Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
< >
page |< < (38) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div158" type="section" level="1" n="52">
          <p>
            <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>
          </p>
        </div>
      </text>
    </echo>