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

Table of contents

< >
[311.] PROPOSITIO XXXIX.
Page: 363 (324)
[312.] PROPOSITIO XXXX.
Page: 364 (325)
[313.] In Sectionem VII. Propoſit: XXXVIII. XXXIX. & XXXX. LEMMA VI.
Page: 366 (327)
[314.] LEMMA VII.
Page: 366 (327)
[315.] LEMMA VIII.
Page: 367 (328)
[316.] LEMMA IX.
Page: 367 (328)
[317.] Notæ in Propoſit. XXXVIII. XXXIX.
Page: 369 (330)
[318.] Notæ in Propoſit. XXXX.
Page: 369 (330)
[319.] SECTIO OCTAVA Continens Propoſit. XXXXIIII. XXXXV. & XXXXVI.
Page: 372 (333)
[320.] PROPOSITIO XXXXVI.
Page: 374 (335)
[321.] In Sectionem VIII. Propoſit. XXXXIIII. XXXXV. & XXXXVI. LEMM A.X.
Page: 375 (336)
[322.] LEMM A XI.
Page: 375 (336)
[323.] LEMM A XII.
Page: 376 (337)
[324.] Notæ in Propoſit. XXXXIV. & XXXXV.
Page: 378 (339)
[325.] Notæ in Propoſit. XXXXVI.
Page: 378 (339)
[326.] SECTIO NONA Continens Propoſit. XXXXI. XXXXVII. & XXXXVIII.
Page: 380 (341)
[327.] PROPOSITIO XXXXI.
Page: 382 (343)
[328.] PROPOSITIO XXXXVII.
Page: 383 (344)
[329.] PROPOSITIO XXXXVIII.
Page: 386 (347)
[330.] In Sectionem IX. Propoſit. XXXXI. XXXXVII. & XXXXVIII. LEMMA. XIII.
Page: 388 (349)
[331.] LEMMA XIV.
Page: 389 (350)
[332.] LEMMA XV.
Page: 389 (350)
[333.] Notæ in Propoſit. XXXXI.
Page: 392 (353)
[334.] Notæ in Propoſit. XXXXVII.
Page: 393 (354)
[335.] Notæ in Propoſit. XXXXVIII.
Page: 394 (355)
[336.] SECTIO DECIMA Continens Propoſit. XXXXIX. XXXXX. & XXXXXI.
Page: 397 (358)
[337.] In Sectionem X. Propoſit. XXXXIX. XXXXX. & XXXXXI. LEMMA XVI.
Page: 400 (361)
[338.] LEMMA XVII.
Page: 400 (361)
[339.] LEMMA XVIII.
Page: 403 (364)
[340.] Notæ in Propoſit. XXXXIX.
Page: 404 (365)
< >
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