Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
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          <chap>
            <p type="main">
              <s id="s.000114">
                <pb xlink:href="023/01/014.jpg"/>
              do in reliquis figuris æquilateris, & æquiangulis, quæ in cir­
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              culo deſcribuntur, probabimus
                <expan abbr="cẽtrum">centrum</expan>
              grauitatis earum,
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              & centrum circuli idem eſſe. </s>
              <s id="s.000115">quod quidem demonſtrare
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              oportebat.</s>
            </p>
            <p type="main">
              <s id="s.000116">Ex quibus apparet cuiuslibet figuræ rectilineæ
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              in circulo plane deſcriptæ centrum grauitatis
                <expan abbr="idẽ">idem</expan>
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              eſſe, quod & circuli centrum.
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                <arrow.to.target n="marg15"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000117">
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                <foreign lang="grc">γνωρίμως</foreign>
              </s>
            </p>
            <p type="main">
              <s id="s.000118">Figuram in circulo plane deſcriptam appella­
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              mus, cuiuſmodi eſt ea, quæ in duodecimo elemen
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              torum libro, propoſitione ſecunda deſcribitur.
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              </s>
              <s id="s.000119">ex æqualibus enim lateribus, & angulis conſtare
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              perſpicuum eſt.</s>
            </p>
            <p type="head">
              <s id="s.000120">THEOREMA II, PROPOSITIO II.</s>
            </p>
            <p type="main">
              <s id="s.000121">Omnis figuræ rectilineæ in ellipſi plane deſcri­
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              ptæ centrum grauitatis eſt idem, quod ellipſis
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              centrum.</s>
            </p>
            <p type="main">
              <s id="s.000122">Quo modo figura rectilinea in ellipſi plane deſcribatur,
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              docuimus in commentarijs in quintam propoſitionem li­
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              bri Archimedis de conoidibus, & ſphæroidibus.</s>
            </p>
            <p type="main">
              <s id="s.000123">Sit ellipſis abcd, cuius maior axis ac, minor bd:
                <expan abbr="iun-ganturq́">iun­
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                ganturque</expan>
              ; ab, bc, cd, da: & bifariam diuidantur in pun­
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              ctis efgh. </s>
              <s id="s.000124">à centro autem, quod ſit k ductæ lineæ ke, kf,
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              kg, kh uſque ad ſectionem in puncta lmno protrahan­
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              tur: & iungantur lm, mn, no, ol, ita ut ac ſecet li­
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              neas lo, mn, in z
                <foreign lang="grc">φ</foreign>
              punctis; & bd ſecet lm, on in
                <foreign lang="grc">χψ.</foreign>
                <lb/>
              erunt lk, kn linea una,
                <expan abbr="itemq́ue">itemque</expan>
              linea una ipſæ mk, ko:
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              & lineæ ba, cd æquidiſtabunt lineæ mo: & bc, ad ipſi
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              ln. </s>
              <s id="s.000125">rurſus lo, mn axi bd æquidiſtabunt: & lm, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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