Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <p>
            <s xml:id="echoid-s2960" xml:space="preserve">
              <pb file="0118" n="118" rhead="FED. COMMANDINI"/>
            do in reliquis figuris æquilateris, & </s>
            <s xml:id="echoid-s2961" xml:space="preserve">æquiangulis, quæ in cir-
              <lb/>
            culo deſcribuntur, probabimus cẽtrum grauitatis earum,
              <lb/>
            & </s>
            <s xml:id="echoid-s2962" xml:space="preserve">centrum circuli idem eſſe. </s>
            <s xml:id="echoid-s2963" xml:space="preserve">quod quidem demonſtrare
              <lb/>
            oportebat.</s>
            <s xml:id="echoid-s2964" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2965" xml:space="preserve">Ex quibus apparet cuiuslibet figuræ rectilineæ
              <lb/>
            in circulo plane deſcriptæ centrum grauitatis idẽ
              <lb/>
            eſſe, quod & </s>
            <s xml:id="echoid-s2966" xml:space="preserve">circuli centrum.</s>
            <s xml:id="echoid-s2967" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2968" xml:space="preserve">Figuram in circulo plane deſcriptam appella-
              <lb/>
              <note position="left" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">γνωρ@ μω@</note>
            mus, cuiuſmodi eſt ea, quæ in duodecimo elemen
              <lb/>
            torum libro, propoſitione ſecunda deſcribitur.
              <lb/>
            </s>
            <s xml:id="echoid-s2969" xml:space="preserve">ex æqualibus enim lateribus, & </s>
            <s xml:id="echoid-s2970" xml:space="preserve">angulis conſtare
              <lb/>
            perſpicuum eſt.</s>
            <s xml:id="echoid-s2971" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div199" type="section" level="1" n="65">
          <head xml:id="echoid-head72" xml:space="preserve">THEOREMA II. PROPOSITIO II.</head>
          <p>
            <s xml:id="echoid-s2972" xml:space="preserve">Omnis figuræ rectilineæ in ellipſi plane deſcri-
              <lb/>
            ptæ centrum grauitatis eſt idem, quod ellipſis
              <lb/>
            centrum.</s>
            <s xml:id="echoid-s2973" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2974" xml:space="preserve">Quo modo figura rectilinea in ellipſi plane deſcribatur,
              <lb/>
            docuimus in commentarijs in quintam propoſitionem li-
              <lb/>
            bri Archimedis de conoidibus, & </s>
            <s xml:id="echoid-s2975" xml:space="preserve">ſphæroidibus.</s>
            <s xml:id="echoid-s2976" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2977" xml:space="preserve">Sit ellipſis a b c d, cuius maior axis a c, minor b d: </s>
            <s xml:id="echoid-s2978" xml:space="preserve">iun-
              <lb/>
            ganturq́; </s>
            <s xml:id="echoid-s2979" xml:space="preserve">a b, b c, c d, d a: </s>
            <s xml:id="echoid-s2980" xml:space="preserve">& </s>
            <s xml:id="echoid-s2981" xml:space="preserve">bifariam diuidantur in pun-
              <lb/>
            ctis e f g h. </s>
            <s xml:id="echoid-s2982" xml:space="preserve">à centro autem, quod ſit k ductæ lineæ k e, k f,
              <lb/>
            k g, k h uſque ad ſectionem in puncta l m n o protrahan-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s2983" xml:space="preserve">& </s>
            <s xml:id="echoid-s2984" xml:space="preserve">iungantur l m, m n, n o, o l, ita ut a c ſecet li-
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            neas l o, m n, in z φ punctis, & </s>
            <s xml:id="echoid-s2985" xml:space="preserve">b d ſecet l m, o n in χ ψ.
              <lb/>
            </s>
            <s xml:id="echoid-s2986" xml:space="preserve">erunt l k, k n linea una, itemq́ue linea unaipſæ m k, k o: </s>
            <s xml:id="echoid-s2987" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s2988" xml:space="preserve">lineæ b a, c d æquidiſtabunt lineæ m o: </s>
            <s xml:id="echoid-s2989" xml:space="preserve">& </s>
            <s xml:id="echoid-s2990" xml:space="preserve">b c, a d ipſi
              <lb/>
            l n. </s>
            <s xml:id="echoid-s2991" xml:space="preserve">rurſus l o, m n axi b d æquidiſtabunt: </s>
            <s xml:id="echoid-s2992" xml:space="preserve">& </s>
            <s xml:id="echoid-s2993" xml:space="preserve">l </s>
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