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

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            <s xml:id="echoid-s4397" xml:space="preserve">
              <pb o="178" file="0198" n="198" rhead="GEOMETRIÆ"/>
            tis, ergo, vt vnum ad vnum, ſic omnia ad omnia .</s>
            <s xml:id="echoid-s4398" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4399" xml:space="preserve">vt quadratum,
              <lb/>
              <note position="left" xlink:label="note-0198-01" xlink:href="note-0198-01a" xml:space="preserve">Coroll. 4.
                <lb/>
              huius.</note>
            EF, ad figuram aliam quamcumq; </s>
            <s xml:id="echoid-s4400" xml:space="preserve">deſcriptam ab, EF, ſic erunt om-
              <lb/>
            nia quadrata figuræ, DEF, regula, EF, ad omnes figuras ſimiles
              <lb/>
            eiuſdem figuræ, DEF, regula eadem, EF, ſimiles inquam deſcri-
              <lb/>
            ptæ ab, EF, vt autem quadratum, EF, ad figuram deſcriptam ab,
              <lb/>
            EF, ita quadratum, BC, ad figuram, quę deſcribitur à, BC, ſimi-
              <lb/>
            lis ei, quę deſcripta eſt ab, EF, ita vt deſcribentes ſint earumdem ho-
              <lb/>
            mologę, vt autem quadratum, BC, ad figuram deſcriptam à, BC,
              <lb/>
            ſic eſſe oſtendemus omnia quadrata figuræ, ABC, regula, BC, ad
              <lb/>
            omnes figuras ſimiles eiuſdem figurę, ABC, ſimiles inquam deſcri-
              <lb/>
            ptæ à, BC, vel ab, EF, eodem modo, quo id oſtendimus in figura,
              <lb/>
            DEF, ergo omnia quadrata figurę, ABC, ad omnes figuras ſimi-
              <lb/>
            les alias quaſcunque eiuſdem figuræ, ABC, erunt, vt omnia qua-
              <lb/>
              <figure xlink:label="fig-0198-01" xlink:href="fig-0198-01a" number="117">
                <image file="0198-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0198-01"/>
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            drata figuræ, DEF, ad omnes figuras ſimi-
              <lb/>
            les prædictis eiuſdem figuræ, DEF, regulis
              <lb/>
            prædictis, BC, EF, ergo permutando, vt
              <lb/>
            omnia quadrata figuræ, ABC, ad omnia
              <lb/>
            quadrata figurę, DEF, ita erunt omnes fi-
              <lb/>
            guræ ſimiles quæcumque figurę, ABC, ad
              <lb/>
            omnes figuras ſimiles prædictis figuræ, DE
              <lb/>
            F, quia verò omnes figuræ ſimiles alicuius
              <lb/>
            figuræ planæ regula quadam ſumptæ, ſunt
              <lb/>
            omnia plana ſolidi, quod dicitur ſimilare, & </s>
            <s xml:id="echoid-s4401" xml:space="preserve">
              <lb/>
            genitum ex tali figura iuxta eandem regulam, ideò, vt omnes figurę
              <lb/>
              <note position="left" xlink:label="note-0198-02" xlink:href="note-0198-02a" xml:space="preserve">B. Diff. 8.
                <lb/>
              huius.</note>
            ſimiles quæcumque ipſius figuræ, ABC, regula, BC, ad omnes fi-
              <lb/>
            guras ſimiles ipſius figuræ, DEF, regula, EF, ſimiles inquam præ-
              <lb/>
              <note position="left" xlink:label="note-0198-03" xlink:href="note-0198-03a" xml:space="preserve">Poſtulatũ
                <lb/>
              2. huius.</note>
            dictis .</s>
            <s xml:id="echoid-s4402" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4403" xml:space="preserve">vt omnia quadrata figuræ, ABC, regula, BC, ad omnia
              <lb/>
            quadrata figuræ, DEF, regula, EF, ita erunt omnia plana ſolidi
              <lb/>
            ſimilaris cuiuſcumque geniti ex figura, ABC, iuxta regulam, BC,
              <lb/>
            ad omnia plana ſolidi ſimilaris geniti ex figura, DEF, iuxta regu-
              <lb/>
            lam, EF, vt au@em omnia plana duorum ſolidorum ſic & </s>
            <s xml:id="echoid-s4404" xml:space="preserve">ipſa ſoli-
              <lb/>
              <note position="left" xlink:label="note-0198-04" xlink:href="note-0198-04a" xml:space="preserve">3. huius.</note>
            da, ergo etiam ſolida ſimilaria genita ex figuris, ABC, DEF, (quę
              <lb/>
            ſunt ſimilaria ad inuicem, quia omnes figuræ ſimiles figuræ, ABC,
              <lb/>
            ſunt etiam ſimiles omnibus figuris ſimilibus figuræ, DEF,) iuxta
              <lb/>
            regulas, BC, EF, erunt ad inuicem, vt omnia quadrata earumdem
              <lb/>
            figurarum eiſdem regulis ſumpta, quod erat oſtendendum.</s>
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        <div xml:id="echoid-div442" type="section" level="1" n="265">
          <head xml:id="echoid-head280" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s4406" xml:space="preserve">_H_Inc patet, ſi in figura, ABC, vtcumq; </s>
            <s xml:id="echoid-s4407" xml:space="preserve">regula, BC, deſcripſerit
              <lb/>
            duas quaſcumque figuras, quod vt vna ad aliam, ita erunt om-
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            nes figuræ ipſius, ABC, ſimiles vni deſcriptarum ad omnes figuras </s>
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