Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div137" type="section" level="1" n="43">
          <pb file="0076" n="76" rhead="ARCHIMEDIS"/>
          <p style="it">
            <s xml:id="echoid-s1916" xml:space="preserve">Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
              <lb/>
            ipſis ſectionibus in eandem proportionem ſecari. </s>
            <s xml:id="echoid-s1917" xml:space="preserve">eſt enim
              <lb/>
            diuidendo, conuertendoque cm ad mb, & </s>
            <s xml:id="echoid-s1918" xml:space="preserve">cf ad fb, ut
              <lb/>
            ce ad ea.</s>
            <s xml:id="echoid-s1919" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div139" type="section" level="1" n="44">
          <head xml:id="echoid-head49" xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:id="echoid-s1920" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1921" xml:space="preserve">illud constare potest; </s>
            <s xml:id="echoid-s1922" xml:space="preserve">lineas, quæ in portioni-
              <lb/>
            bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
              <lb/>
            les angulos contineant, ab ipſis ſimiles quoque portiones
              <lb/>
            abſcindere: </s>
            <s xml:id="echoid-s1923" xml:space="preserve">hoc eſt, ut in propoſita figura, portiones h b c,
              <lb/>
            m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
              <lb/>
            ſimiles eſſe.</s>
            <s xml:id="echoid-s1924" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1925" xml:space="preserve">
              <emph style="sc">D_ividantvr_</emph>
            enim ch, cm bifariam in punctis p q: </s>
            <s xml:id="echoid-s1926" xml:space="preserve">& </s>
            <s xml:id="echoid-s1927" xml:space="preserve">per
              <lb/>
            ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes. </s>
            <s xml:id="echoid-s1928" xml:space="preserve">erit portio-
              <lb/>
            nis b s c diameter p s, & </s>
            <s xml:id="echoid-s1929" xml:space="preserve">portionis m u c diameter q u. </s>
            <s xml:id="echoid-s1930" xml:space="preserve">Itaque fiat
              <lb/>
            ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
              <lb/>
            quæ ſit s x: </s>
            <s xml:id="echoid-s1931" xml:space="preserve">& </s>
            <s xml:id="echoid-s1932" xml:space="preserve">ut quadratum c t ad quadratum c q, ita fiat f o ad
              <lb/>
            u y. </s>
            <s xml:id="echoid-s1933" xml:space="preserve">iam exijs
              <lb/>
              <figure xlink:label="fig-0076-01" xlink:href="fig-0076-01a" number="47">
                <image file="0076-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0076-01"/>
              </figure>
            quæ demóſtra
              <lb/>
            uimus in com-
              <lb/>
            mentarijs in
              <lb/>
            quartam pro-
              <lb/>
            poſitioné. </s>
            <s xml:id="echoid-s1934" xml:space="preserve">Ar-
              <lb/>
            chrmedis de co
              <lb/>
            noidibus, & </s>
            <s xml:id="echoid-s1935" xml:space="preserve">
              <lb/>
            ſphæroidibus,
              <lb/>
            patet quadra-
              <lb/>
            tum c p æqua-
              <lb/>
            le eſſe rectan-
              <lb/>
            gulo p s x:</s>
            <s xml:id="echoid-s1936" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>