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="55">
          <p>
            <s xml:space="preserve">
              <pb file="0094" n="94" rhead="ARCHIMEDIS"/>
            _quæ diametrum ſecet in ψ; </s>
            <s xml:space="preserve">ſecet autem i m eandem in σ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a q in_
              <lb/>
            _v. </s>
            <s xml:space="preserve">Dico angulum a ν d angulo i σ d minoré eſſe. </s>
            <s xml:space="preserve">angulus enimi ψ d_
              <lb/>
            _æqualis est angulo a ν d. </s>
            <s xml:space="preserve">ſed angulus interior i ψ d minor eſt exte-_
              <lb/>
              <anchor type="note" xlink:label="note-0094-01a" xlink:href="note-0094-01"/>
            _riore i σ d. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">a ν d ipſo i σ d minor erit_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <note position="right" xlink:label="note-0093-03" xlink:href="note-0093-03a" xml:space="preserve">C</note>
            <figure xlink:label="fig-0093-01" xlink:href="fig-0093-01a">
              <image file="0093-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0093-01"/>
            </figure>
            <note position="left" xlink:label="note-0094-01" xlink:href="note-0094-01a" xml:space="preserve">29. primi</note>
          </div>
          <note position="left" xml:space="preserve">16. primi</note>
          <p style="it">
            <s xml:space="preserve">_Et quoniam angulus, qui ad χ minor eſt angulo, qui ad_
              <lb/>
              <anchor type="note" xlink:label="note-0094-03a" xlink:href="note-0094-03"/>
            _n.</s>
            <s xml:space="preserve">]_ Ducantur per o duæ lineæ, o c quidem ad diametrum b d per-
              <lb/>
            pendicularis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">o χ in puncto o ſectionem contingens, quæ diame
              <lb/>
            trum ſecet in χ. </s>
            <s xml:space="preserve">æquidiſtabit o χ ipſi a q: </s>
            <s xml:space="preserve">atque erit angulus ad
              <lb/>
              <anchor type="note" xlink:label="note-0094-04a" xlink:href="note-0094-04"/>
            χ æqualis ei, qui ad ν. </s>
            <s xml:space="preserve">ergo angulus ad χ angulo ad σ, uidelicet eo,
              <lb/>
              <anchor type="note" xlink:label="note-0094-05a" xlink:href="note-0094-05"/>
            qui ad n minor erit: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea χ infra n cadet. </s>
            <s xml:space="preserve">linea igitur χ b
              <lb/>
              <anchor type="note" xlink:label="note-0094-06a" xlink:href="note-0094-06"/>
            maior eſt, quàm n b. </s>
            <s xml:space="preserve">Sed cum b c ſit æqualis χ b, & </s>
            <s xml:space="preserve">b s ipſi n b:
              <lb/>
            </s>
            <s xml:space="preserve">erit b c ipſa b s maior.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="left" xlink:label="note-0094-03" xlink:href="note-0094-03a" xml:space="preserve">D</note>
            <note position="left" xlink:label="note-0094-04" xlink:href="note-0094-04a" xml:space="preserve">5. ſecũdi
              <lb/>
            conicoiũ</note>
            <note position="left" xlink:label="note-0094-05" xlink:href="note-0094-05a" xml:space="preserve">29. primi.</note>
            <note position="left" xlink:label="note-0094-06" xlink:href="note-0094-06a" xml:space="preserve">35. primi
              <lb/>
            conicorũ</note>
          </div>
          <p>
            <s xml:space="preserve">Ergo æquales faciunt angulos a q, a m cum diametris
              <lb/>
              <anchor type="note" xlink:label="note-0094-07a" xlink:href="note-0094-07"/>
            portionum.</s>
            <s xml:space="preserve">] _Hoc demonstrabimus ut in commentarijs in ſecun-_
              <lb/>
            _dam partem_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="5">
            <note position="left" xlink:label="note-0094-07" xlink:href="note-0094-07a" xml:space="preserve">E</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Similiter demonſtrabitur, portionem, quæ ad humidũ_
              <lb/>
              <anchor type="note" xlink:label="note-0094-08a" xlink:href="note-0094-08"/>
            _in grauitate ean-_
              <lb/>
              <anchor type="figure" xlink:label="fig-0094-01a" xlink:href="fig-0094-01"/>
            _dem proportio-_
              <lb/>
            _nem habeat, quã_
              <lb/>
            _quadratum p fad_
              <lb/>
            _quadratũ b d; </s>
            <s xml:space="preserve">in_
              <lb/>
            _humidum demiſ-_
              <lb/>
            _ſam, ita ut baſis ip_
              <lb/>
            _ſius non cõtingat_
              <lb/>
            _humidum, incli-_
              <lb/>
            _natam conſiſtere_
              <lb/>
            _adeo, ut baſis in_
              <lb/>
            _uno pũcto humi-_
              <lb/>
            _di ſuperficiem cõ_
              <lb/>
            _tingat: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis cũ_
              <lb/>
            _ipſa faciat angulũ_
              <lb/>
            _angulo φ æqualẽ]_
              <lb/>
            Habeat portio ad humidum in grauitate proportionem eam, quam
              <lb/>
            p f quadratum ad quadratum b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">demiſſa in humidum adeo in-</s>
          </p>
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