Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div175" type="section" level="1" n="55">
          <p style="it">
            <s xml:id="echoid-s2517" xml:space="preserve">
              <pb file="0096" n="96" rhead="ARCHIMEDIS"/>
            minor erit: </s>
            <s xml:id="echoid-s2518" xml:space="preserve">linea uero b c maior, quàm b s: </s>
            <s xml:id="echoid-s2519" xml:space="preserve">& </s>
            <s xml:id="echoid-s2520" xml:space="preserve">s r; </s>
            <s xml:id="echoid-s2521" xml:space="preserve">hoc eſt m χ ma-
              <lb/>
            ior, quàm c r, hoc eſt, quàm p y: </s>
            <s xml:id="echoid-s2522" xml:space="preserve">& </s>
            <s xml:id="echoid-s2523" xml:space="preserve">propterea χ t minor, quàm y f.
              <lb/>
            </s>
            <s xml:id="echoid-s2524" xml:space="preserve">quòd cum p y ſit dupla y f, erit m χ maior, quàm dupla y f; </s>
            <s xml:id="echoid-s2525" xml:space="preserve">& </s>
            <s xml:id="echoid-s2526" xml:space="preserve">
              <lb/>
            multo maior, quàm dupla χ t. </s>
            <s xml:id="echoid-s2527" xml:space="preserve">fiat m h dupla ipſius h t: </s>
            <s xml:id="echoid-s2528" xml:space="preserve">& </s>
            <s xml:id="echoid-s2529" xml:space="preserve">copu-
              <lb/>
            lata h k producatur. </s>
            <s xml:id="echoid-s2530" xml:space="preserve">I am grauitatis centrum totius portionis erit
              <lb/>
            punctum k: </s>
            <s xml:id="echoid-s2531" xml:space="preserve">eius, quæ in humido est, h: </s>
            <s xml:id="echoid-s2532" xml:space="preserve">at rel iquæ partis, quæ ex-
              <lb/>
            tra humidum in linea h k producta; </s>
            <s xml:id="echoid-s2533" xml:space="preserve">quod ſit ω. </s>
            <s xml:id="echoid-s2534" xml:space="preserve">eodem modo demon
              <lb/>
            strabitur, & </s>
            <s xml:id="echoid-s2535" xml:space="preserve">lineam k h, & </s>
            <s xml:id="echoid-s2536" xml:space="preserve">quæ per h ω puncta ipſi k h æquidi-
              <lb/>
            ſtantes ducuntur, ad humidi ſuperficiem perpendiculares eſſe. </s>
            <s xml:id="echoid-s2537" xml:space="preserve">non
              <lb/>
            igitur maneb it
              <lb/>
              <figure xlink:label="fig-0096-01" xlink:href="fig-0096-01a" number="62">
                <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0096-01"/>
              </figure>
            portio, ſed cum
              <lb/>
            uſque eò inclina-
              <lb/>
            ta fuerit, ut in
              <lb/>
            uno puncto con-
              <lb/>
            tingat ſuperfi-
              <lb/>
            cié humidi, tunc
              <lb/>
            conſiſtet. </s>
            <s xml:id="echoid-s2538" xml:space="preserve">an-
              <lb/>
            gulus enim ad n
              <lb/>
            angulo ad φ æ-
              <lb/>
            qualis erit; </s>
            <s xml:id="echoid-s2539" xml:space="preserve">li-
              <lb/>
            neáq; </s>
            <s xml:id="echoid-s2540" xml:space="preserve">b s lineæ
              <lb/>
            b c; </s>
            <s xml:id="echoid-s2541" xml:space="preserve">& </s>
            <s xml:id="echoid-s2542" xml:space="preserve">s r ipſi
              <lb/>
            c r. </s>
            <s xml:id="echoid-s2543" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s2544" xml:space="preserve">m h
              <lb/>
            ipſi p y eſt æqua
              <lb/>
            lis. </s>
            <s xml:id="echoid-s2545" xml:space="preserve">Itaque ducta
              <lb/>
            h k producatur.
              <lb/>
            </s>
            <s xml:id="echoid-s2546" xml:space="preserve">erit totius portionis grauitatis centrum K; </s>
            <s xml:id="echoid-s2547" xml:space="preserve">eius, quæ in humido eſt
              <lb/>
            h; </s>
            <s xml:id="echoid-s2548" xml:space="preserve">& </s>
            <s xml:id="echoid-s2549" xml:space="preserve">reliquæ partis centrum in linea producta; </s>
            <s xml:id="echoid-s2550" xml:space="preserve">ſit autem ω. </s>
            <s xml:id="echoid-s2551" xml:space="preserve">per ean
              <lb/>
            dem igitur rectam lineam k h, quæ eſt ad humidi ſuperficiem perpen
              <lb/>
            dicularis, id quod in humido eſt ſurſum; </s>
            <s xml:id="echoid-s2552" xml:space="preserve">& </s>
            <s xml:id="echoid-s2553" xml:space="preserve">quod extra humidum de
              <lb/>
            orſum feretur. </s>
            <s xml:id="echoid-s2554" xml:space="preserve">atque ob hác cauſſam portio non amplius mouebitur; </s>
            <s xml:id="echoid-s2555" xml:space="preserve">
              <lb/>
            ſed conſiſtet, manebítq, ita, ut eius baſis ſuperficiem humidi in uno
              <lb/>
            punsto contingat; </s>
            <s xml:id="echoid-s2556" xml:space="preserve">& </s>
            <s xml:id="echoid-s2557" xml:space="preserve">axis, cum ipſa angulum faciat æqualem angulo
              <lb/>
            φ. </s>
            <s xml:id="echoid-s2558" xml:space="preserve">at que illud eſt, quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s2559" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum