Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s2222" xml:space="preserve">
              <pb o="38" file="0087" n="87" rhead="DE IIS QVAE VEH. IN AQVA."/>
            æqualibus, & </s>
            <s xml:id="echoid-s2223" xml:space="preserve">ſimilibus, a p o l, a m q l ab extremitati-
              <lb/>
            bus baſium ductæ ſint a o, a q ita, ut portiones ablatæ
              <lb/>
            faciant cum diametris angulos æquales; </s>
            <s xml:id="echoid-s2224" xml:space="preserve">& </s>
            <s xml:id="echoid-s2225" xml:space="preserve">anguli, qui
              <lb/>
            ad y g: </s>
            <s xml:id="echoid-s2226" xml:space="preserve">& </s>
            <s xml:id="echoid-s2227" xml:space="preserve">lineæ y b, g b, & </s>
            <s xml:id="echoid-s2228" xml:space="preserve">b c, b s inter ſe æquales erunt.
              <lb/>
            </s>
            <s xml:id="echoid-s2229" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s2230" xml:space="preserve">ipſæ c r, s r: </s>
            <s xml:id="echoid-s2231" xml:space="preserve">& </s>
            <s xml:id="echoid-s2232" xml:space="preserve">m u, p z: </s>
            <s xml:id="echoid-s2233" xml:space="preserve">& </s>
            <s xml:id="echoid-s2234" xml:space="preserve">u n, z t. </s>
            <s xml:id="echoid-s2235" xml:space="preserve">Quo-
              <lb/>
              <note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">L</note>
            niam igitur m u minor eſt, quàm dupla u n; </s>
            <s xml:id="echoid-s2236" xml:space="preserve">conſtat p z ip-
              <lb/>
            ſius z t minorem eſſe, quàm duplam. </s>
            <s xml:id="echoid-s2237" xml:space="preserve">Sit p α dupla ipſius
              <lb/>
            ω t: </s>
            <s xml:id="echoid-s2238" xml:space="preserve">& </s>
            <s xml:id="echoid-s2239" xml:space="preserve">iuncta α k ad e producatur. </s>
            <s xml:id="echoid-s2240" xml:space="preserve">ergo totius quidem por
              <lb/>
            tionis centrum grauitatis erit puntum κ; </s>
            <s xml:id="echoid-s2241" xml:space="preserve">partis eius, quæ
              <lb/>
            in humido eſt, centrum ω; </s>
            <s xml:id="echoid-s2242" xml:space="preserve">eius uero, quæ extra humidum
              <lb/>
            in linea k e, quod ſit e. </s>
            <s xml:id="echoid-s2243" xml:space="preserve">Sed linea k z perpendicularis erit
              <lb/>
            ad ſuperficiem humidi. </s>
            <s xml:id="echoid-s2244" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s2245" xml:space="preserve">lineæ quæ per puncta e,
              <lb/>
            ω, æ quidiſtantes ipſi κ z ducuntur. </s>
            <s xml:id="echoid-s2246" xml:space="preserve">non ergo manebit por-
              <lb/>
              <note position="right" xlink:label="note-0087-02" xlink:href="note-0087-02a" xml:space="preserve">M</note>
            tio, ſed reuoluetur ita, ut baſis ipſius ſuperficiem humidi
              <lb/>
            nullo modo contingat: </s>
            <s xml:id="echoid-s2247" xml:space="preserve">quoniã nuncin uno puncto contin
              <lb/>
            gens, ſurſum fertur ex parte a. </s>
            <s xml:id="echoid-s2248" xml:space="preserve">perſpicuum eſt igitur por-
              <lb/>
              <note position="right" xlink:label="note-0087-03" xlink:href="note-0087-03a" xml:space="preserve">N</note>
            tionem conſiſt ere ita, ut axis cum ſuperſicie humidi faciat
              <lb/>
            angulum maiorem angulo χ.</s>
            <s xml:id="echoid-s2249" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div160" type="section" level="1" n="53">
          <head xml:id="echoid-head58" xml:space="preserve">COMMENTARIVS.</head>
          <p>
            <s xml:id="echoid-s2250" xml:space="preserve">Siportio ad humidum in grauitate minorẽ proportio-
              <lb/>
              <note position="right" xlink:label="note-0087-04" xlink:href="note-0087-04a" xml:space="preserve">A</note>
            nem habeat; </s>
            <s xml:id="echoid-s2251" xml:space="preserve">quàm quadratum s b ad quadratum b d; </s>
            <s xml:id="echoid-s2252" xml:space="preserve">ma-
              <lb/>
            iorem uero, quàm quadratum x o ad b d quadratum.</s>
            <s xml:id="echoid-s2253" xml:space="preserve">] _Hæc_
              <lb/>
            _eſt ſecunda pars propoſitionis, quam aliæ deinceps, postea ipſarum_
              <lb/>
            _demonstrationes eodem ordine ſequuntur_.</s>
            <s xml:id="echoid-s2254" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2255" xml:space="preserve">SI portio ad humidum in grauitate maiorem quidem
              <lb/>
              <note position="right" xlink:label="note-0087-05" xlink:href="note-0087-05a" xml:space="preserve">B</note>
            proportionẽ habeat, quàm quadratũ f p ad quadratũb d.</s>
            <s xml:id="echoid-s2256" xml:space="preserve">]
              <lb/>
            _Hãc quartá parté nos reſtituimus, quæ ĩ trãſlatione deſiderabatur_.</s>
            <s xml:id="echoid-s2257" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2258" xml:space="preserve">Erit ψ maior quidem, quàm x o, minor uero, quàm ex-
              <lb/>
              <note position="right" xlink:label="note-0087-06" xlink:href="note-0087-06a" xml:space="preserve">C</note>
            ceſſus, quo axis eſt maior, quam ſeſquialter eius, quæ uſque
              <lb/>
            ad axem,] _Sequitur illud ex decima quinti libri elementornm_.</s>
            <s xml:id="echoid-s2259" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2260" xml:space="preserve">Demonſtrabitur m h duplaipſius h n, ſicuti demonſtra
              <lb/>
              <note position="right" xlink:label="note-0087-07" xlink:href="note-0087-07a" xml:space="preserve">D</note>
            tũ eſt o gipſius g x duplam eſſe.</s>
            <s xml:id="echoid-s2261" xml:space="preserve">] _Vt in prima parte huius, &_</s>
            <s xml:id="echoid-s2262" xml:space="preserve">
              <lb/>
            _exijs, quæ nos proxime in ipſam conſcripſimus_.</s>
            <s xml:id="echoid-s2263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2264" xml:space="preserve">Quoniam enim in ſimilibus portionibus a p o l, a x d,
              <lb/>
              <note position="right" xlink:label="note-0087-08" xlink:href="note-0087-08a" xml:space="preserve">E</note>
            </s>
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