space="preserve">Def. Cy-
                <lb/>
              lindrici
                <lb/>
              confor-
                <lb/>
              miter.</note>
            duo puncta earundem circuitus eidem ſemper, VE, parallelę reper-
              <lb/>
            tæ ſunt æquales, ergo, Β Ω erit cylindricus, cu@us oppoſitæ baſes
              <lb/>
            ipſæ, BVG, Η Ε Ω, hoc autem ſecatur plano eildem oppoſit@s </s>
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