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-div41" type="section" level="1" n="22">
          <p>
            <s xml:id="echoid-s590" xml:space="preserve">
              <pb file="0032" n="32" rhead="ARCHIMEDIS"/>
            ceatinclinata. </s>
            <s xml:id="echoid-s591" xml:space="preserve">Demonſtrandum eſt non manere ipſam; </s>
            <s xml:id="echoid-s592" xml:space="preserve">ſed
              <lb/>
            rectam reſtitui. </s>
            <s xml:id="echoid-s593" xml:space="preserve">Itaque ſecta ipſa plano per axem, recto ad
              <lb/>
            planum, quod eſt in ſuperficie humidi, portionis ſectio ſit
              <lb/>
            a p o l rectanguli coni ſectio: </s>
            <s xml:id="echoid-s594" xml:space="preserve">axis portionis, & </s>
            <s xml:id="echoid-s595" xml:space="preserve">ſectionis
              <lb/>
            diameter n o: </s>
            <s xml:id="echoid-s596" xml:space="preserve">ſuperficiei autem humidi ſectio ſit i s. </s>
            <s xml:id="echoid-s597" xml:space="preserve">Si
              <lb/>
            igitur portio non eſt recta; </s>
            <s xml:id="echoid-s598" xml:space="preserve">non utique erit a l ipſi i s æ-
              <lb/>
            quidiſtans. </s>
            <s xml:id="echoid-s599" xml:space="preserve">quare n o cum i s non faciet angulos rectos.
              <lb/>
            </s>
            <s xml:id="echoid-s600" xml:space="preserve">ducatur crgo k ω contingens ſectionem coni in p [quæ
              <lb/>
              <note position="left" xlink:label="note-0032-01" xlink:href="note-0032-01a" xml:space="preserve">Suppleta
                <lb/>
              a. Federi-
                <lb/>
              co Cõm.</note>
            ipſi i s æquidiſtet: </s>
            <s xml:id="echoid-s601" xml:space="preserve">& </s>
            <s xml:id="echoid-s602" xml:space="preserve">à puncto p ad i s ducatur p f æquidi
              <lb/>
            ſtans ipſi o n, quæ erit ſectionis i p o s diameter, & </s>
            <s xml:id="echoid-s603" xml:space="preserve">axis por
              <lb/>
              <note position="left" xlink:label="note-0032-02" xlink:href="note-0032-02a" xml:space="preserve">B</note>
            tionis in humido demerſæ. </s>
            <s xml:id="echoid-s604" xml:space="preserve">ſumantur deinde centra graui
              <lb/>
            tatum: </s>
            <s xml:id="echoid-s605" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s606" xml:space="preserve">ſolidæ magnitudinis a p o l grauitatis centrũ
              <lb/>
              <note position="left" xlink:label="note-0032-03" xlink:href="note-0032-03a" xml:space="preserve">C</note>
            r; </s>
            <s xml:id="echoid-s607" xml:space="preserve">ipſius uero i p o s centrum ſit b: </s>
            <s xml:id="echoid-s608" xml:space="preserve">& </s>
            <s xml:id="echoid-s609" xml:space="preserve">iuncta b r produca-
              <lb/>
              <note position="left" xlink:label="note-0032-04" xlink:href="note-0032-04a" xml:space="preserve">D</note>
            tur ad g, quod ſit centrum grauitatis reliquæ figuræ i s l a.
              <lb/>
            </s>
            <s xml:id="echoid-s610" xml:space="preserve">Quoniam igitur n o ipſius quidem r o ſeſquialtera eſt; </s>
            <s xml:id="echoid-s611" xml:space="preserve">
              <lb/>
            eius autẽ, quæ uſque ad axẽ minor, quam ſeſquialtera; </s>
            <s xml:id="echoid-s612" xml:space="preserve">erit
              <lb/>
              <note position="left" xlink:label="note-0032-05" xlink:href="note-0032-05a" xml:space="preserve">E</note>
            r o minor, quàm quæ uſque ad axem. </s>
            <s xml:id="echoid-s613" xml:space="preserve">Quare angulus r p ω
              <lb/>
              <note position="left" xlink:label="note-0032-06" xlink:href="note-0032-06a" xml:space="preserve">F</note>
            acutus erit: </s>
            <s xml:id="echoid-s614" xml:space="preserve">cum enim linea, quæ uſque ad axem maior ſit
              <lb/>
            ipſa r o; </s>
            <s xml:id="echoid-s615" xml:space="preserve">quæ à puncto r ad k ω perpendicularis ducitur,
              <lb/>
            uidelicet r t, cũ
              <lb/>
              <figure xlink:label="fig-0032-01" xlink:href="fig-0032-01a" number="19">
                <image file="0032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0032-01"/>
              </figure>
            linea f p extra
              <lb/>
            ſectionem con
              <lb/>
            ueniet: </s>
            <s xml:id="echoid-s616" xml:space="preserve">& </s>
            <s xml:id="echoid-s617" xml:space="preserve">pro-
              <lb/>
            pterea inter p
              <lb/>
            & </s>
            <s xml:id="echoid-s618" xml:space="preserve">ω puncta ca-
              <lb/>
            datneceſſe eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s619" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s620" xml:space="preserve">ſi per b g
              <lb/>
            ducantur lineæ
              <lb/>
            ipſi r t æquidi-
              <lb/>
            ſtantes; </s>
            <s xml:id="echoid-s621" xml:space="preserve">angu-
              <lb/>
            los rectos cum
              <lb/>
            ſuperficie humidi continebunt: </s>
            <s xml:id="echoid-s622" xml:space="preserve">& </s>
            <s xml:id="echoid-s623" xml:space="preserve">quod in humido eſt ſur-
              <lb/>
              <note position="left" xlink:label="note-0032-07" xlink:href="note-0032-07a" xml:space="preserve">G</note>
            ſum feretur ſecundum perpendicularem, quæ per b ducta
              <lb/>
            eſt, ipſi r t æquidiſtans: </s>
            <s xml:id="echoid-s624" xml:space="preserve">quod uero eſt extra humi dum </s>
          </p>
        </div>
      </text>
    </echo>
Impressum