Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
31 10
32
33 11
34
35 12
36
37 13
38
39 14
40
41 15
42
43 16
44
45 17
46
47 18
48
49 19
50
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
< >
page |< < (15) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="26">
          <p>
            <s xml:space="preserve">
              <pb o="15" file="0041" n="41" rhead="DE IIS QVAE VEH. IN AQVA."/>
            _quare per o ductaipſi al æquidiſtans cadet extra ſectionem ex 17._
              <lb/>
            </s>
            <s xml:space="preserve">_primi conicorum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cum b p producta coibit inſra p. </s>
            <s xml:space="preserve">ergò & </s>
            <s xml:space="preserve">per-_
              <lb/>
            _pendicularis ducta per b cum eadem infra b coibit, at que inter b &_</s>
            <s xml:space="preserve">
              <lb/>
            _p neceſſario cadet. </s>
            <s xml:space="preserve">multo autem magis illud idem ſequetur, ſi pona-_
              <lb/>
            _mus pf ipſa om maiorem eſſe._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="6">
            <note position="left" xlink:label="note-0040-08" xlink:href="note-0040-08a" xml:space="preserve">G</note>
            <figure xlink:label="fig-0040-01" xlink:href="fig-0040-01a">
              <image file="0040-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0040-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Et quoniam p f quidem æquidiſtans eſt diametro, htau
              <lb/>
              <anchor type="note" xlink:label="note-0041-01a" xlink:href="note-0041-01"/>
            tem ad diametrum perpendicularis; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rh æqualis ei, quæ
              <lb/>
            uſque ad axem, ducta linea ab r ad e, & </s>
            <s xml:space="preserve">producta angulos
              <lb/>
            rectos facere cum linea ſectionem in p contingente.</s>
            <s xml:space="preserve">]
              <lb/>
            _Hoc ſuperius à nobis demonſtratum eſt in ſecundam buin
              <unsure/>
            s._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="7">
            <note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">H</note>
          </div>
        </div>
        <div type="section" level="1" n="27">
          <head xml:space="preserve">PROPOSITIO V.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            leuior humido axem habuerit maiorem, quàm
              <lb/>
            ſeſquialterum eius, quæ uſque ad axem; </s>
            <s xml:space="preserve">ſi ad hu-
              <lb/>
            midum in grauitate non maiorem proportionẽ
              <lb/>
            habeat, quàm exceſſus, quo quadratum quod ſit
              <lb/>
            ab axe maius eſt quadrato, quod ab exceſſu, quo
              <lb/>
            axis maior eſt, quàm ſeſquialter eius, quæ uſque
              <lb/>
            ad axem, ad quadratum, quod ab axe: </s>
            <s xml:space="preserve">demiſſa in
              <lb/>
            humidum, ita ut baſis ipſius tota ſit in humido;
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">poſita inclinata non manebit inclinata, ſed re-
              <lb/>
            ſtituetur ita, ut axis ipſius ſecundum perpendi-
              <lb/>
            cularem fiat.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">DEMITTATVR enim in humidum portio aliqna,
              <lb/>
            qualis dicta eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit baſis ipſius tota in humido. </s>
            <s xml:space="preserve">Secta au-
              <lb/>
            tem ipſa plano per axem, recto ad ſuperſiciem humidi, erit
              <lb/>
            ſectio rectanguli coniſectio, quæ ſit apol: </s>
            <s xml:space="preserve">axis portionis,</s>
          </p>
        </div>
      </text>
    </echo>