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

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            <s xml:id="echoid-s12140" xml:space="preserve">
              <pb o="474" file="0494" n="494" rhead="GEOMETRIÆ"/>
            quadratum ad inſcriptum circulum, & </s>
            <s xml:id="echoid-s12141" xml:space="preserve">in, ℟8, ſumpta, 37, æqua
              <lb/>
            lis exceſſui, quo, 3℟, ſuperat {2/3}. </s>
            <s xml:id="echoid-s12142" xml:space="preserve">tertiæ proportionalis duarum, 8℟,
              <lb/>
            ℟4, patet ergo, quod cylindrus, Sφ, ad tympanum, SYφ, eſt vt, ℟
              <lb/>
            8, ad, 87. </s>
            <s xml:id="echoid-s12143" xml:space="preserve">Quoniam vero, vt, LO, ad, OQ, ſic eſt, QO, ad, OR,
              <lb/>
              <note position="left" xlink:label="note-0494-01" xlink:href="note-0494-01a" xml:space="preserve">Corol. 12.
                <lb/>
              34. l. 3.</note>
            ideò vt, LO, ad, OR, vel, T8, ipſi æqualem, ita quadratum, LO,
              <lb/>
            ad quadratum, OQ, vel ita quadratum, RO, ſeu quadratum, ℟8,
              <lb/>
            ad quadratum, NO, vel ita circulus, ℟φ, ad circulum, NP, ergo
              <lb/>
            duo cylindri, Sφ, KP, quorum axes reciprocè baſibus reſpondent,
              <lb/>
            erunt æquales, quod ſerua. </s>
            <s xml:id="echoid-s12144" xml:space="preserve">Vlterius, quia vt, IE, ad, EG, ſic eſt,
              <lb/>
              <note position="left" xlink:label="note-0494-02" xlink:href="note-0494-02a" xml:space="preserve">E. Cor. 4.
                <lb/>
              gener. 34.
                <lb/>
              l. 2.</note>
            8℟, ad, ℟4, & </s>
            <s xml:id="echoid-s12145" xml:space="preserve">vt, EG, ad, EF, ſic quadratum ad inſcriptum circu-
              <lb/>
            lum, & </s>
            <s xml:id="echoid-s12146" xml:space="preserve">ita etiam, ℟4, ad, ℟3, ergo ex æquali, IE, ad, EF, erit vt,
              <lb/>
            8℟, ad, ℟3. </s>
            <s xml:id="echoid-s12147" xml:space="preserve">Similiter quia, IE, ad, EG, eſt vt, 8℟, ad, ℟4, &</s>
            <s xml:id="echoid-s12148" xml:space="preserve">, E
              <lb/>
            G, ad {2/3}. </s>
            <s xml:id="echoid-s12149" xml:space="preserve">tertiæ proportionalis duarum, IE, EG, eſt vt, 4℟, ad {2/3}.
              <lb/>
            </s>
            <s xml:id="echoid-s12150" xml:space="preserve">tertiæ proportionalis duarum, 8℟, ℟4, ideò ex æquali, vt, IE, ad,
              <lb/>
            {2/3}. </s>
            <s xml:id="echoid-s12151" xml:space="preserve">tertiæ proportionalis duarum, IE, EG, ita, 8℟, erit ad {2/3}. </s>
            <s xml:id="echoid-s12152" xml:space="preserve">tertię
              <lb/>
            proportionalis duarum, 8℟, ℟4, eædem autem, IE, 8℟, ad, FE, 3
              <lb/>
            ℟, erant in eadem ratione, ergo ad exceſſus duarum, EF, ℟3, ſu-
              <lb/>
            per {2/3}. </s>
            <s xml:id="echoid-s12153" xml:space="preserve">tertiarum proportionalium, IE, EG, ex vna parte, &</s>
            <s xml:id="echoid-s12154" xml:space="preserve">, 8℟,
              <lb/>
            ℟4, ex alia, erunt in eadem ratione .</s>
            <s xml:id="echoid-s12155" xml:space="preserve">i. </s>
            <s xml:id="echoid-s12156" xml:space="preserve">vt, IE, ad, FH, ita erit, 8℟,
              <lb/>
            ad, 37, ſed etiam, vt, IE, ad, EF, ſic eſſe oſtenſum eſt, 8℟, ad, ℟3,
              <lb/>
            ergo, coll@gendo, vt, IE, ad, EH, ita, 8℟, ad, ℟7, & </s>
            <s xml:id="echoid-s12157" xml:space="preserve">per conuer-
              <lb/>
            ſionem rationis, & </s>
            <s xml:id="echoid-s12158" xml:space="preserve">conuertendo, vt, Hl, ad, IE, ideſt vt, AD, ad,
              <lb/>
            LO, ideſt vt cylindrus, BAC, ad cylindrum, NLP, vel illi æqualẽ,
              <lb/>
            Sφ, (vt oſtenſum eſt) ita, 78, ad, 8℟, ſed vt, 78, ad, 8℟, ita tym-
              <lb/>
            panum, SYφ, ad cylindrum, Sφ, ergo, vt cylindrus, BAC, ad cy-
              <lb/>
              <note position="left" xlink:label="note-0494-03" xlink:href="note-0494-03a" xml:space="preserve">Corol. 12.
                <lb/>
              34. l. 3.</note>
            lindrum, Sφ, ita tympanum, SYφ, ad cylindrum, Sφ, ergo cylin-
              <lb/>
            drus, BAC, æquaturtympano, SYφ, cuius axis, T8, ſemidiametro
              <lb/>
            baſis, ℟8, eſt æqualis, quod, &</s>
            <s xml:id="echoid-s12159" xml:space="preserve">c.</s>
            <s xml:id="echoid-s12160" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1115" type="section" level="1" n="667">
          <head xml:id="echoid-head697" xml:space="preserve">COROLL ARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s12161" xml:space="preserve">_C_Olligitur autemiuxta Corollarium Propoſit. </s>
            <s xml:id="echoid-s12162" xml:space="preserve">26. </s>
            <s xml:id="echoid-s12163" xml:space="preserve">huius, nos poſ-
              <lb/>
            ſe in uenire tympana ſphæralia, quorum axes ſemidiametris
              <lb/>
            baſium ſint æquales, quæ ad datum quodcunq; </s>
            <s xml:id="echoid-s12164" xml:space="preserve">ex ſolidis in ſectione 3.
              <lb/>
            </s>
            <s xml:id="echoid-s12165" xml:space="preserve">Coroll. </s>
            <s xml:id="echoid-s12166" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12167" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s12168" xml:space="preserve">25. </s>
            <s xml:id="echoid-s12169" xml:space="preserve">huius enumeratis, datam rationem habeant.</s>
            <s xml:id="echoid-s12170" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1116" type="section" level="1" n="668">
          <head xml:id="echoid-head698" xml:space="preserve">PROBLEMA VI. PROPOS. XIX.</head>
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            <s xml:id="echoid-s12171" xml:space="preserve">DAto cylindro anulum ſtrictum circularem æqualem
              <lb/>
            inuenire.</s>
            <s xml:id="echoid-s12172" xml:space="preserve"/>
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