Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Page concordance

< >
Scan Original
181 143
182 144
183 145
184 146
185 147
186 148
187 149
188 150
189 151
190 152
191 153
192 154
193 155
194 156
195 157
196 158
197 159
198 160
199 161
200 162
201 163
202 164
203 165
204 166
205 167
206 168
207 169
208 170
209 171
210 172
< >
page |< < (145) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div540" type="section" level="1" n="176">
          <p style="it">
            <s xml:id="echoid-s5700" xml:space="preserve">
              <pb o="145" file="0183" n="183" rhead="Conicor. Lib. VI."/>
            ſectiones æquales eſſe. </s>
            <s xml:id="echoid-s5701" xml:space="preserve">Sumatur quodlibet punctum B in ſectione B A ducaturque
              <lb/>
            ordinatim applicata B E, ſeceturque C F æqualis A E, & </s>
            <s xml:id="echoid-s5702" xml:space="preserve">ducatur ordinatim
              <lb/>
            D F. </s>
            <s xml:id="echoid-s5703" xml:space="preserve">Maniſeſtum eſt, rectangula E A I, & </s>
            <s xml:id="echoid-s5704" xml:space="preserve">F C N æqualia eße (cum latera
              <lb/>
            ſint æqualia, ſingula ſingulis); </s>
            <s xml:id="echoid-s5705" xml:space="preserve">his verò rectangulis æqualia ſunt quadrata or-
              <lb/>
              <note position="right" xlink:label="note-0183-01" xlink:href="note-0183-01a" xml:space="preserve">11. lib. 1.</note>
            dinatim applicatarum B E, D F; </s>
            <s xml:id="echoid-s5706" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s5707" xml:space="preserve">quadrata ſunt æqualia, atque eorum
              <lb/>
            latera B E, D F æqualia quoque. </s>
            <s xml:id="echoid-s5708" xml:space="preserve">Si igitur parabolæ ſuperponantur ita, vt
              <lb/>
            punctum E ſuper F, & </s>
            <s xml:id="echoid-s5709" xml:space="preserve">diameter A E ſuper C F cadat, neceſſariò punctum A
              <lb/>
            ſuper C cadet (propter æqualitatem abſcißarum) atque punctum B ſuper punctũ
              <lb/>
            D incidet (propterea quod anguli E, & </s>
            <s xml:id="echoid-s5710" xml:space="preserve">F æquales ſunt, pariterque rectæ B E,
              <lb/>
            & </s>
            <s xml:id="echoid-s5711" xml:space="preserve">D F ſunt æquales), & </s>
            <s xml:id="echoid-s5712" xml:space="preserve">quia quodlibet punctum B parabolæ A B cadit ſemper
              <lb/>
            ſuper ſectionem C D; </s>
            <s xml:id="echoid-s5713" xml:space="preserve">ergo duæ ſectiones B A, & </s>
            <s xml:id="echoid-s5714" xml:space="preserve">D C ſibi mutuò congruunt, & </s>
            <s xml:id="echoid-s5715" xml:space="preserve">
              <lb/>
            ideo æquales ſunt. </s>
            <s xml:id="echoid-s5716" xml:space="preserve">Non ſecus conuerſum huius propoſitionis demonſtrari poteſt.</s>
            <s xml:id="echoid-s5717" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5718" xml:space="preserve">Altera verò pars propoſitionis breuius de-
              <lb/>
              <figure xlink:label="fig-0183-01" xlink:href="fig-0183-01a" number="188">
                <image file="0183-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0183-01"/>
              </figure>
            monſtrabitur hac ratione. </s>
            <s xml:id="echoid-s5719" xml:space="preserve">In duabus hyperbo-
              <lb/>
            lis, aut ellipſibus efficiant ordinatim applicatæ
              <lb/>
            B E, D F cum diametris A E, & </s>
            <s xml:id="echoid-s5720" xml:space="preserve">C F angu-
              <lb/>
            los æquales, & </s>
            <s xml:id="echoid-s5721" xml:space="preserve">non rectos; </s>
            <s xml:id="echoid-s5722" xml:space="preserve">ſintque tranſuerſa
              <lb/>
            latera G A, & </s>
