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
221 183
222 184
223 185
224 186
225 187
226 188
227 189
228 190
229 191
230 192
231 193
232 194
233 195
234 196
235 197
236 198
237 199
238 200
239 201
240 202
241 203
242 204
243 205
244 206
245 207
246 208
247 209
248 210
249 211
250 212
< >
page |< < (187) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div654" type="section" level="1" n="218">
          <p style="it">
            <s xml:id="echoid-s7076" xml:space="preserve">
              <pb o="187" file="0225" n="225" rhead="Conicor. Lib. VI."/>
            T ſimilia, pariterque triangula S R K, & </s>
            <s xml:id="echoid-s7077" xml:space="preserve">Q E Z inter ſe ſimilia; </s>
            <s xml:id="echoid-s7078" xml:space="preserve">ideoque erit
              <lb/>
            L B ad B T vt V X ad X H, pariterque Q E ad E Z erit vt S R ad R K;
              <lb/>
            </s>
            <s xml:id="echoid-s7079" xml:space="preserve">erat autem prius V X ad X H, vt S R ad R K; </s>
            <s xml:id="echoid-s7080" xml:space="preserve">igitur L B ad B T eandem
              <lb/>
            proportionem habebit, quàm Q E ad E Z; </s>
            <s xml:id="echoid-s7081" xml:space="preserve">& </s>
            <s xml:id="echoid-s7082" xml:space="preserve">propterea circa roctos angulos B,
              <lb/>
            E, figuræ ſectionum ſimiles erunt inter ſe. </s>
            <s xml:id="echoid-s7083" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s7084" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div656" type="section" level="1" n="219">
          <head xml:id="echoid-head276" xml:space="preserve">Notæ in Propoſit. XVI.</head>
          <p style="it">
            <s xml:id="echoid-s7085" xml:space="preserve">ERgo M A ad A P eſt vt O C ad C Q, & </s>
            <s xml:id="echoid-s7086" xml:space="preserve">angulus O æqualis eſt M,
              <lb/>
              <note position="left" xlink:label="note-0225-01" xlink:href="note-0225-01a" xml:space="preserve">a</note>
            oſtendetur (vt diximus in 11. </s>
            <s xml:id="echoid-s7087" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s7088" xml:space="preserve">quod, &</s>
            <s xml:id="echoid-s7089" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7090" xml:space="preserve">Sequitur enim ex
              <lb/>
            æqualitate ordinata, quod M A ad A P eandem proportionem habet, quàm O C
              <lb/>
            ad C Q, cumque ſint duo ſegmenta parabolica H A G, & </s>
            <s xml:id="echoid-s7091" xml:space="preserve">K C I, quorũ diame-
              <lb/>
            tri A M, & </s>
            <s xml:id="echoid-s7092" xml:space="preserve">C O efficiunt cum baſibus G H, & </s>
            <s xml:id="echoid-s7093" xml:space="preserve">K I angulos M, & </s>
            <s xml:id="echoid-s7094" xml:space="preserve">O æquales
              <lb/>
            inter ſe (cum ſint æquales angulis R A L, & </s>
            <s xml:id="echoid-s7095" xml:space="preserve">S C N æqualibus à contingentibus
              <lb/>
              <figure xlink:label="fig-0225-01" xlink:href="fig-0225-01a" number="253">
                <image file="0225-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0225-01"/>
              </figure>
            verticalibus parallelis baſibus, & </s>
            <s xml:id="echoid-s7096" xml:space="preserve">à diametris contentis) atque abſcißa M A ad
              <lb/>
            latus rectum A P eandem proportionem habet, quàm altera abſcißa O C ad C Q
              <lb/>
            latus rectum alterius ſectionis; </s>
            <s xml:id="echoid-s7097" xml:space="preserve">igitur duo ſegmenta H A G, & </s>
            <s xml:id="echoid-s7098" xml:space="preserve">K C I ſimilia
              <lb/>
              <note position="right" xlink:label="note-0225-02" xlink:href="note-0225-02a" xml:space="preserve">Lem. 6.
                <lb/>
              huius.</note>
            ſunt inter ſe.</s>
            <s xml:id="echoid-s7099" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7100" xml:space="preserve">Et quia G M poteſt A P in A M, & </s>
            <s xml:id="echoid-s7101" xml:space="preserve">ſimiliter I O poteſt C Q in C
              <lb/>
              <note position="left" xlink:label="note-0225-03" xlink:href="note-0225-03a" xml:space="preserve">b</note>
            O; </s>
            <s xml:id="echoid-s7102" xml:space="preserve">ergo P A ad G M eſt, vt C Q ad I O, & </s>
            <s xml:id="echoid-s7103" xml:space="preserve">G M ad M A eſt, vt I O
              <lb/>
            ad O C; </s>
            <s xml:id="echoid-s7104" xml:space="preserve">quia duo ſegmenta ſunt ſimilia, & </s>
            <s xml:id="echoid-s7105" xml:space="preserve">E A ad A M, eſt vt F C ad
              <lb/>
            C O; </s>
            <s xml:id="echoid-s7106" xml:space="preserve">&</s>
            <s xml:id="echoid-s7107" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7108" xml:space="preserve">Senſus huius textus confuſi, talis eſt. </s>
            <s xml:id="echoid-s7109" xml:space="preserve">Quia ſegmenta H A G, & </s>
            <s xml:id="echoid-s7110" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0225-04" xlink:href="note-0225-04a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            K C I ſimilia ſupponuntur erit A M ad M G, vt C O ad O I, & </s>
            <s xml:id="echoid-s7111" xml:space="preserve">quadratum
              <lb/>
            A M ad quadratum M G erit vt quadratum C O ad quadratum O I; </s>
            <s xml:id="echoid-s7112" xml:space="preserve">eſt verò
              <lb/>
              <note position="right" xlink:label="note-0225-05" xlink:href="note-0225-05a" xml:space="preserve">11. lib. 1.</note>
            rectangulum P A M æquale quadrato G M; </s>
            <s xml:id="echoid-s7113" xml:space="preserve">pariterque rectangulum Q C O eſt
              <lb/>
            æquale quadrato I O; </s>
            <s xml:id="echoid-s7114" xml:space="preserve">igitur quadratum A M ad rectangulum P A M eandem
              <lb/>
            proportionem habet, quàm quadratum C O ad rectangulum Q C O; </s>
            <s xml:id="echoid-s7115" xml:space="preserve">& </s>
            <s xml:id="echoid-s7116" xml:space="preserve">propte-
              <lb/>
            rea M A ad A P eandem proportionem habebit, quàm C O ad C Q; </s>
            <s xml:id="echoid-s7117" xml:space="preserve">ſed prius
              <lb/>
            oſt enſa fuit P A ad A E, vt Q C ad C F; </s>
            <s xml:id="echoid-s7118" xml:space="preserve">igitur ex æquali ordinata erit M </s>
          </p>
        </div>
      </text>
    </echo>
Impressum