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
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
81 43
82 44
83 45
84 46
85 47
86 48
87 49
88 50
89 51
90 52
< >
page |< < (67) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div260" type="section" level="1" n="86">
          <pb o="67" file="0105" n="105" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div263" type="section" level="1" n="87">
          <head xml:id="echoid-head120" xml:space="preserve">SECTIO DECIMA</head>
          <head xml:id="echoid-head121" xml:space="preserve">Continens Propof. XXXXIV. XXXXV.
            <lb/>
          Apollonij.</head>
          <p>
            <s xml:id="echoid-s2890" xml:space="preserve">SI ex axe recto ellipſis ſumatur menſura ab origine, quæ ad
              <lb/>
              <note position="left" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">a</note>
            ſemiaxim rectum non habeat minorem proportionem, quàm
              <lb/>
            habet figura ſuæ tranſuerſæ, tunc quicumque ramus ſecans, ab
              <lb/>
            illa origine ad fectionem ductus, abſcindit ex axe tranſuerſo ad
              <lb/>
            verticem ſectionis lineam minorem ea, quàm abſcindit linea
              <lb/>
            breuiſsima egrediens ab eius termino in ſectione poſito ad tran-
              <lb/>
            ſuerſum axim; </s>
            <s xml:id="echoid-s2891" xml:space="preserve">ſi vero fuerit proportio ad ſemirectum minor,
              <lb/>
            tunc ramorum ſecantium vnus eſt breuiſecans; </s>
            <s xml:id="echoid-s2892" xml:space="preserve">reliqui vero, qui
              <lb/>
            ſequuntur extremum tranſuerſæ habent proprietates ſuperius ex-
              <lb/>
            poſitas, & </s>
            <s xml:id="echoid-s2893" xml:space="preserve">qui ſequuntur extremitatem recti, ſecant ex tranſuer-
              <lb/>
            ſa lineam maiorem ea, quàm abſcindit breuiſsima egrediens ab
              <lb/>
            eius termino.</s>
            <s xml:id="echoid-s2894" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div265" type="section" level="1" n="88">
          <head xml:id="echoid-head122" xml:space="preserve">PROPOSITIO XXXXIV.</head>
          <p>
            <s xml:id="echoid-s2895" xml:space="preserve">Sit A D dimidium axis recti, & </s>
            <s xml:id="echoid-s2896" xml:space="preserve">minoris ſectionis ellipticæ
              <lb/>
              <note position="left" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">b</note>
            A B C, & </s>
            <s xml:id="echoid-s2897" xml:space="preserve">meuſura A E, quæ ſit maior, quàm A D, & </s>
            <s xml:id="echoid-s2898" xml:space="preserve">pro-
              <lb/>
            portio illius ad iſtam non ſit minor proportione figuræ ſectionis;
              <lb/>
            </s>
            <s xml:id="echoid-s2899" xml:space="preserve">Dico, quod linea breuiſsima egrediens ab extremitate cuiuſcum-
              <lb/>
            que rami ſecantis educti ex E ad ſectionem A B C, ſecat ex
              <lb/>
            tranuerſa B C cum vertice B, vel C lineam maiorem ea, quàm
              <lb/>
            abſcindit ille ramus.</s>
            <s xml:id="echoid-s2900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2901" xml:space="preserve">Ponatur ramus E F, & </s>
            <s xml:id="echoid-s2902" xml:space="preserve">ducamus ex F ad vtrum-
              <lb/>
              <figure xlink:label="fig-0105-01" xlink:href="fig-0105-01a" number="85">
                <image file="0105-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0105-01"/>
              </figure>
              <note position="left" xlink:label="note-0105-03" xlink:href="note-0105-03a" xml:space="preserve">c</note>
            que axim duas perpendiculares F H, F I. </s>
            <s xml:id="echoid-s2903" xml:space="preserve">Et quia
              <lb/>
            proportio E A ad A D non eſt minor proportio-
              <lb/>
            ne ſiguræ, ſed minor eſt, quàm E H ad H D, nem-
              <lb/>
            pe E F ad F G, ſeu D I ad I G, erit proportio ſigu-
              <lb/>
            ræ minor, quàm D I ad I G, & </s>
            <s xml:id="echoid-s2904" xml:space="preserve">ponamus D I ad
              <lb/>
            I K, vt eſt proportio figuræ, & </s>
            <s xml:id="echoid-s2905" xml:space="preserve">iungamus F K;
              <lb/>
            </s>
            <s xml:id="echoid-s2906" xml:space="preserve">erit ergo F K linea breuiſſima (10. </s>
            <s xml:id="echoid-s2907" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2908" xml:space="preserve">& </s>
            <s xml:id="echoid-s2909" xml:space="preserve">iam
              <lb/>
              <note position="right" xlink:label="note-0105-04" xlink:href="note-0105-04a" xml:space="preserve">10.
                <lb/>
              huius.</note>
            ſecat K B maiorem, quàm B G, & </s>
            <s xml:id="echoid-s2910" xml:space="preserve">G F non erit
              <lb/>
            breuiſſima; </s>
            <s xml:id="echoid-s2911" xml:space="preserve">& </s>
            <s xml:id="echoid-s2912" xml:space="preserve">hoc erat propoſitum.</s>
            <s xml:id="echoid-s2913" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum