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
71 33
72 34
73 35
74 36
75 37
76 38
77 39
78 40
79 41
80 42
81 43
82 44
83 45
84 46
85 47
86 48
87 49
88 50
89 51
90 52
91 53
92 54
93 55
94 56
95 57
96 58
97 59
98 60
99 61
100 62
< >
page |< < (64) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div248" type="section" level="1" n="83">
          <pb o="64" file="0102" n="102" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div252" type="section" level="1" n="84">
          <head xml:id="echoid-head117" xml:space="preserve">Notæ in Propoſit. LIX. LXII. & LXIII.</head>
          <p style="it">
            <s xml:id="echoid-s2796" xml:space="preserve">E T lineis, atque ſignis eodem ſtatu manentibus, &</s>
            <s xml:id="echoid-s2797" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2798" xml:space="preserve">Ideſt punctum
              <lb/>
              <note position="right" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">a</note>
            C extra, aut intra ſectionem ponatur, dummodo non ſit in axi, ducaturq;
              <lb/>
            </s>
            <s xml:id="echoid-s2799" xml:space="preserve">C E perpendicularis ad axim, ſecans eum in E, & </s>
            <s xml:id="echoid-s2800" xml:space="preserve">vt latus tranſuerſum ad re-
              <lb/>
            ctum, ita ſiat D F ad F E, atque C L ad L E, & </s>
            <s xml:id="echoid-s2801" xml:space="preserve">per L producatur O L M pa-
              <lb/>
            rallela A I, & </s>
            <s xml:id="echoid-s2802" xml:space="preserve">per F ducatur F M G parallela C E, quæ ſecet O M in M, & </s>
            <s xml:id="echoid-s2803" xml:space="preserve">per
              <lb/>
            C deſcribatur hyperbole H C B circa aſymptotos G M O, quæ in ellipſi per eius
              <lb/>
              <note position="left" xlink:label="note-0102-02" xlink:href="note-0102-02a" xml:space="preserve">4. lib. 2.</note>
            centrum D tranſibit, & </s>
            <s xml:id="echoid-s2804" xml:space="preserve">ideo eam ſecabit ſicuti oſtenſum eſt in 56. </s>
            <s xml:id="echoid-s2805" xml:space="preserve">huius.</s>
            <s xml:id="echoid-s2806" xml:space="preserve"/>
          </p>
          <figure number="81">
            <image file="0102-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0102-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s2807" xml:space="preserve">Eo quod O M parallela axi D A inclinato ſubtendit, &</s>
            <s xml:id="echoid-s2808" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2809" xml:space="preserve">Quoniam
              <lb/>
              <note position="right" xlink:label="note-0102-03" xlink:href="note-0102-03a" xml:space="preserve">b</note>
            in hyperbola O M parallela axi ſecat vtrãque linearum continentium angulum,
              <lb/>
            qui deinceps eſt ei, qui hyperbolen continet ſectioni occurret, & </s>
            <s xml:id="echoid-s2810" xml:space="preserve">producta ſectio-
              <lb/>
              <note position="left" xlink:label="note-0102-04" xlink:href="note-0102-04a" xml:space="preserve">11. lib. 2.</note>
            nem A B ſecabit, & </s>
            <s xml:id="echoid-s2811" xml:space="preserve">ideo O M cadit intra ſectionem A B, atque hyperbole A B
              <lb/>
            producta ſemper magis, ac magis recedit tum ab M O parallela axi, cum ab M
              <lb/>
            G parallela tangenti verticali, & </s>
            <s xml:id="echoid-s2812" xml:space="preserve">ſectio H C B, & </s>
            <s xml:id="echoid-s2813" xml:space="preserve">asymptoti O M G ad ſe ip-
              <lb/>
              <note position="left" xlink:label="note-0102-05" xlink:href="note-0102-05a" xml:space="preserve">14. lib. 2.</note>
            ſas jemper propius accedunt, igitur ſectiones A B, B C conueniunt; </s>
            <s xml:id="echoid-s2814" xml:space="preserve">ſecent ſe
              <lb/>
            ſe in B, & </s>
            <s xml:id="echoid-s2815" xml:space="preserve">ducamus per B, C lineam occurrentem axi in I, ipſi M O in O, & </s>
            <s xml:id="echoid-s2816" xml:space="preserve">
              <lb/>
            M G in G.</s>
            <s xml:id="echoid-s2817" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2818" xml:space="preserve">Et quia B O æqualis eſt ipſi C G, &</s>
            <s xml:id="echoid-s2819" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2820" xml:space="preserve">Cum lineæ rectæ O M, O G ſe ſe-
              <lb/>
              <note position="right" xlink:label="note-0102-06" xlink:href="note-0102-06a" xml:space="preserve">c</note>
            cantes in O, ſecentur à parallelis E C, K B, F G proportionaliter, erit O N
              <lb/>
            æqualis M L, ſicuti O B æqualis erat C G, & </s>
            <s xml:id="echoid-s2821" xml:space="preserve">O L, æqualis erit N M, ſicuti
              <lb/>
            O C æqualis erat B G, cumque triangula O C L, & </s>
            <s xml:id="echoid-s2822" xml:space="preserve">I C E ſint ſimilia propter
              <lb/>
              <note position="left" xlink:label="note-0102-07" xlink:href="note-0102-07a" xml:space="preserve">8. lib. 2.</note>
            parallelas O L, I E, erit O L ad E I, vt L C ad C E; </s>
            <s xml:id="echoid-s2823" xml:space="preserve">eſt vero M N, ſeu F
              <lb/>
            K æqualis ipſi L O, igitur F K ad E I eſt, vt L C ad E C, ſed ex conſtru-
              <lb/>
            ctione erat D F ad F E, vt C L ad L E, ſciluet vt latus tranſuerſum ad
              <lb/>
            rectum; </s>
            <s xml:id="echoid-s2824" xml:space="preserve">ergo antecedentes ad ſummas terminorum in hyperbola, & </s>
            <s xml:id="echoid-s2825" xml:space="preserve">ad
              <lb/>
              <note position="left" xlink:label="note-0102-08" xlink:href="note-0102-08a" xml:space="preserve">Lem. 1.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum