Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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        <div type="section" level="1" n="53">
          <p>
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              <pb file="0088" n="88" rhead="ARCHIMEDIS"/>
            ductæ ſunt à baſibus ad portiones lineæ a n, a q, quæ angu
              <lb/>
            los æquales continent cum ipſis baſibus, eandem propor-
              <lb/>
            tionem habebit q a ad a n, quam l a ad a d.</s>
            <s xml:space="preserve">] _Hoc nos ſu_-
              <lb/>
            _pra demonstrauimus_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="5">
            <note position="right" xlink:label="note-0087-08" xlink:href="note-0087-08a" xml:space="preserve">E</note>
          </div>
          <p>
            <s xml:space="preserve">Aequalis eſt ergo a n ipſi n q.</s>
            <s xml:space="preserve">] _Cum enim q a ad a n ſit_,
              <lb/>
              <anchor type="note" xlink:label="note-0088-01a" xlink:href="note-0088-01"/>
            _ut l a ad a d; </s>
            <s xml:space="preserve">diuidendo, conuertendoq; </s>
            <s xml:space="preserve">erit an ad n q, ut a d ad_
              <lb/>
            _d l. </s>
            <s xml:space="preserve">eſt autem a d æqualis ipſi d l, quoniam d b ponitur diameter_
              <lb/>
            _portionis. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">a n ipſi n q eſt æqualis_.
              <lb/>
            </s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="6">
            <note position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">F</note>
          </div>
          <note position="left" xml:space="preserve">14. quinti</note>
          <p>
            <s xml:space="preserve">Et a q ipſi m y æquidiſtans.</s>
            <s xml:space="preserve">] _Ex quinta ſecundi libri coni_-
              <lb/>
              <anchor type="note" xlink:label="note-0088-03a" xlink:href="note-0088-03"/>
            _corum. </s>
            <s xml:space="preserve">Apollonij_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="7">
            <note position="left" xlink:label="note-0088-03" xlink:href="note-0088-03a" xml:space="preserve">G</note>
          </div>
          <p>
            <s xml:space="preserve">Etſecetur b d in punctis k r, ut dictum eſt.</s>
            <s xml:space="preserve">] _In prima_
              <lb/>
              <anchor type="note" xlink:label="note-0088-04a" xlink:href="note-0088-04"/>
            _parte huius propoſitionis. </s>
            <s xml:space="preserve">ſecetur autem in K ita, ut b k ſit dupla ip_-
              <lb/>
            _ſius k d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in r, ut K r ſit æqualis ei, quæ uſque ad axcm_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="8">
            <note position="left" xlink:label="note-0088-04" xlink:href="note-0088-04a" xml:space="preserve">H</note>
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          <p>
            <s xml:space="preserve">Quòd cũ in portionibus æqualibus, & </s>
            <s xml:space="preserve">ſimilibus, a p o l,
              <lb/>
              <anchor type="note" xlink:label="note-0088-05a" xlink:href="note-0088-05"/>
            a m q l ab extremitatibus baſium ductæ ſint a o, a q, ita ut
              <lb/>
            portiones ablatæ faciant cum diametris angulos æquales:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">anguli, qui ad y g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">lineæ y b, g b inter ſe æquales erũt.</s>
            <s xml:space="preserve">]
              <lb/>
            _Secet linea a q diametrum d b in θ, & </s>
            <s xml:space="preserve">a o ſecet in η. </s>
            <s xml:space="preserve">Itaque quo_-
              <lb/>
            _niam in portionibus æqualibus, & </s>
            <s xml:space="preserve">ſimilibus a p o l, a m q l ab ex_-
              <lb/>
            _tremitatibus baſium_
              <lb/>
              <anchor type="figure" xlink:label="fig-0088-01a" xlink:href="fig-0088-01"/>
            _ducũtur a o, a q, quæ_
              <lb/>
            _æquales angulos con_
              <lb/>
            _tinent cum ipſis baſi_
              <lb/>
            _bus: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">anguli ad d_
              <lb/>
            _utrique ſunt recti_:
              <lb/>
            </s>
            <s xml:space="preserve">_erũt & </s>
            <s xml:space="preserve">reliqui a η d_,
              <lb/>
            _a θ d inter ſe æqua_-
              <lb/>
            _les. </s>
            <s xml:space="preserve">linea autem p g_
              <lb/>
            _æquidiſtat lineæ a o_: </s>
            <s xml:space="preserve">
              <lb/>
            _itémq; </s>
            <s xml:space="preserve">m y ipſi a q_: </s>
            <s xml:space="preserve">
              <lb/>
            _& </s>
            <s xml:space="preserve">p s, m c ipſis a d_. </s>
            <s xml:space="preserve">
              <lb/>
            _triágula igitur p g s_,
              <lb/>
            _m y c triãgulis a η d_
              <lb/>
            _a θ d, atque inter ſe_
              <lb/>
            _ſunt ſimilia: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut a d ad a η, ita a d ad a θ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando. </s>
            <s xml:space="preserve">li_-
              <lb/>
              <anchor type="note" xlink:label="note-0088-06a" xlink:href="note-0088-06"/>
            </s>
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