Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
31 10
32
33 11
34
35 12
36
37 13
38
39 14
40
41 15
42
43 16
44
45 17
46
47 18
48
49 19
50
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
< >
page |< < (39) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="53">
          <p>
            <s xml:space="preserve">
              <pb o="39" file="0089" n="89" rhead="DE IIS QVAE VEH. IN AQVA."/>
            _neæ autem a d inter ſe æquales ſunt. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">ipſæ a η, a θ. </s>
            <s xml:space="preserve">Sed ſunt_
              <lb/>
            _æquales a o, a q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">earum dimidiæ a t a n. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">reliquæ t η, n θ_
              <lb/>
            _boc eſt p g, m y. </s>
            <s xml:space="preserve">ut autem p g ad g h, ita m y ad y c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutan_
              <lb/>
              <anchor type="note" xlink:label="note-0089-01a" xlink:href="note-0089-01"/>
            _do, ut p g ad m y, ita g s ad y c. </s>
            <s xml:space="preserve">quare g s, y c æquales ſunt: </s>
            <s xml:space="preserve">&_</s>
            <s xml:space="preserve">
              <lb/>
            _ipſarum dimidiæ b s, b c: </s>
            <s xml:space="preserve">ex quibus ſequitur ut & </s>
            <s xml:space="preserve">reliquæ s r, c r_:
              <lb/>
            </s>
            <s xml:space="preserve">_& </s>
            <s xml:space="preserve">idcirco p z, m u & </s>
            <s xml:space="preserve">u n, z t inter ſe ſunt æquales_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="9">
            <note position="left" xlink:label="note-0088-05" xlink:href="note-0088-05a" xml:space="preserve">K</note>
            <figure xlink:label="fig-0088-01" xlink:href="fig-0088-01a">
              <image file="0088-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0088-01"/>
            </figure>
            <note position="left" xlink:label="note-0088-06" xlink:href="note-0088-06a" xml:space="preserve">4. ſexti.</note>
            <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">34. primi</note>
          </div>
          <p>
            <s xml:space="preserve">Quoniam igitur m u minor eſt, quàm dupla u n.</s>
            <s xml:space="preserve">] _Eſt_
              <lb/>
              <anchor type="note" xlink:label="note-0089-02a" xlink:href="note-0089-02"/>
            _enim m h ipſius h n dupla, & </s>
            <s xml:space="preserve">m u minor ipſa m h. </s>
            <s xml:space="preserve">ergo m u minor_
              <lb/>
            _eſt, quàm dupla h n; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">multo minor, quàm dupla ipſius u n_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="10">
            <note position="right" xlink:label="note-0089-02" xlink:href="note-0089-02a" xml:space="preserve">L</note>
          </div>
          <p>
            <s xml:space="preserve">Non ergo manebit portio, ſed reuoluetur, ita ut baſis ip
              <lb/>
              <anchor type="note" xlink:label="note-0089-03a" xlink:href="note-0089-03"/>
            ſius humidi ſuperſiciem nullo modo contingat. </s>
            <s xml:space="preserve">quoniam
              <lb/>
            nunc in uno puncto contingens ſurſum fertur ex parte a.</s>
            <s xml:space="preserve">]
              <lb/>
            _Tranſlatio ſic habet. </s>
            <s xml:space="preserve">non ergo manet portio ſed inclinabitur, ut ba_-
              <lb/>
            _ſis ipſius nec ſecundum unum tang at ſuperficiem humidi, quoniam_
              <lb/>
            _nunc ſecundum unum tacta ipſa reclinatur. </s>
            <s xml:space="preserve">Quæ nos ex alijs Ar_-
              <lb/>
            _chimedis locis, & </s>
            <s xml:space="preserve">perſpicuitatis cauſſa in eum modum corrigenda_
              <lb/>
            _duximus. </s>
            <s xml:space="preserve">In ſexta enim propoſitione huius ita ſcribit, ut habetur in_
              <lb/>
            _tranſlatione. </s>
            <s xml:space="preserve">reuoluetur ergo ſolidum a p o l, & </s>
            <s xml:space="preserve">baſis ipſius nó tan_
              <lb/>
            _get ſuperficiem humidi ſecundum unum ſignum. </s>
            <s xml:space="preserve">Rurſus in ſeptima_
              <lb/>
            _propoſitione. </s>
            <s xml:space="preserve">manifeſtum igitur, quòd reuoluetur ſolidum ita ut ba_-
              <lb/>
            _ſis ipſius nec ſecundum unum ſignum contingat ſuperficiem humidi_,
              <lb/>
            _quoniam nunc ſecundum unum tangens deorſum fertur ex parte l_.
              <lb/>
            </s>
            <s xml:space="preserve">_At uero portionem ſurſum ferri ex parte a manifeſte constat. </s>
            <s xml:space="preserve">nam_
              <lb/>
            _cumperpendicularis ad ſuperficiem humidi, quæ tranſit per ω ad_
              <lb/>
            _partes a cadat, & </s>
            <s xml:space="preserve">quæ per e ad partes l, neceſſe eſt ut centrum ω_
              <lb/>
            _ſurſum, e uero deorſum feratur_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="11">
            <note position="right" xlink:label="note-0089-03" xlink:href="note-0089-03a" xml:space="preserve">M</note>
          </div>
          <p>
            <s xml:space="preserve">Perſpicuum eſtigitur portionem conſiſtere ita, ut axis
              <lb/>
              <anchor type="note" xlink:label="note-0089-04a" xlink:href="note-0089-04"/>
            cum ſuperficie humidi faciat angulum maiorem angu-
              <lb/>
            10 χ.</s>
            <s xml:space="preserve">] _Iuncta enim a x producatur, ut diametrum b d ſe_-
              <lb/>
            _cet in λ, & </s>
            <s xml:space="preserve">ab o puncto ipſi æquidistans ducatur o χ. </s>
            <s xml:space="preserve">con_-
              <lb/>
            _tinget eaſectionem in o, ut in prima figura: </s>
            <s xml:space="preserve">atque erit angu_-
              <lb/>
              <anchor type="note" xlink:label="note-0089-05a" xlink:href="note-0089-05"/>
            _lus ad χ angulo ad λ æqualis. </s>
            <s xml:space="preserve">Sed angulus ad y æqualis est_
              <lb/>
            _angulo ad θ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">angulus a θ d maior angulo a λ d; </s>
            <s xml:space="preserve">quod ex_-
              <lb/>
              <anchor type="note" xlink:label="note-0089-06a" xlink:href="note-0089-06"/>
            _traipſum cadat. </s>
            <s xml:space="preserve">ergo angulus ad y eo, qui ad χ maior erit_.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>