Valerio, Luca, De centro gravitatis solidorum, 1604

Page concordance

< >
Scan Original
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
< >
page |< < of 283 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/192.jpg" pagenum="13"/>
              LM altitudo autem eadem priſmati HKF, hoc eſt priſma
                <lb/>
              ACGLFM illi æquale per vltimam XI. elem. </s>
              <s>ad priſma
                <lb/>
              HKF: vt igitur prima cum quinta, rectangulum DGE
                <lb/>
              vna cum quadrato EG, hoc eſt rectangulum DEG, ad
                <lb/>
              ſecundam quadratum DE, ita erit tertia cum ſexta, duo
                <lb/>
              priſmata BGL, ACGLFM, ad quartam priſma HKF.
                <lb/>
              </s>
              <s>Præterea quoniam vt quadratum DG ad quadratum
                <lb/>
              DE, ita erat triangulum DGM ad triangulum DEF: ſed
                <lb/>
              vt triangulum DGM ad triangulum DEF, ita eſt priſma,
                <lb/>
              HGM, ad priſma HKF: & tertiæ antecedentium par­
                <lb/>
              tes, videlicet, vt tertia pars quadrati DG, ad quadra­
                <lb/>
              tum DE, ita pyramis ADGM ad priſma HKF: ſed
                <lb/>
              vt rectangulum DEG ad DE quadratum, ita erant duo
                <lb/>
              priſmata BGL, ACGLFM, ad priſma HKF; vt igi­
                <lb/>
              tur prima cum quinta, rectangulum DEG vna cum ter­
                <lb/>
              tia parte DG quadrati, ad quadratum GD ſecundam,
                <lb/>
              ita erit tertia cum ſexta, duo priſmata BGL, ACGLFM
                <lb/>
              vna cum pyramide ADGM, hoc eſt integrum fruſtum
                <lb/>
              ABCDEF ad priſma HKF quartam. </s>
              <s>Ex hoc patet ſe­
                <lb/>
              cunda pars propoſiti. </s>
              <s>Quoniam enim eſt vt rectangulum
                <lb/>
              DEG, vna cum tertia parte quadrati DG, ad quadra­
                <lb/>
              tum DE, ita fruſtum ABGDEF ad priſma HKF: vt
                <lb/>
              autem quadratum DE, ad tertiam ſui partem, ita eſt priſ­
                <lb/>
              ma HKF ad pyramidem, cuius baſis triangulum DEF,
                <lb/>
              altitudo eadem priſmati HKF; erit ex æquali vt re­
                <lb/>
              ctangulum DEG vna cum tertia parte quadrati DG
                <lb/>
              ad tertiam partem quadrati DE, ita fruſtum ABCDEF,
                <lb/>
              ad pyramidem ſi compleatur ADEF. </s>
              <s>Manifeſtum eſt
                <lb/>
              igitur propoſitum. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum