Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
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
< >
page |< < (22) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div111" type="section" level="1" n="38">
          <p>
            <s xml:id="echoid-s1612" 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:id="echoid-s1613" 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:id="echoid-s1614" xml:space="preserve">quoniam quæ ex parte 1
              <lb/>
              <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">F</note>
            deorſum; </s>
            <s xml:id="echoid-s1615" xml:space="preserve">quæ uero ex parte a ſurſum ferentur, ut ex iam de
              <lb/>
            monſtratis apparere poteſt. </s>
            <s xml:id="echoid-s1616" xml:space="preserve">Quòd ſi axis cum ſuperficie
              <lb/>
            humidi fecerit angulum minorem angulo b, ſimiliter de-
              <lb/>
              <note position="right" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">G</note>
            monſtrabitur, nõ manere portionem, ſed inclinari, donec
              <lb/>
            utique axis cum ſuperficie humidi faciat angulum angulo
              <lb/>
            b æqualem.</s>
            <s xml:id="echoid-s1617" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div113" type="section" level="1" n="39">
          <head xml:id="echoid-head44" xml:space="preserve">COMMENTARIVS.</head>
          <p>
            <s xml:id="echoid-s1618" xml:space="preserve">QVARE quadratum b d magis excedit quadratum
              <lb/>
              <note position="right" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">A</note>
            f q, quàm b c quadratum: </s>
            <s xml:id="echoid-s1619" xml:space="preserve">& </s>
            <s xml:id="echoid-s1620" xml:space="preserve">idcirco linea f q minor eſt,
              <lb/>
            quàm b c: </s>
            <s xml:id="echoid-s1621" xml:space="preserve">itemq; </s>
            <s xml:id="echoid-s1622" xml:space="preserve">f minor quam b r.</s>
            <s xml:id="echoid-s1623" 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:id="echoid-s1624" 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:id="echoid-s1625" xml:space="preserve">ergo quadratum f q minus est quadrato b c: </s>
            <s xml:id="echoid-s1626" xml:space="preserve">&_</s>
            <s xml:id="echoid-s1627" xml:space="preserve">
              <lb/>
            _propterea linea f q minor linea b c. </s>
            <s xml:id="echoid-s1628" xml:space="preserve">Sed f q ad f eandem proportionẽ_
              <lb/>
            _habet, quam b c ad b r; </s>
            <s xml:id="echoid-s1629" xml:space="preserve">utraque enim utriuſque ſeſquialtera est. </s>
            <s xml:id="echoid-s1630" xml:space="preserve">cum_
              <lb/>
              <note position="right" xlink:label="note-0067-04" xlink:href="note-0067-04a" xml:space="preserve">14. quinti</note>
            _igitur f q ſit minor b c, & </s>
            <s xml:id="echoid-s1631" xml:space="preserve">f ipſa b r minor erit_.</s>
            <s xml:id="echoid-s1632" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1633" xml:space="preserve">Et propterea k r ad ſ y maiorem habet, quàm dimidium
              <lb/>
              <note position="right" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve">B</note>
            ipſius k r ad ψ b.</s>
            <s xml:id="echoid-s1634" xml:space="preserve">] _Est enim k r ad ſ y, ut quadratum p s ad qua_
              <lb/>
            _dratum ſ y
              <unsure/>
            : </s>
            <s xml:id="echoid-s1635" xml:space="preserve">& </s>
            <s xml:id="echoid-s1636" xml:space="preserve">dimidium lineæ K r ad lineam ψ b, ut quadratum e ψ_
              <lb/>
            _ad quadratum ψ b_.</s>
            <s xml:id="echoid-s1637" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1638" xml:space="preserve">Et s o minor quàm ψ b] _Est enim ſ y dupla ipſius ſ o._</s>
            <s xml:id="echoid-s1639" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">C</note>
          <p>
            <s xml:id="echoid-s1640" xml:space="preserve">Et p h maior, quàm f.</s>
            <s xml:id="echoid-s1641" xml:space="preserve">] _Nam p h eſt æqualis ſ ω, & </s>
            <s xml:id="echoid-s1642" xml:space="preserve">r ψ_
              <lb/>
              <note position="right" xlink:label="note-0067-07" xlink:href="note-0067-07a" xml:space="preserve">D</note>
            _ipſi f_.</s>
            <s xml:id="echoid-s1643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1644" xml:space="preserve">Habebit ergo tota portio ad eam, quæ eſt extra humi-
              <lb/>
              <note position="right" xlink:label="note-0067-08" xlink:href="note-0067-08a" xml:space="preserve">E</note>
            dum proportionem eandem, quam quadratum b d ad qua
              <lb/>
            dratum f q.</s>
            <s xml:id="echoid-s1645" 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:id="echoid-s1646" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>