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 |< < (49) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div187" type="section" level="1" n="72">
          <p>
            <s xml:id="echoid-s2312" xml:space="preserve">
              <pb o="49" file="0087" n="87" rhead="Conicor. Lib. V."/>
            mas in ellipſi, & </s>
            <s xml:id="echoid-s2313" xml:space="preserve">eo-
              <lb/>
              <figure xlink:label="fig-0087-01" xlink:href="fig-0087-01a" number="64">
                <image file="0087-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0087-01"/>
              </figure>
            rundem differentias
              <lb/>
            in hyperbola C X ad
              <lb/>
              <note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">Lem. 4.</note>
            c V, vel (propter
              <lb/>
            ſimilitudinem triã-
              <lb/>
            gulorum X C Z, V c
              <lb/>
            Z) C Z ad Z c ma-
              <lb/>
            iorem proportionem
              <lb/>
            habet, quàm I C ad
              <lb/>
            C S, vel C D ad D
              <lb/>
            F; </s>
            <s xml:id="echoid-s2314" xml:space="preserve">& </s>
            <s xml:id="echoid-s2315" xml:space="preserve">componendo
              <lb/>
            in ellipſi, & </s>
            <s xml:id="echoid-s2316" xml:space="preserve">diui-
              <lb/>
            dendo in hyperbola
              <lb/>
            C c ad c Z maiorẽ
              <lb/>
            proportionem habe-
              <lb/>
            bit, quàm C F ad
              <lb/>
              <note position="right" xlink:label="note-0087-02" xlink:href="note-0087-02a" xml:space="preserve">9. 10.
                <lb/>
              huius.</note>
            F D, & </s>
            <s xml:id="echoid-s2317" xml:space="preserve">ideo breuiſ-
              <lb/>
            ſima egrediens ex V
              <lb/>
            abſcindit lineã ma-
              <lb/>
            iorem, quàm A Z.</s>
            <s xml:id="echoid-s2318" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2319" xml:space="preserve">Simili modo cõ-
              <lb/>
            ſtat, quod breuiſ-
              <lb/>
              <note position="left" xlink:label="note-0087-03" xlink:href="note-0087-03a" xml:space="preserve">t</note>
            ſima egrediens ex
              <lb/>
            l eiuſdem ſit ratio-
              <lb/>
            nis, &</s>
            <s xml:id="echoid-s2320" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2321" xml:space="preserve">Abſque no-
              <lb/>
            ua demonſtratione
              <lb/>
            in ſecunda, & </s>
            <s xml:id="echoid-s2322" xml:space="preserve">quar
              <lb/>
            ta figura propoſitum oſtenſum erit.</s>
            <s xml:id="echoid-s2323" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2324" xml:space="preserve">Deinde ſit E D æqualis Q, inde demonſtrabitur (quemadmodum ſu-
              <lb/>
              <note position="left" xlink:label="note-0087-04" xlink:href="note-0087-04a" xml:space="preserve">a</note>
            pra factum eſt) quod B H tantum ſit linea breuiſſima, &</s>
            <s xml:id="echoid-s2325" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2326" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div208" type="section" level="1" n="73">
          <head xml:id="echoid-head106" style="it" xml:space="preserve">Secunda pars buius propoſitionis, quam Apollonius non expoſuit hac
            <lb/>
          ratione ſuppleri poteſt.</head>
          <p style="it">
            <s xml:id="echoid-s2327" xml:space="preserve">Sit E D æqualis Trutinæ Q habebunt E D, atque Q eandem proportionem
              <lb/>
            ad B O, componitur verò proportio E D ad B O ex rationibus E D ad D K, & </s>
            <s xml:id="echoid-s2328" xml:space="preserve">
              <lb/>
            D K ad B O, ſeu O G ad B O; </s>
            <s xml:id="echoid-s2329" xml:space="preserve">componebatur autem proportio Trutinæ Q ad B O
              <lb/>
            ex rationibus C D ad D F, & </s>
            <s xml:id="echoid-s2330" xml:space="preserve">F O ad O C; </s>
            <s xml:id="echoid-s2331" xml:space="preserve">ergo ablata communiter proportione
              <lb/>
            E D ad D K, vel C D ad D F, relinquetur proportio G O ad O B eadem propor-
              <lb/>
            tioni F O ad O C; </s>
            <s xml:id="echoid-s2332" xml:space="preserve">ergo rectangulum G O C ſub extremis contentum æquale erit
              <lb/>
            rectangulo B O F ſub intermedijs compræbenſo, addatur in hyperbola, & </s>
            <s xml:id="echoid-s2333" xml:space="preserve">aufe-
              <lb/>
            ratur in ellipſi communiter rectangulum F G, erit rectangulum F S æquale re-
              <lb/>
            ctangulo B G M; </s>
            <s xml:id="echoid-s2334" xml:space="preserve">Et quia I S ad S C, vel E K ad K D, velad F M erat, vt C
              <lb/>
            F ad F D, vel vt S M ad M K; </s>
            <s xml:id="echoid-s2335" xml:space="preserve">ergo rectangulum E M æquale eſt rectangulo
              <lb/>
            F S; </s>
            <s xml:id="echoid-s2336" xml:space="preserve">& </s>
            <s xml:id="echoid-s2337" xml:space="preserve">propterea rectangulum E M æquale erit rectangulo B G M; </s>
            <s xml:id="echoid-s2338" xml:space="preserve">quapropter
              <lb/>
            vt E K ad B G, ſeu K R ad R G, ita erit G M ad M K, & </s>
            <s xml:id="echoid-s2339" xml:space="preserve">componendo, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum