Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
181 35
182
183 36
184
185 37
186
187 38
188
189 39
190
191 40
192
193 41
194
195 42
196
197 43
198
199 44
200
201 45
202
203 46
204
205 47
206
207
208
209
210
< >
page |< < (45) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="94">
          <p>
            <s xml:space="preserve">
              <pb o="45" file="0201" n="201" rhead="DE CENTRO GRAVIT. SOLID."/>
            ad punctum ω. </s>
            <s xml:space="preserve">Sed quoniam π circum ſcripta itidem alia
              <lb/>
            figura æquali interuallo ad portionis centrum accedit, ubi
              <lb/>
            primum φ applieuerit ſe ad ω, & </s>
            <s xml:space="preserve">π ad punctũ ψ, hoc eſt ad
              <lb/>
            portionis centrum ſe applicabit. </s>
            <s xml:space="preserve">quod fieri nullo modo
              <lb/>
            poſſe perſpicuum eſt. </s>
            <s xml:space="preserve">non aliter idem abſurdum ſequetur,
              <lb/>
            ſi ponamus centrum portionis recedere à medio ad par-
              <lb/>
            tes ω; </s>
            <s xml:space="preserve">eſſet enim aliquando centrum figuræ inſcriptæ idem
              <lb/>
            quod portionis centrũ. </s>
            <s xml:space="preserve">ergo punctum e centrum erit gra
              <lb/>
            uitatis portionis a b c. </s>
            <s xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0195-01" xlink:href="fig-0195-01a">
              <image file="0195-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0195-01"/>
            </figure>
            <note position="right" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">7. huius</note>
            <figure xlink:label="fig-0196-01" xlink:href="fig-0196-01a">
              <image file="0196-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0196-01"/>
            </figure>
            <note position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">8. primi
              <lb/>
            libri Ar-
              <lb/>
            chimedis</note>
            <note position="left" xlink:label="note-0196-02" xlink:href="note-0196-02a" xml:space="preserve">11. duo-
              <lb/>
            decimi.</note>
            <note position="left" xlink:label="note-0196-03" xlink:href="note-0196-03a" xml:space="preserve">15. quinti</note>
            <note position="left" xlink:label="note-0196-04" xlink:href="note-0196-04a" xml:space="preserve">2. duode-
              <lb/>
            cimi.</note>
            <note position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">20. primi
              <lb/>
            conicorũ</note>
            <figure xlink:label="fig-0198-01" xlink:href="fig-0198-01a">
              <image file="0198-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0198-01"/>
            </figure>
            <note position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">19. quinti</note>
            <figure xlink:label="fig-0200-01" xlink:href="fig-0200-01a">
              <image file="0200-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0200-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Quod autem ſupra demõſtratum eſt in portione conoi-
              <lb/>
            dis recta per figuras, quæ ex cylindris æqualem altitudi-
              <lb/>
            dinem habentibus conſtant, idem ſimiliter demonſtrabi-
              <lb/>
            mus per figuras ex cylindri portionibus conſtantes in ea
              <lb/>
            portione, quæ plano non ad axem recto abſcinditur. </s>
            <s xml:space="preserve">ut
              <lb/>
            enim tradidimus in commentariis in undecimam propoſi
              <lb/>
            tionem libri Archimedis de conoidibus & </s>
            <s xml:space="preserve">ſphæroidibus.
              <lb/>
            </s>
            <s xml:space="preserve">portiones cylindri, quæ æquali ſunt altitudine eam inter ſe
              <lb/>
            ſe proportionem habent, quam ipſarum baſes; </s>
            <s xml:space="preserve">baſes autẽ
              <lb/>
            quæ ſunt ellipſes ſimiles eandem proportionem habere,
              <lb/>
              <anchor type="note" xlink:label="note-0201-01a" xlink:href="note-0201-01"/>
            quam quadrata diametrorum eiuſdem rationis, ex corol-
              <lb/>
            lario ſeptimæ propoſitionis libri de conoidibus, & </s>
            <s xml:space="preserve">ſphæ-
              <lb/>
            roidibus, manifeſte apparet.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">corol. 15
              <lb/>
            deconoi-
              <lb/>
            dibus &
              <lb/>
            ſphæroi-
              <lb/>
            dibus.</note>
          </div>
        </div>
        <div type="section" level="1" n="95">
          <head xml:space="preserve">THEOREMA XXIIII. PROPOSITIO XXX.</head>
          <p>
            <s xml:space="preserve">SI à portione conoidis rectanguli alia portio
              <lb/>
            abſcindatur, plano baſi æquidiſtante; </s>
            <s xml:space="preserve">habebit
              <lb/>
            portio tota ad eam, quæ abſciſſa eſt, duplam pro
              <lb/>
            portio nem eius, quæ eſt baſis maioris portionis
              <lb/>
            ad baſi m minoris, uel quæ axis maioris ad axem
              <lb/>
            minoris.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>