Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
131 10
132
133 11
134
135 12
136
137 13
138
139 14
140
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
< >
page |< < of 213 > >|
ARCHIMEDIS
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="43">
          <pb file="0076" n="76" rhead="ARCHIMEDIS"/>
          <p style="it">
            <s xml:space="preserve">Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
              <lb/>
            ipſis ſectionibus in eandem proportionem ſecari. </s>
            <s xml:space="preserve">eſt enim
              <lb/>
            diuidendo, conuertendoque cm ad mb, & </s>
            <s xml:space="preserve">cf ad fb, ut
              <lb/>
            ce ad ea.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
        <div type="section" level="1" n="44">
          <head xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:space="preserve">Sed & </s>
            <s xml:space="preserve">illud constare potest; </s>
            <s 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: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:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">
              <emph style="sc">D_ividantvr_</emph>
            enim ch, cm bifariam in punctis p q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per
              <lb/>
            ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes. </s>
            <s xml:space="preserve">erit portio-
              <lb/>
            nis b s c diameter p s, & </s>
            <s xml:space="preserve">portionis m u c diameter q u. </s>
            <s 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:space="preserve">& </s>
            <s xml:space="preserve">ut quadratum c t ad quadratum c q, ita fiat f o ad
              <lb/>
            u y. </s>
            <s xml:space="preserve">iam exijs
              <lb/>
              <anchor type="figure" xlink:label="fig-0076-01a" xlink:href="fig-0076-01"/>
            quæ demóſtra
              <lb/>
            uimus in com-
              <lb/>
            mentarijs in
              <lb/>
            quartam pro-
              <lb/>
            poſitioné. </s>
            <s xml:space="preserve">Ar-
              <lb/>
            chrmedis de co
              <lb/>
            noidibus, & </s>
            <s 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:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>