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 |< < (22) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="38">
          <p>
            <s xml:space="preserve">
              <pb o="22" file="0067" n="67" rhead="DE IIS QVAE VEH. IN AQVA."/>
            dum eam, quæ per g ſurſum eleuabitur. </s>
            <s xml:space="preserve">non igitur manebit
              <lb/>
            portio ſic inclinata, nec conuertetur ita, ut axis ad ſuperfi-
              <lb/>
            ciem humidi ſit perpendicularis: </s>
            <s xml:space="preserve">quoniam quæ ex parte 1
              <lb/>
              <anchor type="note" xlink:label="note-0067-01a" xlink:href="note-0067-01"/>
            deorſum; </s>
            <s xml:space="preserve">quæ uero ex parte a ſurſum ferentur, ut ex iam de
              <lb/>
            monſtratis apparere poteſt. </s>
            <s xml:space="preserve">Quòd ſi axis cum ſuperficie
              <lb/>
            humidi fecerit angulum minorem angulo b, ſimiliter de-
              <lb/>
              <anchor type="note" xlink:label="note-0067-02a" xlink:href="note-0067-02"/>
            monſtrabitur, nõ manere portionem, ſed inclinari, donec
              <lb/>
            utique axis cum ſuperficie humidi faciat angulum angulo
              <lb/>
            b æqualem.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0064-01" xlink:href="fig-0064-01a">
              <image file="0064-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0064-01"/>
            </figure>
            <note position="left" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve">A</note>
            <note position="right" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">B</note>
            <note position="right" xlink:label="note-0065-02" xlink:href="note-0065-02a" xml:space="preserve">C</note>
            <note position="right" xlink:label="note-0065-03" xlink:href="note-0065-03a" xml:space="preserve">D</note>
            <note position="right" xlink:label="note-0065-04" xlink:href="note-0065-04a" xml:space="preserve">E</note>
            <figure xlink:label="fig-0066-01" xlink:href="fig-0066-01a">
              <image file="0066-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0066-01"/>
            </figure>
            <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">F</note>
            <note position="right" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">G</note>
          </div>
        </div>
        <div type="section" level="1" n="39">
          <head xml:space="preserve">COMMENTARIVS.</head>
          <p>
            <s xml:space="preserve">QVARE quadratum b d magis excedit quadratum
              <lb/>
              <anchor type="note" xlink:label="note-0067-03a" xlink:href="note-0067-03"/>
            f q, quàm b c quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco linea f q minor eſt,
              <lb/>
            quàm b c: </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">f minor quam b r.</s>
            <s xml:space="preserve">] _Quoniani exceſſus, quo_
              <lb/>
            _quadratum b d excedit quadratum b c ad quadratum b d minorem_
              <lb/>
            _proportionem habet, quàm exceſſus, quo quadratum b d excedit qua_
              <lb/>
            _dratum f q, ad idem quadratum: </s>
            <s xml:space="preserve">erit ex octaua quinti exceſſus, quo_
              <lb/>
            _quadratum b d excedit quadratum b c, minor quàm exceſſus, quo ex_
              <lb/>
            _cedit quadratum f q. </s>
            <s xml:space="preserve">ergo quadratum f q minus est quadrato b c: </s>
            <s xml:space="preserve">&_</s>
            <s xml:space="preserve">
              <lb/>
            _propterea linea f q minor linea b c. </s>
            <s xml:space="preserve">Sed f q ad f eandem proportionẽ_
              <lb/>
            _habet, quam b c ad b r; </s>
            <s xml:space="preserve">utraque enim utriuſque ſeſquialtera est. </s>
            <s xml:space="preserve">cum_
              <lb/>
              <anchor type="note" xlink:label="note-0067-04a" xlink:href="note-0067-04"/>
            _igitur f q ſit minor b c, & </s>
            <s xml:space="preserve">f ipſa b r minor erit_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <note position="right" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">A</note>
            <note position="right" xlink:label="note-0067-04" xlink:href="note-0067-04a" xml:space="preserve">14. quinti</note>
          </div>
          <p>
            <s xml:space="preserve">Et propterea k r ad ſ y maiorem habet, quàm dimidium
              <lb/>
              <anchor type="note" xlink:label="note-0067-05a" xlink:href="note-0067-05"/>
            ipſius k r ad ψ b.</s>
            <s xml:space="preserve">] _Est enim k r ad ſ y, ut quadratum p s ad qua_
              <lb/>
            _dratum ſ y
              <unsure/>
            : </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">dimidium lineæ K r ad lineam ψ b, ut quadratum e ψ_
              <lb/>
            _ad quadratum ψ b_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="right" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve">B</note>
          </div>
          <p>
            <s xml:space="preserve">Et s o minor quàm ψ b] _Est enim ſ y dupla ipſius ſ o._</s>
            <s xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">C</note>
          <p>
            <s xml:space="preserve">Et p h maior, quàm f.</s>
            <s xml:space="preserve">] _Nam p h eſt æqualis ſ ω, & </s>
            <s xml:space="preserve">r ψ_
              <lb/>
              <anchor type="note" xlink:label="note-0067-07a" xlink:href="note-0067-07"/>
            _ipſi f_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <note position="right" xlink:label="note-0067-07" xlink:href="note-0067-07a" xml:space="preserve">D</note>
          </div>
          <p>
            <s xml:space="preserve">Habebit ergo tota portio ad eam, quæ eſt extra humi-
              <lb/>
              <anchor type="note" xlink:label="note-0067-08a" xlink:href="note-0067-08"/>
            dum proportionem eandem, quam quadratum b d ad qua
              <lb/>
            dratum f q.</s>
            <s xml:space="preserve">] _Cum pars demerſa ad totam portionem ita ſit, ut_
              <lb/>
            _exceſſus, quo quadratum b d excedit quadratum f q ad b d quadratu
              <unsure/>
            :_</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum