Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
101 43
102
103
104
105
106
107
108
109
110
< >
page |< < (17) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="29">
          <pb o="17" file="0045" n="45" rhead="DE IIS QVAE VEH. IN AQVA."/>
          <p>
            <s xml:space="preserve">SIT portio, qualis dicta eſt, & </s>
            <s xml:space="preserve">in humidum demittatur,
              <lb/>
            ſicuti diximus, adeo ut baſis eius in uno puncto contingat
              <lb/>
            humidum. </s>
            <s xml:space="preserve">demonſtrandum eſtnon manere ipſam portio-
              <lb/>
            nem, ſed reuoluiita, ut baſis nullo modo humidi ſuperſicie
              <lb/>
              <anchor type="note" xlink:label="note-0045-01a" xlink:href="note-0045-01"/>
            contingat. </s>
            <s xml:space="preserve">Secta enim ipſa per axem, plano ad ſuper ſiciem
              <lb/>
            humidi recto, ſit ſectio ſuperſiciei portionis a p o l re-
              <lb/>
            ctãguli coni ſe
              <lb/>
              <anchor type="figure" xlink:label="fig-0045-01a" xlink:href="fig-0045-01"/>
            ctio: </s>
            <s xml:space="preserve">ſuperſi-
              <lb/>
            ciei humidi ſe-
              <lb/>
            ctio ſit a s: </s>
            <s xml:space="preserve">axis
              <lb/>
            autem portio-
              <lb/>
            nis, ac ſectio-
              <lb/>
            nis diameter n
              <lb/>
            o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſccetur in
              <lb/>
            f quidẽ ita, ut
              <lb/>
            o f ſit dupla ip
              <lb/>
            ſius ſn; </s>
            <s xml:space="preserve">in ω ue
              <lb/>
            ro, ut n o ad
              <lb/>
            f ω eandem ha
              <lb/>
            beat proportionem, quam quindecim ad quatuor: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ipſi
              <lb/>
            n o ad rectos angulos ducatur ω k. </s>
            <s xml:space="preserve">Itaque quoniam n o
              <lb/>
              <anchor type="note" xlink:label="note-0045-02a" xlink:href="note-0045-02"/>
            ad f ω maiorem habet proportionem, quàm ad eam, quæ
              <lb/>
            uſque ad axem; </s>
            <s xml:space="preserve">ſit ei, quæ uſque ad axem æqualis f b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">du
              <lb/>
            catur p c quidem ipſi a s æquidiſtans, cõtingensq; </s>
            <s xml:space="preserve">ſectio-
              <lb/>
            nem a p o l in p; </s>
            <s xml:space="preserve">pi uero æquidiſtans ipſi n o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">primum
              <lb/>
            ſecet pi ipſam κ ω in h. </s>
            <s xml:space="preserve">Quoniã ergo in portione a p o l,
              <lb/>
              <anchor type="note" xlink:label="note-0045-03a" xlink:href="note-0045-03"/>
            quæ continetur recta linea, & </s>
            <s xml:space="preserve">rectanguli coni ſectione, κ ω
              <lb/>
            quidem æ quidiſtans eſtipſi a l; </s>
            <s xml:space="preserve">p i uero diametro æquidi-
              <lb/>
            ſtat: </s>
            <s xml:space="preserve">ſecaturq; </s>
            <s xml:space="preserve">ab ipſa κ ω in h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a s æquidiſtat contingen-
              <lb/>
            ti in p: </s>
            <s xml:space="preserve">neceſſarium eſtipſam p i ad p h uel ean dem pro-
              <lb/>
            portionem habere, quam habet n ω ad ω o, uel maiorem:
              <lb/>
            </s>
            <s xml:space="preserve">hocenim iam demonſtratum eſt. </s>
            <s xml:space="preserve">At uero n ω ſeſquialtera
              <lb/>
            eſt ipſius ω o. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pi igitur uel ſeſquialtera eſt ipſius h p; </s>
            <s xml:space="preserve">
              <lb/>
            uel maior, quàm ſeſquialtera. </s>
            <s xml:space="preserve">Quare ph ipſius h i aut du
              <lb/>
              <anchor type="note" xlink:label="note-0045-04a" xlink:href="note-0045-04"/>
            </s>
          </p>
        </div>
      </text>
    </echo>