Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[81.] THE OREMA XII. PROPOSITIO XVI.
[82.] THE OREMA XIII. PROPOSITIO XVII.
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
[84.] THEOREMA XV. PROPOSITIO XIX.
[85.] THE OREMA XVI. PROPOSITIO XX.
[86.] THEOREMA XVII. PROPOSITIO XXI.
[87.] THE OREMA XVIII. PROPOSITIO XXII.
[88.] THEOREMA XIX. PROPOSITIO XXIII.
[89.] PROBLEMA V. PROPOSITIO XXIIII.
[90.] THEOREMA XX. PROPOSITIO XXV.
[91.] THEOREMA XXI. PROPOSITIO XXVI.
[92.] THEOREMA XXII. PROPOSITIO XXVII.
[93.] PROBLEMA VI. PROPOSITIO XX VIII.
[94.] THE OREMA XXIII. PROPOSITIO XXIX.
[95.] THEOREMA XXIIII. PROPOSITIO XXX.
[96.] THEOREMA XXV. PROPOSITIO XXXI.
[97.] FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.
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            _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-_
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              <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"/>
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            _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>
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