Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div175" type="section" level="1" n="55">
          <p>
            <s xml:id="echoid-s2454" xml:space="preserve">
              <pb file="0094" n="94" rhead="ARCHIMEDIS"/>
            _quæ diametrum ſecet in ψ; </s>
            <s xml:id="echoid-s2455" xml:space="preserve">ſecet autem i m eandem in σ: </s>
            <s xml:id="echoid-s2456" xml:space="preserve">& </s>
            <s xml:id="echoid-s2457" xml:space="preserve">a q in_
              <lb/>
            _v. </s>
            <s xml:id="echoid-s2458" xml:space="preserve">Dico angulum a ν d angulo i σ d minoré eſſe. </s>
            <s xml:id="echoid-s2459" xml:space="preserve">angulus enimi ψ d_
              <lb/>
            _æqualis est angulo a ν d. </s>
            <s xml:id="echoid-s2460" xml:space="preserve">ſed angulus interior i ψ d minor eſt exte-_
              <lb/>
              <note position="left" xlink:label="note-0094-01" xlink:href="note-0094-01a" xml:space="preserve">29. primi</note>
            _riore i σ d. </s>
            <s xml:id="echoid-s2461" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s2462" xml:space="preserve">a ν d ipſo i σ d minor erit_.</s>
            <s xml:id="echoid-s2463" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">16. primi</note>
          <p style="it">
            <s xml:id="echoid-s2464" xml:space="preserve">_Et quoniam angulus, qui ad χ minor eſt angulo, qui ad_
              <lb/>
              <note position="left" xlink:label="note-0094-03" xlink:href="note-0094-03a" xml:space="preserve">D</note>
            _n.</s>
            <s xml:id="echoid-s2465" xml:space="preserve">]_ Ducantur per o duæ lineæ, o c quidem ad diametrum b d per-
              <lb/>
            pendicularis: </s>
            <s xml:id="echoid-s2466" xml:space="preserve">& </s>
            <s xml:id="echoid-s2467" xml:space="preserve">o χ in puncto o ſectionem contingens, quæ diame
              <lb/>
            trum ſecet in χ. </s>
            <s xml:id="echoid-s2468" xml:space="preserve">æquidiſtabit o χ ipſi a q: </s>
            <s xml:id="echoid-s2469" xml:space="preserve">atque erit angulus ad
              <lb/>
              <note position="left" xlink:label="note-0094-04" xlink:href="note-0094-04a" xml:space="preserve">5. ſecũdi
                <lb/>
              conicoiũ</note>
            χ æqualis ei, qui ad ν. </s>
            <s xml:id="echoid-s2470" xml:space="preserve">ergo angulus ad χ angulo ad σ, uidelicet eo,
              <lb/>
              <note position="left" xlink:label="note-0094-05" xlink:href="note-0094-05a" xml:space="preserve">29. primi.</note>
            qui ad n minor erit: </s>
            <s xml:id="echoid-s2471" xml:space="preserve">& </s>
            <s xml:id="echoid-s2472" xml:space="preserve">propterea χ infra n cadet. </s>
            <s xml:id="echoid-s2473" xml:space="preserve">linea igitur χ b
              <lb/>
              <note position="left" xlink:label="note-0094-06" xlink:href="note-0094-06a" xml:space="preserve">35. primi
                <lb/>
              conicorũ</note>
            maior eſt, quàm n b. </s>
            <s xml:id="echoid-s2474" xml:space="preserve">Sed cum b c ſit æqualis χ b, & </s>
            <s xml:id="echoid-s2475" xml:space="preserve">b s ipſi n b:
              <lb/>
            </s>
            <s xml:id="echoid-s2476" xml:space="preserve">erit b c ipſa b s maior.</s>
            <s xml:id="echoid-s2477" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2478" xml:space="preserve">Ergo æquales faciunt angulos a q, a m cum diametris
              <lb/>
              <note position="left" xlink:label="note-0094-07" xlink:href="note-0094-07a" xml:space="preserve">E</note>
            portionum.</s>
            <s xml:id="echoid-s2479" xml:space="preserve">] _Hoc demonstrabimus ut in commentarijs in ſecun-_
              <lb/>
            _dam partem_.</s>
            <s xml:id="echoid-s2480" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2481" xml:space="preserve">_Similiter demonſtrabitur, portionem, quæ ad humidũ_
              <lb/>
              <note position="left" xlink:label="note-0094-08" xlink:href="note-0094-08a" xml:space="preserve">F</note>
            _in grauitate ean-_
              <lb/>
              <figure xlink:label="fig-0094-01" xlink:href="fig-0094-01a" number="60">
                <image file="0094-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0094-01"/>
              </figure>
            _dem proportio-_
              <lb/>
            _nem habeat, quã_
              <lb/>
            _quadratum p fad_
              <lb/>
            _quadratũ b d; </s>
            <s xml:id="echoid-s2482" 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:id="echoid-s2483" xml:space="preserve">& </s>
            <s xml:id="echoid-s2484" 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:id="echoid-s2485" xml:space="preserve">& </s>
            <s xml:id="echoid-s2486" xml:space="preserve">demiſſa in humidum adeo </s>
          </p>
        </div>
      </text>
    </echo>