Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <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>
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