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

< >
[231.] Notæ in Propoſit. XXIII.
[232.] Notæ in Propoſit. XXIV.
[233.] SECTIO NONA Continens Propoſit. XXV.
[234.] Notæ in Propoſit. XXV.
[235.] LEMMA IX.
[236.] SECTIO DECIMA Continens Propoſit. XXVI. XXVII. & XXVIII. PROPOSITIO XXVI.
[237.] PROPOSITIO XXVII.
[238.] PROPOSITIO XXVIII.
[239.] Notæ in Propoſit. XXVI.
[240.] Notæ in Propoſit. XXVII.
[241.] Notæ in Propoſit. XXVIII.
[242.] LEMMAX.
[243.] SECTIO VNDECIMA Continens Propoſit. XXIX. XXX. & XXXI. PROPOSTIO XXIX.
[244.] PROPOSITIO XXX.
[245.] PROPOSITIO XXXI.
[246.] Notæ in Propoſit. XXIX.
[247.] Notæ in Propoſit. XXX.
[248.] Notæ in Propoſit. XXXI.
[249.] LIBRI SEXTI FINIS.
[250.] DEFINITIONES. I.
[251.] II.
[252.] III.
[253.] IV.
[255.] VI.
[256.] VII.
[257.] VIII.
[258.] NOTÆ.
[259.] SECTIO PRIMA Continens Propoſit. I. V. & XXIII. Apollonij. PROPOSITIO I.
[260.] PROPOSITIO V. & XXIII.
< >
page |< < (233) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div749" type="section" level="1" n="235">
          <p style="it">
            <s xml:id="echoid-s8728" xml:space="preserve">
              <pb o="233" file="0271" n="271" rhead="Conicor. Lib. VI."/>
            parallela conſeruantur; </s>
            <s xml:id="echoid-s8729" xml:space="preserve">igitur duæ ſectiones K H M, & </s>
            <s xml:id="echoid-s8730" xml:space="preserve">L X S, exiſtentes in
              <lb/>
            eodem plano ſecante duas ſuperficies, quæ licet in infinitum producantur vbique
              <lb/>
            ſeparatæ ſunt, erunt aſymptoticæ. </s>
            <s xml:id="echoid-s8731" xml:space="preserve">Quartò, quia duæ hyperbolæ H K M, & </s>
            <s xml:id="echoid-s8732" xml:space="preserve">L
              <lb/>
            X S ſunt æquales, ſimiles, & </s>
            <s xml:id="echoid-s8733" xml:space="preserve">ſimiliter poſitæ circa communem diametrum H X
              <lb/>
              <note position="right" xlink:label="note-0271-01" xlink:href="note-0271-01a" xml:space="preserve">Prop. 7.
                <lb/>
              addit.</note>
            I, earum diſtantiæ ſemper magis, ac magis diminuuntur; </s>
            <s xml:id="echoid-s8734" xml:space="preserve">nunquam tamen mi-
              <lb/>
            nores efſici poſſunt interuallo duarum æquidiſtantium, hyperbolas continentium.
              <lb/>
            </s>
            <s xml:id="echoid-s8735" xml:space="preserve">Et hoc erat propoſitum.</s>
            <s xml:id="echoid-s8736" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8737" xml:space="preserve">Data hyperbola X duos conos ſimiles exhibere vt idem planum in eis
              <lb/>
              <note position="right" xlink:label="note-0271-02" xlink:href="note-0271-02a" xml:space="preserve">PROP.
                <lb/>
              13.
                <lb/>
              Addit.</note>
            efficiat duas hyperbolas ſimiles, & </s>
            <s xml:id="echoid-s8738" xml:space="preserve">æquales datæ, quæ aſymptoticæ ſint,
              <lb/>
            & </s>
            <s xml:id="echoid-s8739" xml:space="preserve">ex vna parte ſibi ipſis viciniores fiant interuallo minori quolibet da-
              <lb/>
            to: </s>
            <s xml:id="echoid-s8740" xml:space="preserve">ex altera verò parte ad ſe ipſas propius accedant interuallo tamen
              <lb/>
            maiore dato: </s>
            <s xml:id="echoid-s8741" xml:space="preserve">oportet autem vt angulus ab aſymptotis ſectionis X con-
              <lb/>
            tentus ſit acutus.</s>
            <s xml:id="echoid-s8742" xml:space="preserve"/>
          </p>
          <figure number="318">
            <image file="0271-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0271-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s8743" xml:space="preserve">In quolibet @l@no fiat angulus A d O æqualis angulo inclinationis diametri,
              <lb/>
            & </s>
            <s xml:id="echoid-s8744" xml:space="preserve">baſis hyperb l@ X; </s>
            <s xml:id="echoid-s8745" xml:space="preserve">& </s>
            <s xml:id="echoid-s8746" xml:space="preserve">per o d extenſo quolibet alio planol, ducatur in eo re-
              <lb/>
            cta linea B d C perpendicularis ad O d G, & </s>
            <s xml:id="echoid-s8747" xml:space="preserve">ſumpto quolibet alio puncto b in
              <lb/>
            recta linea G O in plano per B G C O ducto, centris d, & </s>
            <s xml:id="echoid-s8748" xml:space="preserve">b deſcribantur </s>
          </p>
        </div>
      </text>
    </echo>