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
51 13
52 14
53 15
54 16
55 17
56 18
57 19
58 20
59 21
60 22
61 23
62 24
63 25
64 26
65 27
66 28
67 29
68 30
69 31
70 32
71 33
72 34
73 35
74 36
75 37
76 38
77 39
78 40
79 41
80 42
< >
page |< < (68) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div265" type="section" level="1" n="88">
          <pb o="68" file="0106" n="106" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div268" type="section" level="1" n="89">
          <head xml:id="echoid-head123" xml:space="preserve">PROPOSITIO XXXXV.</head>
          <p>
            <s xml:id="echoid-s2914" xml:space="preserve">SI autem fuerit ratio E A ad A D minor,
              <lb/>
              <figure xlink:label="fig-0106-01" xlink:href="fig-0106-01a" number="86">
                <image file="0106-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0106-01"/>
              </figure>
              <note position="right" xlink:label="note-0106-01" xlink:href="note-0106-01a" xml:space="preserve">a</note>
            quàm proportio figuræ, ponamus E H ad H
              <lb/>
            D in proportione figuræ, & </s>
            <s xml:id="echoid-s2915" xml:space="preserve">producamus per-
              <lb/>
            pendicularem H F, & </s>
            <s xml:id="echoid-s2916" xml:space="preserve">iungamus F E, & </s>
            <s xml:id="echoid-s2917" xml:space="preserve">duca-
              <lb/>
            mus perpendicularem F I. </s>
            <s xml:id="echoid-s2918" xml:space="preserve">Et quoniam E H ad
              <lb/>
            H D, nempe D I ad I G eſt, vt proportio figu-
              <lb/>
            ræ, erit F G linea breuiſſima (10. </s>
            <s xml:id="echoid-s2919" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2920" xml:space="preserve">Et quo-
              <lb/>
            niam iam educti ſunt ex E duo breuiſecantes
              <lb/>
            F E, & </s>
            <s xml:id="echoid-s2921" xml:space="preserve">E A (11. </s>
            <s xml:id="echoid-s2922" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2923" xml:space="preserve">tunc à terminis ramo-
              <lb/>
            rum egredientium ex E, qui terminantur ad ſe-
              <lb/>
            ctionem B F, linea breuiſſima egrediens erit re-
              <lb/>
            motior ab ipſo B, & </s>
            <s xml:id="echoid-s2924" xml:space="preserve">qui terminatur ad ſectio-
              <lb/>
            nem A F, breuiſſima egrediens ab extremitate illius erit proximior, ipſi
              <lb/>
            B (51. </s>
            <s xml:id="echoid-s2925" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2926" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2927" xml:space="preserve">& </s>
            <s xml:id="echoid-s2928" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s2929" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div270" type="section" level="1" n="90">
          <head xml:id="echoid-head124" xml:space="preserve">Notæ in Propoſ. XXXXIV.</head>
          <p style="it">
            <s xml:id="echoid-s2930" xml:space="preserve">PVto, numeros 53. </s>
            <s xml:id="echoid-s2931" xml:space="preserve">& </s>
            <s xml:id="echoid-s2932" xml:space="preserve">54. </s>
            <s xml:id="echoid-s2933" xml:space="preserve">Propoſitionum huius ſe-
              <lb/>
              <figure xlink:label="fig-0106-02" xlink:href="fig-0106-02a" number="87">
                <image file="0106-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0106-02"/>
              </figure>
            ctionis mendoſos eſſe, nam Propoſitio 53. </s>
            <s xml:id="echoid-s2934" xml:space="preserve">poſita
              <lb/>
            fuit in præmiſſa ſectione, & </s>
            <s xml:id="echoid-s2935" xml:space="preserve">Propoſitio 54. </s>
            <s xml:id="echoid-s2936" xml:space="preserve">inferius
              <lb/>
            appoſita reperitur; </s>
            <s xml:id="echoid-s2937" xml:space="preserve">Cenſeo igitur, eſſe Propoſitiones
              <lb/>
            XXXXIV. </s>
            <s xml:id="echoid-s2938" xml:space="preserve">& </s>
            <s xml:id="echoid-s2939" xml:space="preserve">XXXXV.</s>
            <s xml:id="echoid-s2940" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2941" xml:space="preserve">Si ex axe recto ellipſis ſumatur menſura, &</s>
            <s xml:id="echoid-s2942" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s2943" xml:space="preserve">
              <note position="right" xlink:label="note-0106-02" xlink:href="note-0106-02a" xml:space="preserve">a</note>
            Hoc eſt ſi ex axe minori, recto ellipſis ſumatur menſu-
              <lb/>
            ra, quæ habeat non minorem proportionem ad ſemi-
              <lb/>
            axim rectum, quàm habet axis tranſuerſus ad ſuum
              <lb/>
            latus rectum, quilibet ramus ſecans, ab origine ad ſe-
              <lb/>
            ctionem ductus, abſcindit ex axe tranſuerſo ad ver-
              <lb/>
            ticem ſectionis minorem lineam, quàm ſecat linea breuiſsima ab eius termi-
              <lb/>
            no ad axim tranſuer ſum ducta. </s>
            <s xml:id="echoid-s2944" xml:space="preserve">Si vero menſura ad minorem ſemiaxim re-
              <lb/>
            ctum proportionem minorem habuerit, quàm latus tranſuer ſum ad rectum, tunc
              <lb/>
            vnicus ramus erit breuiſecans; </s>
            <s xml:id="echoid-s2945" xml:space="preserve">reliqui vero ſequentes terminum tranſuerſi, ha-
              <lb/>
            bent ſuperius expoſitas proprietates, & </s>
            <s xml:id="echoid-s2946" xml:space="preserve">ſequentes extr emitates axis recti, ſecant
              <lb/>
            ex tranſuer ſa maiorem lineam, quàm ſecet breuiſsima ab eius termino ad axim
              <lb/>
            tranſuer ſum ducta. </s>
            <s xml:id="echoid-s2947" xml:space="preserve">Quod autem menſura neceßario ſumi debeat in axe minori
              <lb/>
            ellipſis patet, nàm ex hypotheſi rami ſunt ſecantes non quidem ex concurſu, ſed
              <lb/>
            ex origine ducti igitur origo cadit infra centrum, & </s>
            <s xml:id="echoid-s2948" xml:space="preserve">menſura maior erit medie-
              <lb/>
            tate axis vt in textu habetur; </s>
            <s xml:id="echoid-s2949" xml:space="preserve">debet autem habere menſura ad ſemiaxim rectum
              <lb/>
            maiorem aut eandem proportionem, quàm axis tranſuerſus habet ad eius latus
              <lb/>
            rectum, ergo proportio axis tranſuerſi ad ſuum latus rectum erit maioris inæqua-
              <lb/>
            litatis, & </s>
            <s xml:id="echoid-s2950" xml:space="preserve">propterea tranſuerſus axis erit maior quàm axis rectus.</s>
            <s xml:id="echoid-s2951" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum