Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
111
112
113 1
114
115 2
116
117 3
118
119 4
120
< >
page |< < (47) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="96">
          <p>
            <s xml:space="preserve">
              <pb o="47" file="0205" n="205" rhead="DE CENTRO GRAVIT. SOLID."/>
            eani proportionem habeat, quam a b c d fruſtum ad por-
              <lb/>
            tionem a g d; </s>
            <s xml:space="preserve">erit punctum l eius fruſti grauitatis cẽtrum:
              <lb/>
            </s>
            <s xml:space="preserve">habebitq; </s>
            <s xml:space="preserve">componendo K l ad 1 h proportionem eandem,
              <lb/>
            quam portio conoidis b gc ad a g d portionem. </s>
            <s xml:space="preserve">Itaq; </s>
            <s xml:space="preserve">quo
              <lb/>
              <anchor type="note" xlink:label="note-0205-01a" xlink:href="note-0205-01"/>
            niam quadratum b f ad quadratum a e, hoc eſt quadratum
              <lb/>
            b c ad quadratum a d eſt, ut linea f g ad g e: </s>
            <s xml:space="preserve">erunt duæ ter-
              <lb/>
            tiæ quadrati b c ad duas tertias quadrati a d, ut h g ad g _k_:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi à duabus tertiis quadrati b c demptæ fuerint duæ ter-
              <lb/>
            tiæ quadrati a d: </s>
            <s xml:space="preserve">erit diuidẽdo id, quod relinquitur ad duas
              <lb/>
            tertias quadrati a d, ut h k ad k g. </s>
            <s xml:space="preserve">Rurſus duæ tertiæ quadra
              <lb/>
            ti a d ad duas tertias quadrati b c ſunt, ut _k_ g ad g h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">duæ
              <lb/>
            tertiæ quadrati b c ad tertiã partẽ ipſius, ut g h ad h f. </s>
            <s xml:space="preserve">ergo
              <lb/>
            ex æ quali id, quod relinquitur ex duabus tertiis quadrati
              <lb/>
            b c, demptis ab ipſis quadrati a d duabus tertiis, ad tertiã
              <lb/>
            partem quadrati b c, ut _k_ h ad h f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ad portionem eiuſdẽ
              <lb/>
            tertiæ partis, ad quam unà cum ipſa portione, duplam pro
              <lb/>
            portionem habeat eius, quæ eſt quadrati b c ad quadratũ
              <lb/>
            a d, ut K 1 ad 1 h. </s>
            <s xml:space="preserve">habet enim _K_l ad 1 h ean dem proportio-
              <lb/>
            nem, quam conoidis portio b g c ad portionem a g d: </s>
            <s xml:space="preserve">por-
              <lb/>
            tio autem b g c ad portionem a g d duplam proportionem
              <lb/>
            habet eius, quæ eſt baſis b c ad baſim a d: </s>
            <s xml:space="preserve">hoc eſt quadrati
              <lb/>
            b c ad quadratum a d; </s>
            <s xml:space="preserve">ut proxime demonſtratum eſt. </s>
            <s xml:space="preserve">quare
              <lb/>
              <anchor type="note" xlink:label="note-0205-02a" xlink:href="note-0205-02"/>
            dempto a d quadrato à duabus tertiis quadrati b c, erit id,
              <lb/>
            quod relin quitur unà cum dicta portione tertiæ partis ad
              <lb/>
            reliquam eiuſdem portionem, ut el ad 1 f. </s>
            <s xml:space="preserve">Cum igitur cen-
              <lb/>
            trum grauitatis fruſti a b c d ſit l, à quo axis e f in eam, quã
              <lb/>
            diximus, proportionem diuidatur; </s>
            <s xml:space="preserve">conſtat uerũ eſſe illud,
              <lb/>
            quod demonſtrandum propoſuimus.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0204-01" xlink:href="fig-0204-01a">
              <image file="0204-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0204-01"/>
            </figure>
            <note position="right" xlink:label="note-0205-01" xlink:href="note-0205-01a" xml:space="preserve">20. I. coni
              <lb/>
            corum.</note>
            <note position="right" xlink:label="note-0205-02" xlink:href="note-0205-02a" xml:space="preserve">30. huius</note>
          </div>
        </div>
        <div type="section" level="1" n="97">
          <head xml:space="preserve">FINIS LIBRI DE CENTRO
            <lb/>
          GRAVITATIS SOLIDORVM.</head>
          <p>
            <s xml:space="preserve">Impreſſ. </s>
            <s xml:space="preserve">Bononiæ cum licentia Superiorum.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>