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

< >
[101.] PROPOSITIO LXXII.
Page: 115 (77)
[102.] MONITVM.
Page: 116 (78)
[103.] LEMMA IX.
Page: 116 (78)
[104.] LEMMA X.
Page: 116 (78)
[105.] LEMMA XI.
Page: 117 (79)
[106.] Notæ in Propoſ. LXIV. & LXV.
Page: 117 (79)
[107.] Notæ in Propoſ. LXVI.
Page: 120 (82)
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
Page: 120 (82)
[109.] Notæ in Propoſ. LXVII.
Page: 121 (83)
[110.] COROLLARIVM PROPOSIT. LXVII.
Page: 122 (84)
[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
< >
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>
Impressum