Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
181 35
182
183 36
184
185 37
186
187 38
188
189 39
190
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div8" type="section" level="1" n="8">
          <pb file="0014" n="14" rhead="ARCHIMEDIS"/>
          <p>
            <s xml:id="echoid-s105" xml:space="preserve">SECETVR ſuperficies aliqua plano per k punctum
              <lb/>
            ducto: </s>
            <s xml:id="echoid-s106" xml:space="preserve">& </s>
            <s xml:id="echoid-s107" xml:space="preserve">ſicſectio ſemper circuli circunferentia, centrum
              <lb/>
            habens punctum k. </s>
            <s xml:id="echoid-s108" xml:space="preserve">Dico eam ſphæræ ſuperficiem eſſe. </s>
            <s xml:id="echoid-s109" xml:space="preserve">Si
              <lb/>
            enim non eſt ſphæræ ſuperfi-
              <lb/>
              <figure xlink:label="fig-0014-01" xlink:href="fig-0014-01a" number="4">
                <image file="0014-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0014-01"/>
              </figure>
            cies; </s>
            <s xml:id="echoid-s110" xml:space="preserve">rectæ lineæ, quæ à pun-
              <lb/>
            cto k ad circunferentiam du-
              <lb/>
            cuntur non omnes æquales e-
              <lb/>
            runt. </s>
            <s xml:id="echoid-s111" xml:space="preserve">Itaque ſint a b puncta
              <lb/>
            in ſuperficie; </s>
            <s xml:id="echoid-s112" xml:space="preserve">& </s>
            <s xml:id="echoid-s113" xml:space="preserve">inæquales li-
              <lb/>
            neæ a k k b: </s>
            <s xml:id="echoid-s114" xml:space="preserve">per ipſas autem
              <lb/>
            a k k b planum ducatur, quod
              <lb/>
            ſectionem faciat in ſuperficie
              <lb/>
            lineam d a b c. </s>
            <s xml:id="echoid-s115" xml:space="preserve">ergo d a b c cir
              <lb/>
            culi circunferentia eſt, cuius
              <lb/>
            centrum k; </s>
            <s xml:id="echoid-s116" xml:space="preserve">quoniam ſuperficies eiuſmodi ponebatur: </s>
            <s xml:id="echoid-s117" xml:space="preserve">& </s>
            <s xml:id="echoid-s118" xml:space="preserve">
              <lb/>
            idcirco æquales inter ſe ſunt a k k b, ſed & </s>
            <s xml:id="echoid-s119" xml:space="preserve">inæquales; </s>
            <s xml:id="echoid-s120" xml:space="preserve">quod
              <lb/>
            fieri non poteſt. </s>
            <s xml:id="echoid-s121" xml:space="preserve">conſtat igitur ſuperficiem eam eſſe ſphæ-
              <lb/>
            ræ ſuperficiem.</s>
            <s xml:id="echoid-s122" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div10" type="section" level="1" n="9">
          <head xml:id="echoid-head12" xml:space="preserve">PROPOSITIO II.</head>
          <p>
            <s xml:id="echoid-s123" xml:space="preserve">
              <emph style="sc">Omnis</emph>
            humidi conſiſtentis, atque manen-
              <lb/>
            tis ſuperficies ſphærica eſt; </s>
            <s xml:id="echoid-s124" xml:space="preserve">cuius ſphæræ centrũ
              <lb/>
            eſtidem, quod centrum terræ.</s>
            <s xml:id="echoid-s125" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s126" xml:space="preserve">INTELLIGATVR humidũ conſiſtens, manẽsq;</s>
            <s xml:id="echoid-s127" xml:space="preserve">:
              <lb/>
            & </s>
            <s xml:id="echoid-s128" xml:space="preserve">ſecetur ipſius ſuperficies plano per centrum terræ du-
              <lb/>
            cto. </s>
            <s xml:id="echoid-s129" xml:space="preserve">ſit autem terræ centrum k: </s>
            <s xml:id="echoid-s130" xml:space="preserve">& </s>
            <s xml:id="echoid-s131" xml:space="preserve">ſuperficieiſectio, linea
              <lb/>
            a b c d. </s>
            <s xml:id="echoid-s132" xml:space="preserve">Dico lineam a b c d circuli circunferentiam eſſe, cu
              <lb/>
            ius centrum k. </s>
            <s xml:id="echoid-s133" xml:space="preserve">Si enim non eſt, rectæ lineæ à puncto k ad
              <lb/>
            lineam a b c d ductæ non erunt æquales. </s>
            <s xml:id="echoid-s134" xml:space="preserve">Sumatur recta li
              <lb/>
            nea quibuſdam quidem à puncto k ad ipſam a b c d ductis
              <lb/>
            maior; </s>
            <s xml:id="echoid-s135" xml:space="preserve">quibuſdam uero minor; </s>
            <s xml:id="echoid-s136" xml:space="preserve">& </s>
            <s xml:id="echoid-s137" xml:space="preserve">ex centro k, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum