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

List of thumbnails

< >
241
241 (203) 		242
242 (204)
243
243 (205) 		244
244 (206)
245
245 (207) 		246
246 (208)
247
247 (209) 		248
248 (210)
249
249 (211) 		250
250 (212)
< >
page |< < (229) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div711" type="section" level="1" n="234">
          <p style="it">
            <s xml:id="echoid-s8557" xml:space="preserve">
              <pb o="229" file="0267" n="267" rhead="Conicor. Lib. VI."/>
            ad L S eſt vt quadratum D Z ad quadratum Z F ; </s>
            <s xml:id="echoid-s8558" xml:space="preserve">igitur P G ad G R ean-
              <lb/>
            dem proportionem habet, quàm Z L ad L S, & </s>
            <s xml:id="echoid-s8559" xml:space="preserve">propterea figuræ ſectionem
              <lb/>
              <note position="right" xlink:label="note-0267-01" xlink:href="note-0267-01a" xml:space="preserve">ex 12.
                <lb/>
              huius.</note>
            erunt ſimiles; </s>
            <s xml:id="echoid-s8560" xml:space="preserve">ijs autẽ figuris æqualia oſtenſa ſunt quadrata dupliciũ O Y, & </s>
            <s xml:id="echoid-s8561" xml:space="preserve">K
              <lb/>
            Z, quæ ſuppoſitæ fuerunt æquales; </s>
            <s xml:id="echoid-s8562" xml:space="preserve">igitur figuræ P G R, & </s>
            <s xml:id="echoid-s8563" xml:space="preserve">Z L S ſimiles, & </s>
            <s xml:id="echoid-s8564" xml:space="preserve">
              <lb/>
            æquales ſunt inter ſe, atque diametri æquæ inclinatæ ſunt ad ordinatim ad eas
              <lb/>
            applicatas H I, M N; </s>
            <s xml:id="echoid-s8565" xml:space="preserve">igitur ſectiones H G I, M L N æquales ſunt inter ſe,
              <lb/>
              <note position="right" xlink:label="note-0267-02" xlink:href="note-0267-02a" xml:space="preserve">Prop. 10.
                <lb/>
              huius.</note>
            ſimiles, & </s>
            <s xml:id="echoid-s8566" xml:space="preserve">congruentes, quarum figuræ æquales ſunt quadratis duplicium inter-
              <lb/>
            ceptarum O Y, & </s>
            <s xml:id="echoid-s8567" xml:space="preserve">K Z, quod erat propoſitum.</s>
            <s xml:id="echoid-s8568" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div749" type="section" level="1" n="235">
          <head xml:id="echoid-head296" xml:space="preserve">LEMMA IX.</head>
          <p style="it">
            <s xml:id="echoid-s8569" xml:space="preserve">S I in duobus conis A B C, D E F, baſes ſint in eodem plano, & </s>
            <s xml:id="echoid-s8570" xml:space="preserve">
              <lb/>
            duo triangula per axes A B C, D E F fuerint ſimilia, & </s>
            <s xml:id="echoid-s8571" xml:space="preserve">ſimi-
              <lb/>
            liter poſita, & </s>
            <s xml:id="echoid-s8572" xml:space="preserve">in eodem plano exiſtentia, erunt coni ſimiles inter ſe.</s>
            <s xml:id="echoid-s8573" xml:space="preserve"/>
          </p>
          <figure number="314">
            <image file="0267-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0267-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s8574" xml:space="preserve">Ducantur à verticibus A, & </s>
            <s xml:id="echoid-s8575" xml:space="preserve">D duæ rectæ A G, & </s>
            <s xml:id="echoid-s8576" xml:space="preserve">D H perpendiculares ad
              <lb/>
            baſes conorũ, & </s>
            <s xml:id="echoid-s8577" xml:space="preserve">à terminis axium A Y, & </s>
            <s xml:id="echoid-s8578" xml:space="preserve">D Z coniungantur rectæ lineæ Y G,
              <lb/>
            & </s>
            <s xml:id="echoid-s8579" xml:space="preserve">Z H. </s>
            <s xml:id="echoid-s8580" xml:space="preserve">Quoniã planum, in quo exiſtunt duo triangula A B C, D E F ſecat
              <lb/>
            planum, in quo baſes conorum iacent in vna recta linea, quæ baſis eſt vtriuſque
              <lb/>
            trianguli per axes conorum ducti; </s>
            <s xml:id="echoid-s8581" xml:space="preserve">ideoque B C, & </s>
            <s xml:id="echoid-s8582" xml:space="preserve">E F in directum conſtitutæ
              <lb/>
            erunt, & </s>
            <s xml:id="echoid-s8583" xml:space="preserve">circa angulos æquales B, & </s>
            <s xml:id="echoid-s8584" xml:space="preserve">E latera A B ad B C, atque D E ad E
              <lb/>
            F ſunt proportionalia ( propter triangulorum A B C, & </s>
            <s xml:id="echoid-s8585" xml:space="preserve">D E F ſimilitudinem)
              <lb/>
            erunt quoque ad conſequẽtium ſemiſſes proportionales, ſcilicet A B ad B Y erit,
              <lb/>
            vt D E ad E Z circa angulos æquales, & </s>
            <s xml:id="echoid-s8586" xml:space="preserve">propterea triangula A B Y, & </s>
            <s xml:id="echoid-s8587" xml:space="preserve">D E
              <lb/>
            Z ſimilia erunt: </s>
            <s xml:id="echoid-s8588" xml:space="preserve">& </s>
            <s xml:id="echoid-s8589" xml:space="preserve">ideò duo anguli B Y A, & </s>
            <s xml:id="echoid-s8590" xml:space="preserve">E Z D, externus interno, æqua-
              <lb/>
            les erunt inter ſe; </s>
            <s xml:id="echoid-s8591" xml:space="preserve">igitur Y A, & </s>
            <s xml:id="echoid-s8592" xml:space="preserve">Z D in eodem plano exiſtentes, parallelæ
              <lb/>
            erunt inter ſe; </s>
            <s xml:id="echoid-s8593" xml:space="preserve">ſunt quoque A G, D H inter ſe parallelæ ( cum ſint perpendicu-
              <lb/>
            lares ad idem planum baſium ) ergo duo anguli Y A G, & </s>
            <s xml:id="echoid-s8594" xml:space="preserve">Z D H æquales ſunt
              <lb/>
            inter ſe; </s>
            <s xml:id="echoid-s8595" xml:space="preserve">atquè anguli G, & </s>
            <s xml:id="echoid-s8596" xml:space="preserve">H æquales ſunt, nempe recti; </s>
            <s xml:id="echoid-s8597" xml:space="preserve">igitur in triangu-
              <lb/>
            lis A Y G, & </s>
            <s xml:id="echoid-s8598" xml:space="preserve">D Z H, duo poſtremi anguli A Y G, & </s>
            <s xml:id="echoid-s8599" xml:space="preserve">D Z H æquales </s>
          </p>
        </div>
      </text>
    </echo>
Impressum