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
291 253
292 254
293 255
294 256
295 257
296 258
297 259
298 260
299 261
300 262
301 263
302 264
303 265
304 266
305 267
306 268
307 269
308 270
309 271
310 272
311 273
312 274
313 275
314 276
315 277
316 278
317 279
318 280
319 281
320 282
< >
page |< < (293) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div902" type="section" level="1" n="280">
          <p>
            <s xml:id="echoid-s10674" xml:space="preserve">
              <pb o="293" file="0331" n="332" rhead="Conicor. Lib. VII."/>
            differentia I L, & </s>
            <s xml:id="echoid-s10675" xml:space="preserve">N O maior ſit, quàm differentia quarumlibet duarum
              <lb/>
            coniugatarum ab axi remotiorum. </s>
            <s xml:id="echoid-s10676" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s10677" xml:space="preserve"/>
          </p>
          <figure number="384">
            <image file="0331-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0331-01"/>
          </figure>
        </div>
        <div xml:id="echoid-div904" type="section" level="1" n="281">
          <head xml:id="echoid-head351" xml:space="preserve">Notæ in Propoſit. XII.</head>
          <p style="it">
            <s xml:id="echoid-s10678" xml:space="preserve">IN eiſdem figuris, quia quadratum A C ad quadratum ſui coniugati in
              <lb/>
              <note position="left" xlink:label="note-0331-01" xlink:href="note-0331-01a" xml:space="preserve">a</note>
            propoſitione 12. </s>
            <s xml:id="echoid-s10679" xml:space="preserve">& </s>
            <s xml:id="echoid-s10680" xml:space="preserve">25. </s>
            <s xml:id="echoid-s10681" xml:space="preserve">nempe A C ad A F erectum ipſius eſt vt præ-
              <lb/>
            ſecta C G ad Interceptam G A, ſeu C H: </s>
            <s xml:id="echoid-s10682" xml:space="preserve">ergo quadratum A C in hy-
              <lb/>
            perbola ad differentiam quadratorum axium ipſius, & </s>
            <s xml:id="echoid-s10683" xml:space="preserve">in ellipſi ad illo-
              <lb/>
            rum ſnmmam eſt, vt C G ad H G, &</s>
            <s xml:id="echoid-s10684" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10685" xml:space="preserve">Ideſt. </s>
            <s xml:id="echoid-s10686" xml:space="preserve">Quia quadratum A C ad
              <lb/>
            quadratum axis ei coniugati Q R, ſiue C A ad eius erectum A F eandem pro-
              <lb/>
              <note position="right" xlink:label="note-0331-02" xlink:href="note-0331-02a" xml:space="preserve">Defin. 1.
                <lb/>
              & 2.
                <lb/>
              huius.</note>
            portionem habet, quàm præſecta C G ad Interceptam G A, vel ad C H, & </s>
            <s xml:id="echoid-s10687" xml:space="preserve">
              <lb/>
            comparando antecedentes ad terminorum differentias in hyperbola, & </s>
            <s xml:id="echoid-s10688" xml:space="preserve">ad ter-
              <lb/>
            minorum ſummas in ellipſi, quadratum C A ad differentiam quadratorum ex axi
              <lb/>
            A C, & </s>
            <s xml:id="echoid-s10689" xml:space="preserve">ex axi Q R habebit in hyperbola eandem proportionem, quàm C G
              <lb/>
            ad differentiam inter C G, & </s>
            <s xml:id="echoid-s10690" xml:space="preserve">C H: </s>
            <s xml:id="echoid-s10691" xml:space="preserve">in ellipſi verò quadratum A C ad ſum-
              <lb/>
            mam quadratorum ex A C, & </s>
            <s xml:id="echoid-s10692" xml:space="preserve">ex Q R eandem proportionem habebit, quàm
              <lb/>
            C G ad ſummam ipſius C G cum C H.</s>
            <s xml:id="echoid-s10693" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10694" xml:space="preserve">Et quia iam demonſtratum eſt, quod quadratum C A ad quadratum
              <lb/>
              <note position="left" xlink:label="note-0331-03" xlink:href="note-0331-03a" xml:space="preserve">b</note>
            I L ſit, vt C G ad E H, &</s>
            <s xml:id="echoid-s10695" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10696" xml:space="preserve">Relicta abſtruſa complicatione propoſitionum
              <lb/>
            Arabici Interpretis diſtinctiori methodo, ſicuti in præcedenti ſectione factum eſt
              <lb/>
              <note position="right" xlink:label="note-0331-04" xlink:href="note-0331-04a" xml:space="preserve">6. huius.</note>
            propoſitiones declarabimus. </s>
            <s xml:id="echoid-s10697" xml:space="preserve">Quoniam in hyperbola quadratum I L ad quadra-
              <lb/>
            tum N O eandem proportionem habet, quàm H E ad E G comparando antece-
              <lb/>
            dentes ad terminorum differentias, quadratum I L ad differentiam quadrati
              <lb/>
            I L à quadrato N O eandem proportionem habebit, quàm H E ad ipſarum H
              <lb/>
            E, & </s>
            <s xml:id="echoid-s10698" xml:space="preserve">E G differentiam; </s>
            <s xml:id="echoid-s10699" xml:space="preserve">ſed quadratum A C ad quadratum I L eſt vt C G
              <lb/>
            ad H E (veluti in propoſitione 8. </s>
            <s xml:id="echoid-s10700" xml:space="preserve">oſtenſum eſt) ergo ex æqualitate quadratum
              <lb/>
            A C ad quadratorum ex I L, & </s>
            <s xml:id="echoid-s10701" xml:space="preserve">ex N O differentiam eandem </s>
          </p>
        </div>
      </text>
    </echo>
Impressum