            <s xml:id="echoid-s5723" xml:space="preserve">H C æqualia, pariterque late-
              <lb/>
            ra recta A I, & </s>
            <s xml:id="echoid-s5724" xml:space="preserve">C N æqualia. </s>
            <s xml:id="echoid-s5725" xml:space="preserve">Dico, ſectiones
              <lb/>
            B A, C D æquales eſſe. </s>
            <s xml:id="echoid-s5726" xml:space="preserve">Sumatur quodlibet
              <lb/>
            punctum B ſectionis B A, ducaturque ad A E
              <lb/>
            diametrum ordinatim applicata B E, ſecetur-
              <lb/>
            que C F æqualis abſciſſæ A E, ducaturque F D
              <lb/>
            ad H C F diametrũ ordinatim applicata. </s>
            <s xml:id="echoid-s5727" xml:space="preserve">Erit
              <lb/>
            rectangulum G E A ad quadr atum B E, vt la-
              <lb/>
            tus tranſuerſum G A ad rectum A I; </s>
            <s xml:id="echoid-s5728" xml:space="preserve">pariter-
              <lb/>
            que rectangulum H F C ad quadratum F D
              <lb/>
            erit, vt H C ad C N: </s>
            <s xml:id="echoid-s5729" xml:space="preserve">habent vero duæ æqua-
              <lb/>
            les G A, & </s>
            <s xml:id="echoid-s5730" xml:space="preserve">H C eandem proportionem ad duas
              <lb/>
            æquales A I, & </s>
            <s xml:id="echoid-s5731" xml:space="preserve">C N; </s>
            <s xml:id="echoid-s5732" xml:space="preserve">igitur rectangulum G E
              <lb/>
            A ad quadratum B E eandem proportionem ha-
              <lb/>
              <figure xlink:label="fig-0183-02" xlink:href="fig-0183-02a" number="189">
                <image file="0183-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0183-02"/>
              </figure>
            bebit, quàm rectangulum.
              <lb/>
            </s>
            <s xml:id="echoid-s5733" xml:space="preserve">H F C ad quadratum D F,
              <lb/>
            ſunt verò rectangula G E
              <lb/>
            A, H F C æqualia inter, ſe
              <lb/>
            (quandoquidem eorum la-
              <lb/>
            tera A E, C F facta ſunt
              <lb/>
            æqualia) quæ addita ipſis
              <lb/>
            A G, & </s>
            <s xml:id="echoid-s5734" xml:space="preserve">C H æqualibus eſ-
              <lb/>
            eſſiciunt latera E G, & </s>
            <s xml:id="echoid-s5735" xml:space="preserve">F
              <lb/>
            H æqualia; </s>
            <s xml:id="echoid-s5736" xml:space="preserve">ergo quadrat a
              <lb/>
            d a um B E, & </s>
            <s xml:id="echoid-s5737" xml:space="preserve">D F æqua-
              <lb/>
            lia ſunt inter ſe; </s>
            <s xml:id="echoid-s5738" xml:space="preserve">& </s>
            <s xml:id="echoid-s5739" xml:space="preserve">ideo ordinatim applicatæ B E, & </s>
            <s xml:id="echoid-s5740" xml:space="preserve">D F æquales erunt. </s>
            <s xml:id="echoid-s5741" xml:space="preserve">
              <lb/>
            Quare facta, vt prius, intellectuali ſuperpoſitione; </s>
            <s xml:id="echoid-s5742" xml:space="preserve">nedum veriex A ſuper C,
              <lb/>
            ſed etiam quodlibet punctum B ſectionis A B ſuper ſectionem C D cadet; </s>
            <s xml:id="echoid-s5743" xml:space="preserve">ideo-
              <lb/>
            que ſectiones ſibi mutuò congruent, & </s>
            <s xml:id="echoid-s5744" xml:space="preserve">æquales erunt.</s>
            <s xml:id="echoid-s5745" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5746" xml:space="preserve">E conuerſo, ſi ſectiones B A, & </s>
            <s xml:id="echoid-s5747" xml:space="preserve">C D æquales ſupponantur, ſibi mutuò </s>
          </p>
        </div>
      </text>
    </echo>
Impressum