Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div216" type="section" level="1" n="73">
          <p>
            <s xml:id="echoid-s3559" xml:space="preserve">
              <pb file="0140" n="140" rhead="FED. COMMANDINI"/>
            habeat circulus, uel ellipſis g h ad aliud ſpacium, in quo u:
              <lb/>
            </s>
            <s xml:id="echoid-s3560" xml:space="preserve">& </s>
            <s xml:id="echoid-s3561" xml:space="preserve">in circulo, uel ellipſi plane deſcribatur rectilinea figura,
              <lb/>
            ita ut tãdem relinquãtur portiones minores ſpacio u, quæ
              <lb/>
            ſit o p g q r s h t: </s>
            <s xml:id="echoid-s3562" xml:space="preserve">deſcriptaq; </s>
            <s xml:id="echoid-s3563" xml:space="preserve">ſimili figura in oppoſitis pla-
              <lb/>
            nis c d, f e, per lineas ſibi ipſis reſpondentes plana ducãtur. </s>
            <s xml:id="echoid-s3564" xml:space="preserve">
              <lb/>
            Itaque cylindrus, uel cylindri portio diuiditur in priſma,
              <lb/>
            cuius quidem baſis eſt figura rectilinea iam dicta, centrum
              <lb/>
            que grauitatis punctum K: </s>
            <s xml:id="echoid-s3565" xml:space="preserve">& </s>
            <s xml:id="echoid-s3566" xml:space="preserve">in multa ſolida, quæ pro baſi
              <lb/>
            bus habent relictas portiones, quas nos ſolidas portiones
              <lb/>
            appellabimus. </s>
            <s xml:id="echoid-s3567" xml:space="preserve">cum igitur portiones ſint minores ſpacio
              <lb/>
            u, circulus, uel ellipſis g h ad portiones maiorem propor-
              <lb/>
            tionem habebit, quàm linea m k ad K l. </s>
            <s xml:id="echoid-s3568" xml:space="preserve">fiat n k ad K l, ut
              <lb/>
            circulus uel ellipſis g h ad ipſas portiones. </s>
            <s xml:id="echoid-s3569" xml:space="preserve">Sed ut circulus
              <lb/>
            uel ellipſis g h ad figuram rectilineam in ipſa deſcri-
              <lb/>
            ptam, ita eſt cylindrus uel cylindri portio c e ad priſma,
              <lb/>
            quod rectilineam figuram pro baſi habet, & </s>
            <s xml:id="echoid-s3570" xml:space="preserve">altitudinem
              <lb/>
            æqualem; </s>
            <s xml:id="echoid-s3571" xml:space="preserve">id, quod infra demonſtrabitur, ergo per conuer
              <lb/>
            ſionem rationis, ut circulus, uel ellipſis g h ad portiones re
              <lb/>
            lictas, ita cylindrus, uel cylindri portio c e ad ſolidas por-
              <lb/>
            tiones, quare cylindrus uel cylindri portio ad ſolidas por-
              <lb/>
            tiones eandem proportionem habet, quam linea n k a d _k_
              <lb/>
            & </s>
            <s xml:id="echoid-s3572" xml:space="preserve">diuidendo priſma, cuius baſis eſt rectilinea figura ad ſo-
              <lb/>
            lidas portiones eandem proportionem habet, quam n lad
              <lb/>
            1 _k_. </s>
            <s xml:id="echoid-s3573" xml:space="preserve">& </s>
            <s xml:id="echoid-s3574" xml:space="preserve">quoniam a cylindro uel cylindri portione, cuius gra-
              <lb/>
            uitatis centrum eſt l, aufertur priſma baſim habens rectili-
              <lb/>
            neam figurã, cuius centrũ grauitatis eſt _K_: </s>
            <s xml:id="echoid-s3575" xml:space="preserve">reſiduæ magnitu
              <lb/>
            dinis ex ſolidis portionibus cõpoſitæ grauitatis cẽtrũ erit
              <lb/>
            in linea k l protracta, & </s>
            <s xml:id="echoid-s3576" xml:space="preserve">in puncto n; </s>
            <s xml:id="echoid-s3577" xml:space="preserve">quod eſt abſurdū. </s>
            <s xml:id="echoid-s3578" xml:space="preserve">relin
              <lb/>
            quitur ergo, ut cẽtrum grauitatis cylindri; </s>
            <s xml:id="echoid-s3579" xml:space="preserve">uel cylin dri por
              <lb/>
            tionis ſit punctũ k. </s>
            <s xml:id="echoid-s3580" xml:space="preserve">quæ omnia demonſtrãda propoſuimus.</s>
            <s xml:id="echoid-s3581" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3582" xml:space="preserve">At uero cylindrum, uel cylindri portionẽ ce
              <lb/>
            ad priſma, cuius baſis eſt rectilinea figura in ſpa-
              <lb/>
            cio g h deſcripta, & </s>
            <s xml:id="echoid-s3583" xml:space="preserve">altitudo æqualis; </s>
            <s xml:id="echoid-s3584" xml:space="preserve">eandem </s>
          </p>
        </div>
      </text>
    </echo>