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-div24" type="section" level="1" n="17">
          <p>
            <s xml:id="echoid-s366" xml:space="preserve">
              <pb file="0024" n="24" rhead="ARCHIMEDIS"/>
            in linea ft. </s>
            <s xml:id="echoid-s367" xml:space="preserve">nam ſit primum figura maior dimidia ſphære:
              <lb/>
            </s>
            <s xml:id="echoid-s368" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s369" xml:space="preserve">in dimidia ſphæra ſphæræ centrum t; </s>
            <s xml:id="echoid-s370" xml:space="preserve">in minori por-
              <lb/>
            tioneſit centrum p; </s>
            <s xml:id="echoid-s371" xml:space="preserve">& </s>
            <s xml:id="echoid-s372" xml:space="preserve">in maiori _k_: </s>
            <s xml:id="echoid-s373" xml:space="preserve">per _k_ uero, & </s>
            <s xml:id="echoid-s374" xml:space="preserve">terræ cen
              <lb/>
            trum l ducatur _k_ l ſecans circunferentiam e f h in pun-
              <lb/>
            cto n. </s>
            <s xml:id="echoid-s375" xml:space="preserve">Quoniam igitur unaquæque ſphæræportio axem
              <lb/>
              <note position="left" xlink:label="note-0024-01" xlink:href="note-0024-01a" xml:space="preserve">C</note>
            habet in linea, quæ à cẽtro ſphæræ ad cius baſim perpen-
              <lb/>
            dicularis ducitur: </s>
            <s xml:id="echoid-s376" xml:space="preserve">habetq; </s>
            <s xml:id="echoid-s377" xml:space="preserve">in axe grauitatis centrum:
              <lb/>
            </s>
            <s xml:id="echoid-s378" xml:space="preserve">portionis in humido demerſæ, quæ ex duabus ſphæræ
              <lb/>
            portionibus conſtat, axis erit in perpendiculari per _k_ du-
              <lb/>
            cta. </s>
            <s xml:id="echoid-s379" xml:space="preserve">& </s>
            <s xml:id="echoid-s380" xml:space="preserve">idcirco centrum grauitatis ipſius erit in linea n _k_,
              <lb/>
            quod ſit r. </s>
            <s xml:id="echoid-s381" xml:space="preserve">ſed totius portionis grauitatis centrum eſt in li
              <lb/>
              <note position="left" xlink:label="note-0024-02" xlink:href="note-0024-02a" xml:space="preserve">D</note>
            nea f t inter _k_, & </s>
            <s xml:id="echoid-s382" xml:space="preserve">f, quod ſit x. </s>
            <s xml:id="echoid-s383" xml:space="preserve">reliquæ ergo figuræ, quæ eſt
              <lb/>
              <note position="left" xlink:label="note-0024-03" xlink:href="note-0024-03a" xml:space="preserve">E</note>
            extra humidum, centrum erit in linea r x producta ad par
              <lb/>
            tes x; </s>
            <s xml:id="echoid-s384" xml:space="preserve">& </s>
            <s xml:id="echoid-s385" xml:space="preserve">aſſumpta ex ea, linea quadam, quæ ad r x eandem
              <lb/>
            proportionem habeat, quam grauitas portionis in humi-
              <lb/>
            do demerſæ habet ad grauitatem figuræ, quæ eſt extra hu-
              <lb/>
            midum. </s>
            <s xml:id="echoid-s386" xml:space="preserve">Sit autem s centrum dictæ figuræ: </s>
            <s xml:id="echoid-s387" xml:space="preserve">& </s>
            <s xml:id="echoid-s388" xml:space="preserve">per s duca-
              <lb/>
            tur perpendicularis l s. </s>
            <s xml:id="echoid-s389" xml:space="preserve">Feretur ergo grauitas figuræ qui-
              <lb/>
              <note position="left" xlink:label="note-0024-04" xlink:href="note-0024-04a" xml:space="preserve">F</note>
            dem, quæ extra humidum per rectam s l deorſum; </s>
            <s xml:id="echoid-s390" xml:space="preserve">portio
              <lb/>
            nis autem, quæ in humido, ſurſum per rectam r l. </s>
            <s xml:id="echoid-s391" xml:space="preserve">quare
              <lb/>
            non manebit figura: </s>
            <s xml:id="echoid-s392" xml:space="preserve">ſed partes eius, quæ ſunt ad e, deor-
              <lb/>
            ſum; </s>
            <s xml:id="echoid-s393" xml:space="preserve">& </s>
            <s xml:id="echoid-s394" xml:space="preserve">quæ ad h ſurſum ſerẽtur: </s>
            <s xml:id="echoid-s395" xml:space="preserve">idq; </s>
            <s xml:id="echoid-s396" xml:space="preserve">cõtinenter fiet, quoad
              <lb/>
            ſ t ſit ſecundum perpendicularem. </s>
            <s xml:id="echoid-s397" xml:space="preserve">Eodem modo in aliis
              <lb/>
            portionibus idem demonſtrabitur.</s>
            <s xml:id="echoid-s398" xml:space="preserve">]</s>
          </p>
          <figure number="13">
            <image file="0024-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0024-01"/>
          </figure>
        </div>
      </text>
    </echo>