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
261 223
262 224
263 225
264 226
265 227
266 228
267 229
268 230
269 231
270 232
271 233
272 234
273 235
274 236
275 237
276 238
277 239
278 240
279 241
280 242
281 243
282 244
283 245
284 246
285 247
286 248
287 249
288 250
289 251
290 252
< >
page |< < (278) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div865" type="section" level="1" n="264">
          <pb o="278" file="0316" n="316" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div868" type="section" level="1" n="265">
          <head xml:id="echoid-head333" xml:space="preserve">PROPOSITIO VI. & VII.</head>
          <p>
            <s xml:id="echoid-s10297" xml:space="preserve">SI in hyperbole, aut ellipſi addantur axi tranſuerſo, vel au-
              <lb/>
              <note position="right" xlink:label="note-0316-01" xlink:href="note-0316-01a" xml:space="preserve">a</note>
            ferantur ab inclinato duæ interceptæ A G, C H ab eius
              <lb/>
            terminis A, C, atque à vertice ſectionis A educatur recta linea
              <lb/>
            A B ad terminum alicuius potentialis B E, & </s>
            <s xml:id="echoid-s10298" xml:space="preserve">per centrum D
              <lb/>
              <figure xlink:label="fig-0316-01" xlink:href="fig-0316-01a" number="365">
                <image file="0316-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0316-01"/>
              </figure>
            ducãtur diametri coniugatæ I L, N O, ita vt rectus N O æqui-
              <lb/>
            diſtet ipſi lineæ A B: </s>
            <s xml:id="echoid-s10299" xml:space="preserve">vtiquè proportio figuræ inclinatæ, vel
              <lb/>
            tranſuerſæ coniugatarum, quæ eſt eadem proportioni quadrati
              <lb/>
            I L ad quadratum N O, erit quoquè eadem, quàm habent li-
              <lb/>
            neæ inter incidentiam illius ordinatim applicatæ ad axim, & </s>
            <s xml:id="echoid-s10300" xml:space="preserve">ter-
              <lb/>
            minos diuidentes duarum interceptarũ, ſcilicet vt H E ad E G.</s>
            <s xml:id="echoid-s10301" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10302" xml:space="preserve">Educamus I M tangentem, & </s>
            <s xml:id="echoid-s10303" xml:space="preserve">I S perpendicularem. </s>
            <s xml:id="echoid-s10304" xml:space="preserve">Et quia A D eſt
              <lb/>
              <note position="right" xlink:label="note-0316-02" xlink:href="note-0316-02a" xml:space="preserve">b</note>
            æqualis D C, & </s>
            <s xml:id="echoid-s10305" xml:space="preserve">A K æqualis K B (eo quod I L cum ſit coniugata N O
              <lb/>
            bifariam diuidit A B) erit C B parallela ipſi I D, & </s>
            <s xml:id="echoid-s10306" xml:space="preserve">propterea M S ad
              <lb/>
            S D, nempè A E ad E C (propter ſimilitudinem triangulorum) eſt vt
              <lb/>
            quadratum I M ad quadratum N D (4. </s>
            <s xml:id="echoid-s10307" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10308" xml:space="preserve">& </s>
            <s xml:id="echoid-s10309" xml:space="preserve">quadratum I D ad qua-
              <lb/>
            dratum I M eſt vt quadratum C B ad quadratum B A (propter ſimilitu-
              <lb/>
            dinem triangulorum); </s>
            <s xml:id="echoid-s10310" xml:space="preserve">ergo proportio quadrati I D ad quadratum N D
              <lb/>
            eſt compoſita ex ratione A E ad E C, & </s>
            <s xml:id="echoid-s10311" xml:space="preserve">ex ratione quadrati C B ad qua-
              <lb/>
            dratum B A; </s>
            <s xml:id="echoid-s10312" xml:space="preserve">ſed proportio quadrati C B ad quadratum B A eſt compo-
              <lb/>
            ſita ex ratione quadrati C B ad C E in E H, & </s>
            <s xml:id="echoid-s10313" xml:space="preserve">ex ratione C E in E H
              <lb/>
            ad A E in E G, & </s>
            <s xml:id="echoid-s10314" xml:space="preserve">ex ratione A E in E G ad quadratum A B; </s>
            <s xml:id="echoid-s10315" xml:space="preserve">eſt vero
              <lb/>
            quadratum C B ad C E in E H, vt C A ad A H (3. </s>
            <s xml:id="echoid-s10316" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10317" xml:space="preserve">atquè A E
              <lb/>
            in E G ad quadratum A B eſt vt G C ad C A (2. </s>
            <s xml:id="echoid-s10318" xml:space="preserve">ex 7.)</s>
            <s xml:id="echoid-s10319" xml:space="preserve">, & </s>
            <s xml:id="echoid-s10320" xml:space="preserve">proportio
              <lb/>
            C E in E H ad A E in E G, componitur ex ratione C E ad A E, & </s>
            <s xml:id="echoid-s10321" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum