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

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              <pb o="162" file="0182" n="182" rhead="GEOMETRIÆ"/>
            AE, ED, ſint, MO, OQ, & </s>
            <s xml:id="echoid-s3825" xml:space="preserve">interceptę figuris ſint, IO, OP, le-
              <lb/>
            periamus, MO, ad, OI, eſſe vt, QO, ad, OP. </s>
            <s xml:id="echoid-s3826" xml:space="preserve">Dico omnes li-
              <lb/>
            neas, AE, ad omnes lineas figurę, BCE, eſſe vt omnes lineę, BF,
              <lb/>
            ad omnes lineas figuræ, B E F, ſi verò vice linearum comparentur
              <lb/>
              <figure xlink:label="fig-0182-01" xlink:href="fig-0182-01a" number="105">
                <image file="0182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0182-01"/>
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            ab eiſdem deſcriptę figurę, ſimi-
              <lb/>
            libus exiſtentibus, quę ab omni-
              <lb/>
            bus lineis vniuſcuiuſque propo-
              <lb/>
            ſitarum figurarum deſcribuntur,
              <lb/>
            cuius deſcribentes ſint earum li-
              <lb/>
            neę, vel latera homologa. </s>
            <s xml:id="echoid-s3827" xml:space="preserve">Di-
              <lb/>
            co omnes figuras ſimiles ipſius,
              <lb/>
            A E, ad omnes figuras ſimiles
              <lb/>
            ſigurę, BCE, eſſe vt omnes fi-
              <lb/>
            guras ſimiles ipſius, BF, ad omnes figuras ſimiles figuræ, BEF,
              <lb/>
            quia enim, MQ, vtcunque ducta eſt parallela ipſi, CF, & </s>
            <s xml:id="echoid-s3828" xml:space="preserve">eſt, M
              <lb/>
            O, ad, OI, vt, QO, ad, OP, permutando erit, vt, MO, ad, O
              <lb/>
            Q, ſic, IO, ad, OP, i. </s>
            <s xml:id="echoid-s3829" xml:space="preserve">vt, CE, ad, EF, ſic, IO, ad, OP, & </s>
            <s xml:id="echoid-s3830" xml:space="preserve">ſic
              <lb/>
            oſtendemus, vt, CE, ad, EF, ita eſſe quaſlibet alias duas in figu-
              <lb/>
            ris, BCE, BEF, exiſtentes ipſi, CF, parallelas, & </s>
            <s xml:id="echoid-s3831" xml:space="preserve">vt vna ad vnam
              <lb/>
            ſic omnia ad omnia .</s>
            <s xml:id="echoid-s3832" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3833" xml:space="preserve">vt, CE, ad, EF, ita omnes lineæ figurę, B
              <lb/>
              <note position="left" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">Coroll. 4.
                <lb/>
              huius.</note>
            CE, ad omnes lineas figurę, BEF, vt autem, CE, ad, EF, ita ſunt
              <lb/>
            omnes lineæ, AE, ad omnes lineas, ED, ergo omnes lineę, AE,
              <lb/>
            ad omnes lineas, ED, erunt vt omnes lineę figurę, BCE, ad om-
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            nes lineas figuræ, BEF.</s>
            <s xml:id="echoid-s3834" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3835" xml:space="preserve">Si verò vice linearum ſumamus deſcriptas, vt dictum eſt, ab eiſdem
              <lb/>
            figuras, ex. </s>
            <s xml:id="echoid-s3836" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3837" xml:space="preserve">ſi, vt quadratum, MO, ad triangulum &</s>
            <s xml:id="echoid-s3838" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3839" xml:space="preserve">quilaterum,
              <lb/>
            cuius latus, IO, ita reperiamus eſſe circulum, cuius diameter, OQ,
              <lb/>
            ad polygonum, cuius latus, OQ, omnium autem linearum, AE,
              <lb/>
            fingulæ deſcribant quadrata, & </s>
            <s xml:id="echoid-s3840" xml:space="preserve">omnium linearum figuræ, BCE,
              <lb/>
            ſingulę deſcribant, triangula &</s>
            <s xml:id="echoid-s3841" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3842" xml:space="preserve">quilatera, & </s>
            <s xml:id="echoid-s3843" xml:space="preserve">omnium linearum, BF,
              <lb/>
            ſingulæ deſcribant circulos, & </s>
            <s xml:id="echoid-s3844" xml:space="preserve">figuræ, B E F, ſingulę deſcribant po-
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            lygona prædicto ſimilia, ita vt quæ in eadem figura ſunt lineæ, vel
              <lb/>
            latera deſcribentia ſint homologa, erit vt quadratum, MO, permu-
              <lb/>
            tando, ad circulum, OQ, ita triangulum &</s>
            <s xml:id="echoid-s3845" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3846" xml:space="preserve">quilaterum, IO, ad po-
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            lygonum, OP, quia verò, MO, &</s>
            <s xml:id="echoid-s3847" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3848" xml:space="preserve">quaturipſi, CE, &</s>
            <s xml:id="echoid-s3849" xml:space="preserve">, OQ, ipſi,
              <lb/>
            EF, ideò quadratum, MO, &</s>
            <s xml:id="echoid-s3850" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3851" xml:space="preserve">quatur quadrato, CE, & </s>
            <s xml:id="echoid-s3852" xml:space="preserve">circulus,
              <lb/>
            OQ, circulo, EF, & </s>
            <s xml:id="echoid-s3853" xml:space="preserve">ideò, vt quadratum, CE, ad circulum, EF,
              <lb/>
              <note position="left" xlink:label="note-0182-02" xlink:href="note-0182-02a" xml:space="preserve">@5. lib. 1.</note>
            ita erit triangulum &</s>
            <s xml:id="echoid-s3854" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3855" xml:space="preserve">quilaterum, IO, ad polygonum, OP, vnde,
              <lb/>
            quia, MQ, vtcunq; </s>
            <s xml:id="echoid-s3856" xml:space="preserve">ducta eſt parallelaipſi, CF, concludemus om-
              <lb/>
            nia quadrata, AE, ad omnes circulos, BF, eſſe, vt omnia triangu-
              <lb/>
            la &</s>
            <s xml:id="echoid-s3857" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3858" xml:space="preserve">quilatera figuræ, BCE, ad omnia polygona vni ſimilia figuræ,
              <lb/>
              <note position="left" xlink:label="note-0182-03" xlink:href="note-0182-03a" xml:space="preserve">Ex 4. hu-
                <lb/>
              ius.</note>
            BEF, & </s>
            <s xml:id="echoid-s3859" xml:space="preserve">permutando omnia quadrata, AE, ad omnia triangula </s>
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