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
81 43
82 44
83 45
84 46
85 47
86 48
87 49
88 50
89 51
90 52
91 53
92 54
93 55
94 56
95 57
96 58
97 59
98 60
99 61
100 62
101 63
102 64
103 65
104 66
105 67
106 68
107 69
108 70
109 71
110 72
< >
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