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

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            <s xml:id="echoid-s11225" xml:space="preserve">
              <pb o="429" file="0451" n="451" rhead="LIBER VI."/>
            ſunt circulorum, à quibus abſcinduntur partes proportionales, ipſi au-
              <lb/>
            tem circuli ſunt, vt diametrorum quadrata.</s>
            <s xml:id="echoid-s11226" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1033" type="section" level="1" n="622">
          <head xml:id="echoid-head652" xml:space="preserve">THEOREMA IV. PROPOS. IV.</head>
          <p>
            <s xml:id="echoid-s11227" xml:space="preserve">DAti circuli, necnon ſimiles fectores inter ſe ſunt, vt
              <lb/>
            omnes eorundem circumferentiæ.</s>
            <s xml:id="echoid-s11228" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11229" xml:space="preserve">Sint in eadem antecedentis figura circuli quinque, BADC,
              <lb/>
            FXZ, deſcripti ſuper eodem centro, E, & </s>
            <s xml:id="echoid-s11230" xml:space="preserve">abijſdem intelligantur
              <lb/>
              <figure xlink:label="fig-0451-01" xlink:href="fig-0451-01a" number="310">
                <image file="0451-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0451-01"/>
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            abſciſſi ſimiles ſectores, D
              <lb/>
            ED, XEZ. </s>
            <s xml:id="echoid-s11231" xml:space="preserve">Dico circulos,
              <lb/>
            DABC, FZX, necnon ſe-
              <lb/>
            ctores, DEC, XEZ, inter ſe
              <lb/>
            eſſe, vt omnes iplorum cir-
              <lb/>
            cumferentiæ. </s>
            <s xml:id="echoid-s11232" xml:space="preserve">Sit denuò
              <lb/>
            expoſitũ triãgulum, HOM,
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            cuius ſit angulus rectus, H
              <lb/>
            MO, latus, HM, æquale ra-
              <lb/>
            dio, ED, &</s>
            <s xml:id="echoid-s11233" xml:space="preserve">, MO, circum-
              <lb/>
            ferentiæ, DCBA, abſciſſa
              <lb/>
            autem, HR, æqualr ipſi,
              <lb/>
            EX, & </s>
            <s xml:id="echoid-s11234" xml:space="preserve">per, R, ducta paral-
              <lb/>
            lela ipſi, OM, quæ ſit, SR, intercepta lateribus, HO, HM, patet,
              <lb/>
            vt dicebatur in Corol. </s>
            <s xml:id="echoid-s11235" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11236" xml:space="preserve">ant. </s>
            <s xml:id="echoid-s11237" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s11238" xml:space="preserve">quod circumferentia, FZX,
              <lb/>
            æquatur ipſi, SR, eodem modo abſcindentes ab ipſis, HM, ED,
              <lb/>
            verſus, H, E, puncta æquales quaſcunque rectas lineas, & </s>
            <s xml:id="echoid-s11239" xml:space="preserve">per ea-
              <lb/>
            rum terminos ducentes parallelam quidem ipſi, OM, in triangulo,
              <lb/>
            & </s>
            <s xml:id="echoid-s11240" xml:space="preserve">circumfer entiam iuper cenrro, E, in circulo, ABCD, manife-
              <lb/>
            ſtum erit prædictam circumferentiam æquari prædictæ parallelæ,
              <lb/>
            lateribus, HO, HM, interceptæ, & </s>
            <s xml:id="echoid-s11241" xml:space="preserve">vnicuique circumferentiæ in
              <lb/>
            circulo, ABCD, fic deſcriptæ reſpondere ſuam parallelam in triã-
              <lb/>
            gulo, HOM, cum ſint rectę, HM, ED, æquales, igitur conclude-
              <lb/>
            mus omnes circumferentias circuli, DABC, æquari omnibus li-
              <lb/>
            neis trianguli, HOM, regula, OM, ſicut etiam omnes circumfe-
              <lb/>
            rentias circuli, FZX, æquari omnibus lineis trianguli, HSR, regu-
              <lb/>
            la eadem, OM, quapropter, vt omnes lineæ trianguli, HOM, ad
              <lb/>
            omnes lineas trianguli, HSR, ideſi vt triãgulum, HOM, ad, HSR,
              <lb/>
              <note position="right" xlink:label="note-0451-01" xlink:href="note-0451-01a" xml:space="preserve">3. l. 2.</note>
            ideſt vt circulus, DABC, ad circulum, FZX, ita omnes circumfe-
              <lb/>
            rentiæ circuli, ABCD, erunt ad omnes circumfarentias circuli
              <lb/>
            ciuidem, FZX; </s>
            <s xml:id="echoid-s11242" xml:space="preserve">quod & </s>
            <s xml:id="echoid-s11243" xml:space="preserve">fimuli methodo de ſectoribus ex. </s>
            <s xml:id="echoid-s11244" xml:space="preserve">g. </s>
            <s xml:id="echoid-s11245" xml:space="preserve"/>
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