Archimedes, Archimedis De insidentibvs aqvae

List of thumbnails

< >
11
11 (4) 		12
12
13
13 (5) 		14
14
15
15 (6) 		16
16
17
17 		18
18
19
19 (2) 		20
20
< >
page |< < of 51 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div12" type="section" level="1" n="10">
          <p style="it">
            <s xml:id="echoid-s112" xml:space="preserve">
              <pb file="0012" n="12" rhead="DE IN SIDENTIBVS AQV AE"/>
            guram in r. </s>
            <s xml:id="echoid-s113" xml:space="preserve">Centrum autem terræ ſit K. </s>
            <s xml:id="echoid-s114" xml:space="preserve">Intelligatur autem quædam pyra-
              <lb/>
            mis comprendens figuram r, ſecundum quod & </s>
            <s xml:id="echoid-s115" xml:space="preserve">prius uerticem habens ſi-
              <lb/>
            gnum K. </s>
            <s xml:id="echoid-s116" xml:space="preserve">Secentur autem ipſius plana aſuperficie plani a, b, g, ſecundum a,
              <lb/>
            K, K, b. </s>
            <s xml:id="echoid-s117" xml:space="preserve">Accipiatur autem, & </s>
            <s xml:id="echoid-s118" xml:space="preserve">aliqua alia pyramis æqualis, & </s>
            <s xml:id="echoid-s119" xml:space="preserve">ſimilis huic.
              <lb/>
            </s>
            <s xml:id="echoid-s120" xml:space="preserve">Secentur autem ipſius plana a plano a, b, g, ſecundum K, b, K, g, deſcribatur
              <lb/>
            autem & </s>
            <s xml:id="echoid-s121" xml:space="preserve">quædam alterius ſphæræ ſuperficies in humido circa centrum K. </s>
            <s xml:id="echoid-s122" xml:space="preserve">
              <lb/>
            Sub ſolida autem magnitudine ſecetur ipſa ab eodem plano ſecundũ x, o, p. </s>
            <s xml:id="echoid-s123" xml:space="preserve">
              <lb/>
            Intelligatur autem, & </s>
            <s xml:id="echoid-s124" xml:space="preserve">magnitudo abſumpta ab humido quæ ſecundumh,
              <lb/>
            in poſteriori pyramide æqualis ſolidæ quæ ſecundum r, partes aũt humidi,
              <lb/>
            quòd in prima pyramide quæ ſub ſuperficiebus, quæ ſecundum ſuperficiem
              <lb/>
            x, o, & </s>
            <s xml:id="echoid-s125" xml:space="preserve">quod in ſecunda quæ ſub ſuperficiebus quę ſuperficie o p, ex quo ſunt
              <lb/>
            poſitæ, & </s>
            <s xml:id="echoid-s126" xml:space="preserve">continuæ inuicem non ſimiliter autem premuntur quæ quidẽ in
              <lb/>
            prima pyramide premitur a ſolida magnitudine, quæ ſecundumr, & </s>
            <s xml:id="echoid-s127" xml:space="preserve">ab hu
              <lb/>
            mido continente ipſas, & </s>
            <s xml:id="echoid-s128" xml:space="preserve">exiſtente in loco pyramidis, quæ ſecundum a, b, o,
              <lb/>
            x. </s>
            <s xml:id="echoid-s129" xml:space="preserve">Quæ autem in altera pyramide præmittitur ab humido continent ipſam
              <lb/>
            exiſtente in loco pyramidis qui ſecundum p, o, b, g, eſt autem, & </s>
            <s xml:id="echoid-s130" xml:space="preserve">grauitas
              <lb/>
            quæ ſccundum r, minor grauitate humidi, quod ſecundum h, quoniam ma-
              <lb/>
            gnitudinem quidem eſt æqualis. </s>
            <s xml:id="echoid-s131" xml:space="preserve">Solida autem magnitudo ſupponitur eß le
              <lb/>
            uior humido humidi continentis magnitudines r, b, eritq́ pyramidum æ-
              <lb/>
            qualis. </s>
            <s xml:id="echoid-s132" xml:space="preserve">Magis igitur premitur pars humidi quòd ſub ſuperficiebus, quæſe-
              <lb/>
            cundum periferiam o, p, expellet ergo quod minus premitur, & </s>
            <s xml:id="echoid-s133" xml:space="preserve">non manet
              <lb/>
            humidum non motum. </s>
            <s xml:id="echoid-s134" xml:space="preserve">Supponebatur autem non motum n n ergo demerge
              <lb/>
            tur tota, ſed erit aliquid ipſius extra ſuperficiem humidi.</s>
            <s xml:id="echoid-s135" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div14" type="section" level="1" n="11">
          <head xml:id="echoid-head17" xml:space="preserve">Theorema v. Propoſitio v.</head>
          <p>
            <s xml:id="echoid-s136" xml:space="preserve">Solidarum magnitudinum quæcunque fuerit leuior dimiſſa
              <lb/>
            in humidũ in tanto demergetur ut tanta moles humidi quan-
              <lb/>
            ta eſt moles demerſæ habeat æ qualem grauitatem cumtota ma
              <lb/>
            gnitudine.</s>
            <s xml:id="echoid-s137" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s138" xml:space="preserve">D Iſponantur autem eandem prioribus, & </s>
            <s xml:id="echoid-s139" xml:space="preserve">ſit humidum nou motum.
              <lb/>
            </s>
            <s xml:id="echoid-s140" xml:space="preserve">Sit autem ma nitudo e, z, b, t, leuior humido. </s>
            <s xml:id="echoid-s141" xml:space="preserve">Siigitur humidum eſt
              <lb/>
            non motum ſimiliter prementur partes ipſius ex æquo poſitæ, ſimi-
              <lb/>
            liter ergo premetur humidum quodſub ſuperficiebus, quæ ſecundum perife
              <lb/>
            rias x, o, & </s>
            <s xml:id="echoid-s142" xml:space="preserve">p, o. </s>
            <s xml:id="echoid-s143" xml:space="preserve">Quare æqualis eſt grauitas quæ premitur. </s>
            <s xml:id="echoid-s144" xml:space="preserve">eſt autem, & </s>
            <s xml:id="echoid-s145" xml:space="preserve">
              <lb/>
            bumidi grauitas, quod in prima pyramide ſine b, h, t, g, ſolido æqualis graui
              <lb/>
            tati bumidi, quod in altera pyramide ſiue r, s, c, y, humido palam igitur, ꝙ
              <lb/>
            grauitas magnitudinis e, Z, h, t, eſt æqualis grauitati humidir, s, c, y. </s>
            <s xml:id="echoid-s146" xml:space="preserve">Mani
              <lb/>
            feſtum igitur quòd tanta moles humidi quanta eſt demerſa pars ſolidæ ma
              <lb/>
            gnitudinis habet grauitatem æqualem toti magnitudini.</s>
            <s xml:id="echoid-s147" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum