Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
121 5
122
123 6
124
125 7
126
127 8
128
129 9
130
131 10
132
133 11
134
135 12
136
137 13
138
139 14
140
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
< >
page |< < (46) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="95">
          <p>
            <s xml:space="preserve">
              <pb o="46" file="0203" n="203" rhead="DE CENTRO GRAVIT. SOLID."/>
            ro ita demonſtrabitur. </s>
            <s xml:space="preserve">Ducatur à puncto b ad planum ba-
              <lb/>
            ſis a c perpendicularis linea b h, quæ ipſam e fin K ſecet.
              <lb/>
            </s>
            <s xml:space="preserve">erit b h altitudo coni, uel coni portionis a b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b K altitu
              <lb/>
              <anchor type="note" xlink:label="note-0203-01a" xlink:href="note-0203-01"/>
            do e f g. </s>
            <s xml:space="preserve">Quod cum lineæ a c, e f inter ſe æ quidiſtent, ſunt
              <lb/>
            enim planorum æ quidiſtantium ſectiones: </s>
            <s xml:space="preserve">habebit d b ad
              <lb/>
              <anchor type="note" xlink:label="note-0203-02a" xlink:href="note-0203-02"/>
            b g proportionem ean dem, quam h b ad b k. </s>
            <s xml:space="preserve">quare por-
              <lb/>
            tio conoidis a b c ad portionem e f g proportionem habet
              <lb/>
            compoſitam ex proportione baſis a c ad baſim e f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex
              <lb/>
            proportione d b axis ad axem b g. </s>
            <s xml:space="preserve">Sed circulus, uel
              <lb/>
              <anchor type="note" xlink:label="note-0203-03a" xlink:href="note-0203-03"/>
            ellipſis circa diametrum a c ad circulum, uel ellipſim
              <lb/>
              <anchor type="note" xlink:label="note-0203-04a" xlink:href="note-0203-04"/>
            circa e f, eſt ut quadratum a c ad quadratum e f; </s>
            <s xml:space="preserve">hoc eſt ut
              <lb/>
            quadratũ a d ad quadratũ e g. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quadratum a d ad quadra
              <lb/>
            tum e g eſt, ut linea d b ad lineam b g. </s>
            <s xml:space="preserve">circulus igitur, uel el
              <lb/>
            lipſis circa diametrum a c ad circulũ, uel ellipſim circa e f,
              <lb/>
              <anchor type="note" xlink:label="note-0203-05a" xlink:href="note-0203-05"/>
            hoc eſt baſis ad baſim eandem proportionem habet, quã
              <lb/>
              <anchor type="note" xlink:label="note-0203-06a" xlink:href="note-0203-06"/>
            d b axis ad axem b g. </s>
            <s xml:space="preserve">ex quibus ſequitur portionem a b c
              <lb/>
            ad portionem e b f habere proportionem duplam eius,
              <lb/>
            quæ eſt baſis a c ad bafim e f: </s>
            <s xml:space="preserve">uel axis d b ad b g axem. </s>
            <s xml:space="preserve">quod
              <lb/>
            demonſtrandum proponebatur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0202-01" xlink:href="fig-0202-01a">
              <image file="0202-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0202-01"/>
            </figure>
            <note position="right" xlink:label="note-0203-01" xlink:href="note-0203-01a" xml:space="preserve">16. unde-
              <lb/>
            cimi.</note>
            <note position="right" xlink:label="note-0203-02" xlink:href="note-0203-02a" xml:space="preserve">4 ſexti.</note>
            <note position="right" xlink:label="note-0203-03" xlink:href="note-0203-03a" xml:space="preserve">2. duode
              <lb/>
            cimi</note>
            <note position="right" xlink:label="note-0203-04" xlink:href="note-0203-04a" xml:space="preserve">7. de co-
              <lb/>
            noidibus
              <lb/>
            & ſphæ-
              <lb/>
            roidibus</note>
            <note position="right" xlink:label="note-0203-05" xlink:href="note-0203-05a" xml:space="preserve">15. quinti</note>
            <note position="right" xlink:label="note-0203-06" xlink:href="note-0203-06a" xml:space="preserve">20. primi
              <lb/>
            conicorũ</note>
          </div>
        </div>
        <div type="section" level="1" n="96">
          <head xml:space="preserve">THEOREMA XXV. PROPOSITIO XXXI.</head>
          <p>
            <s xml:space="preserve">Cuiuslibet fruſti à portione rectanguli conoi
              <lb/>
            dis abſcisſi, centrum grauitatis eſt in axe, ita ut
              <lb/>
            demptis primum à quadrato, quod fit ex diame-
              <lb/>
            tro maioris baſis, tertia ipſius parte, & </s>
            <s xml:space="preserve">duabus
              <lb/>
            tertiis quadrati, quod fit ex diametro baſis mino-
              <lb/>
            ris: </s>
            <s xml:space="preserve">deinde à tertia parte quadrati maioris baſis
              <lb/>
            rurſus dempta portione, ad quam reliquum qua
              <lb/>
            drati baſis maioris unà cum dicta portione duplã
              <lb/>
            proportionem habeat eius, quæ eſt quadrati ma-</s>
          </p>
        </div>
      </text>
    </echo>