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
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39 1
40 2
< >
page |< < (46) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div187" type="section" level="1" n="72">
          <pb o="46" file="0084" n="84" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s2190" xml:space="preserve">Et ponamus quamlibet duarum proportionum C F ad F D, & </s>
            <s xml:id="echoid-s2191" xml:space="preserve">I S ad S C,
              <lb/>
              <note position="right" xlink:label="note-0084-01" xlink:href="note-0084-01a" xml:space="preserve">b</note>
            vt proportio figuræ, & </s>
            <s xml:id="echoid-s2192" xml:space="preserve">educamus ex E, S, &</s>
            <s xml:id="echoid-s2193" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2194" xml:space="preserve">Ideſt fiat diſtantia ex centro
              <lb/>
            vſque ad perpendicularem E D ad eius portionem D F in hyperbola, vt ſumma late-
              <lb/>
            ris tranſuerſi, & </s>
            <s xml:id="echoid-s2195" xml:space="preserve">recti ad latus rectum, & </s>
            <s xml:id="echoid-s2196" xml:space="preserve">vt eorum differentia in ellipſi ad latus
              <lb/>
            rectum ita fiat C D ad eius productionem D F; </s>
            <s xml:id="echoid-s2197" xml:space="preserve">tunc enim C F ad F D diuidendo in
              <lb/>
            hyperbola, & </s>
            <s xml:id="echoid-s2198" xml:space="preserve">compo-
              <lb/>
              <figure xlink:label="fig-0084-01" xlink:href="fig-0084-01a" number="61">
                <image file="0084-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0084-01"/>
              </figure>
            nendo in ellipſi habe-
              <lb/>
            bit eandem propor-
              <lb/>
            tionem, quàm latus
              <lb/>
            tranſuerſum ad re-
              <lb/>
            ctum; </s>
            <s xml:id="echoid-s2199" xml:space="preserve">pariterq; </s>
            <s xml:id="echoid-s2200" xml:space="preserve">fiat
              <lb/>
            E K ad K D in eadẽ
              <lb/>
            proportione figuræ,
              <lb/>
            & </s>
            <s xml:id="echoid-s2201" xml:space="preserve">ex E, K educamus
              <lb/>
            rectas E I, K S pa-
              <lb/>
            rallelas axi A C D,
              <lb/>
            ſecantes I C, & </s>
            <s xml:id="echoid-s2202" xml:space="preserve">L F
              <lb/>
            parallelas ipſi E D
              <lb/>
            in I, S, L, & </s>
            <s xml:id="echoid-s2203" xml:space="preserve">M.
              <lb/>
            </s>
            <s xml:id="echoid-s2204" xml:space="preserve">Immutaui poſtremã
              <lb/>
            partem conſtructio-
              <lb/>
            nis, vt manifeſte er-
              <lb/>
            roneã in textu Ara-
              <lb/>
            bico; </s>
            <s xml:id="echoid-s2205" xml:space="preserve">Si enim I C ad
              <lb/>
            libitum ſumpta ſeca-
              <lb/>
            tur in S in ratione
              <lb/>
            C F ad F D non ca-
              <lb/>
            det neceſſariò E L
              <lb/>
            parallela C D ſuper
              <lb/>
            punctum I.</s>
            <s xml:id="echoid-s2206" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2207" xml:space="preserve">Et interponamus
              <lb/>
              <note position="right" xlink:label="note-0084-02" xlink:href="note-0084-02a" xml:space="preserve">c</note>
            inter F C, C A du-
              <lb/>
            as C N, C O pro-
              <lb/>
            portionales illis duabus, &</s>
            <s xml:id="echoid-s2208" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2209" xml:space="preserve">Textum corruptum ſic reſtituo: </s>
            <s xml:id="echoid-s2210" xml:space="preserve">Interponamus in-
              <lb/>
            ter F C, & </s>
            <s xml:id="echoid-s2211" xml:space="preserve">A C duas medias proportionales, itaut F C, N C, C O, C A ſint continuè
              <lb/>
            proportionales, quod fieri poſſe conſtat ex lemmate 7. </s>
            <s xml:id="echoid-s2212" xml:space="preserve">huius librt.</s>
            <s xml:id="echoid-s2213" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2214" xml:space="preserve">Et ponamus proportionem lineæ alicuius, vt eſt Q compoſitam, &</s>
            <s xml:id="echoid-s2215" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2216" xml:space="preserve">Vo-
              <lb/>
              <note position="right" xlink:label="note-0084-03" xlink:href="note-0084-03a" xml:space="preserve">d</note>
            catur Trutina in hyperbola, & </s>
            <s xml:id="echoid-s2217" xml:space="preserve">ellipſi linea recta Q, quæ ad B O compoſitam propor-
              <lb/>
            tionem habet ex C D ad D F, & </s>
            <s xml:id="echoid-s2218" xml:space="preserve">ex ratione F O ad O C.</s>
            <s xml:id="echoid-s2219" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2220" xml:space="preserve">Producatur priùs E B ſecans axim in H, &</s>
            <s xml:id="echoid-s2221" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2222" xml:space="preserve">Producatur priùs E B ſecans
              <lb/>
              <note position="right" xlink:label="note-0084-04" xlink:href="note-0084-04a" xml:space="preserve">e</note>
            axim in H, & </s>
            <s xml:id="echoid-s2223" xml:space="preserve">rectam S K in R, nec non rectam I C in puncto T.</s>
            <s xml:id="echoid-s2224" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2225" xml:space="preserve">Ergo E D ad B O, quæ componitur ex E D ad D K, &</s>
            <s xml:id="echoid-s2226" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2227" xml:space="preserve">Nam poſita inter-
              <lb/>
              <note position="right" xlink:label="note-0084-05" xlink:href="note-0084-05a" xml:space="preserve">f</note>
            media D K, proportio E D ad B O compoſita erit ex ratione E D ad D K, & </s>
            <s xml:id="echoid-s2228" xml:space="preserve">ex ra-
              <lb/>
            tione D K ad B O; </s>
            <s xml:id="echoid-s2229" xml:space="preserve">eſt verò I C ad C S, vt E D ad D K (propter parallelas I E, S K,
              <lb/>
            C D) atque D K eſt æqualis G O in parallelogrammo G D; </s>
            <s xml:id="echoid-s2230" xml:space="preserve">ergo proportio E D ad B O
              <lb/>
            componitur ex ratione I C ad C S, & </s>
            <s xml:id="echoid-s2231" xml:space="preserve">ex ratione G O ad O B.</s>
            <s xml:id="echoid-s2232" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2233" xml:space="preserve">Sed E D ad D K eſt, vt CD ad DF, quia quælibet earum vt proportio
              <lb/>
              <note position="right" xlink:label="note-0084-06" xlink:href="note-0084-06a" xml:space="preserve">g</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum