Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s3103" xml:space="preserve">
              <pb file="0122" n="122" rhead="FED. COMMANDINI"/>
            teſt in portione, quæ recta linea & </s>
            <s xml:id="echoid-s3104" xml:space="preserve">obtuſianguli coni ſe-
              <lb/>
            ctione, ſeu hyperbola continetur.</s>
            <s xml:id="echoid-s3105" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div204" type="section" level="1" n="67">
          <head xml:id="echoid-head74" xml:space="preserve">THE OREMA IIII. PROPOSITIO IIII.</head>
          <p>
            <s xml:id="echoid-s3106" xml:space="preserve">
              <emph style="sc">In</emph>
            circulo & </s>
            <s xml:id="echoid-s3107" xml:space="preserve">ellipſiidem eſt figuræ & </s>
            <s xml:id="echoid-s3108" xml:space="preserve">graui-
              <lb/>
            tatis centrum.</s>
            <s xml:id="echoid-s3109" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3110" xml:space="preserve">SIT circulus, uel ellipſis, cuius centrum a. </s>
            <s xml:id="echoid-s3111" xml:space="preserve">Dico a gra-
              <lb/>
            uitatis quoque centrum eſſe. </s>
            <s xml:id="echoid-s3112" xml:space="preserve">Si enim fieri poteſt, ſit b cen-
              <lb/>
            trum grauitatis: </s>
            <s xml:id="echoid-s3113" xml:space="preserve">& </s>
            <s xml:id="echoid-s3114" xml:space="preserve">iuncta a b extra figuram in c produca
              <lb/>
            tur: </s>
            <s xml:id="echoid-s3115" xml:space="preserve">quam uero proportionem habetlinea c a ad a b, ha-
              <lb/>
            beat circulus a ad alium circulum, in quo d; </s>
            <s xml:id="echoid-s3116" xml:space="preserve">uel ellipſis ad
              <lb/>
            aliam ellipſim: </s>
            <s xml:id="echoid-s3117" xml:space="preserve">& </s>
            <s xml:id="echoid-s3118" xml:space="preserve">in circulo, uel ellipſi ſigura rectilinea pla-
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            ne deſcribatur adeo, ut tandem relinquantur portiones
              <lb/>
            quædam minores circulo, uel ellipſid; </s>
            <s xml:id="echoid-s3119" xml:space="preserve">quæ figura ſit e f g
              <lb/>
            h _k_ l m n. </s>
            <s xml:id="echoid-s3120" xml:space="preserve">Illud uero in circulo fieri poſſe ex duodecimo
              <lb/>
            elementorum libro, propoſitione ſecunda manifeſte con-
              <lb/>
            ſtat; </s>
            <s xml:id="echoid-s3121" xml:space="preserve">at in ellipſi nos demonſtra-
              <lb/>
              <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a" number="78">
                <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0122-01"/>
              </figure>
            uinius in commentariis in quin-
              <lb/>
            tam propoſitionem Archimedis
              <lb/>
            de conoidibus, & </s>
            <s xml:id="echoid-s3122" xml:space="preserve">ſphæroidibus.
              <lb/>
            </s>
            <s xml:id="echoid-s3123" xml:space="preserve">erit igitur a centrum grauitatis
              <lb/>
            ipſius figuræ, quod proxime oſtē
              <lb/>
            dimus. </s>
            <s xml:id="echoid-s3124" xml:space="preserve">Itaque quoniam circulus
              <lb/>
            a ad circulum d; </s>
            <s xml:id="echoid-s3125" xml:space="preserve">uel ellipſis a ad
              <lb/>
            ellipſim d eandem proportionē
              <lb/>
            habet, quam linea c a ad a b: </s>
            <s xml:id="echoid-s3126" xml:space="preserve">
              <lb/>
            portiones uero ſunt minores cir
              <lb/>
              <note position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">8. quinti.</note>
            culo uel ellipſi d: </s>
            <s xml:id="echoid-s3127" xml:space="preserve">habebit circu-
              <lb/>
            lus, uel ellipſis ad portiones ma-
              <lb/>
            iorem proportionem, quàm c a
              <lb/>
              <note position="left" xlink:label="note-0122-02" xlink:href="note-0122-02a" xml:space="preserve">19. quinti
                <lb/>
              apud Cã
                <lb/>
              panum.</note>
            ad a b: </s>
            <s xml:id="echoid-s3128" xml:space="preserve">& </s>
            <s xml:id="echoid-s3129" xml:space="preserve">diuidendo figura recti-
              <lb/>
            linea e f g h _k_ l m n ad </s>
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