Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
161 25
162
163 26
164
165 27
166
167 28
168
169 29
170
171 30
172
173 31
174
175 32
176
177 33
178
179 34
180
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div44" type="section" level="1" n="23">
          <pb file="0034" n="34" rhead="ARCHIMEDIS"/>
          <p style="it">
            <s xml:id="echoid-s655" xml:space="preserve">_Erit r o minor, quàm, quæ uſque ad axem]_ Ex decima
              <lb/>
              <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">E</note>
            propoſitione quinti libri elementorum. </s>
            <s xml:id="echoid-s656" xml:space="preserve">Linea, quæ uſque ad axem
              <lb/>
            apud Archimedem, eſt dimidia eius, iuxta quam poſſunt, quæ à ſe-
              <lb/>
            ctione ducuntur; </s>
            <s xml:id="echoid-s657" xml:space="preserve">ut ex quarta propoſitione libri de conoidibus, & </s>
            <s xml:id="echoid-s658" xml:space="preserve">
              <lb/>
            ſphæroidibus apparet. </s>
            <s xml:id="echoid-s659" xml:space="preserve">cur uero ita appellata ſit, nos in commentarijs
              <lb/>
            in eam editis tradidimus.</s>
            <s xml:id="echoid-s660" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s661" xml:space="preserve">_Quare angulus r p ω acutus erit]_ producatur linea n o ad
              <lb/>
              <note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve">F</note>
            h, ut ſit r h æqualis ei, quæ uſque ad axem. </s>
            <s xml:id="echoid-s662" xml:space="preserve">ſi igitur à puncto h du-
              <lb/>
            catur linea ad rectos angulos ipſi n h, conueniet cum f p extra ſe-
              <lb/>
            ctionem: </s>
            <s xml:id="echoid-s663" xml:space="preserve">ducta enim per o ipſi a l æquidiſtans, extra ſectionem ca
              <lb/>
            dit ex decima ſepti-
              <lb/>
              <figure xlink:label="fig-0034-01" xlink:href="fig-0034-01a" number="20">
                <image file="0034-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0034-01"/>
              </figure>
            ma primi libri coni-
              <lb/>
            corum. </s>
            <s xml:id="echoid-s664" xml:space="preserve">Itaque con-
              <lb/>
            ueniat in u. </s>
            <s xml:id="echoid-s665" xml:space="preserve">& </s>
            <s xml:id="echoid-s666" xml:space="preserve">quo
              <lb/>
            niam f p est æqui-
              <lb/>
            distans diametro;
              <lb/>
            </s>
            <s xml:id="echoid-s667" xml:space="preserve">h u uero ad diame-
              <lb/>
            trum perpendicula-
              <lb/>
            ris; </s>
            <s xml:id="echoid-s668" xml:space="preserve">& </s>
            <s xml:id="echoid-s669" xml:space="preserve">r h æqualis
              <lb/>
            ei, quæ uſq; </s>
            <s xml:id="echoid-s670" xml:space="preserve">ad axẽ,
              <lb/>
            linea à puncto r ad
              <lb/>
            u ducta angulos re-
              <lb/>
            ctos faciet cum ea, quæ ſectionem in puncto p contingit, hoc eſt cum
              <lb/>
            k ω, ut mox demonstrabitur. </s>
            <s xml:id="echoid-s671" xml:space="preserve">quare perpendicularis r t inter p & </s>
            <s xml:id="echoid-s672" xml:space="preserve">
              <lb/>
            ω cadet; </s>
            <s xml:id="echoid-s673" xml:space="preserve">erítque r p ω angulus acutus.</s>
            <s xml:id="echoid-s674" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s675" xml:space="preserve">Sit rectanguli coni ſectio, ſeu parabole a b c, cuius
              <lb/>
            diameter b d: </s>
            <s xml:id="echoid-s676" xml:space="preserve">atque ipſam contingat linea e f in pun-
              <lb/>
            cto g: </s>
            <s xml:id="echoid-s677" xml:space="preserve">ſumatur autem in diametro b d linea h k æqua-
              <lb/>
            lis ei, quæ uſque ad axem: </s>
            <s xml:id="echoid-s678" xml:space="preserve">& </s>
            <s xml:id="echoid-s679" xml:space="preserve">per g ducta g l, diame-
              <lb/>
            tro æquidistante, à puncto _k_ ad rectos angulos ipſi b d
              <lb/>
            ducatur _k_ m, ſecans g l in m. </s>
            <s xml:id="echoid-s680" xml:space="preserve">Dico lineam ab h </s>
          </p>
        </div>
      </text>
    </echo>
Impressum