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
101 63
102 64
103 65
104 66
105 67
106 68
107 69
108 70
109 71
110 72
111 73
112 74
113 75
114 76
115 77
116 78
117 79
118 80
119 81
120 82
121 83
122 84
123 85
124 86
125 87
126 88
127 89
128 90
129 91
130 92
< >
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