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 |< < (188) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div656" type="section" level="1" n="219">
          <p style="it">
            <s xml:id="echoid-s7118" xml:space="preserve">
              <pb o="188" file="0226" n="226" rhead="Apollonij Pergæi"/>
            ad A E, vt O C ad C F, ſuntque anguli E, & </s>
            <s xml:id="echoid-s7119" xml:space="preserve">F æquales, vt dictum eſt. </s>
            <s xml:id="echoid-s7120" xml:space="preserve">Et
              <lb/>
            hoc erat propoſitum.</s>
            <s xml:id="echoid-s7121" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div659" type="section" level="1" n="220">
          <head xml:id="echoid-head277" xml:space="preserve">Notæ in Propoſit. XVII.</head>
          <p style="it">
            <s xml:id="echoid-s7122" xml:space="preserve">DEinde ſint ſectiones hyperbolicæ, aut ellipticæ, & </s>
            <s xml:id="echoid-s7123" xml:space="preserve">reliqua in ſuo
              <lb/>
              <note position="right" xlink:label="note-0226-01" xlink:href="note-0226-01a" xml:space="preserve">a</note>
            ſtatu, &</s>
            <s xml:id="echoid-s7124" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7125" xml:space="preserve">Ideſt. </s>
            <s xml:id="echoid-s7126" xml:space="preserve">Supponantur ſectiones hyperbolicæ, vel ellipticæ A B,
              <lb/>
            & </s>
            <s xml:id="echoid-s7127" xml:space="preserve">C D ſimiles inter ſe, ſcilicet figuræ axium V B, & </s>
            <s xml:id="echoid-s7128" xml:space="preserve">γ D ſint ſimiles inter ſe,
              <lb/>
            atque à verticibus A, & </s>
            <s xml:id="echoid-s7129" xml:space="preserve">C duarum diametrorum A M, & </s>
            <s xml:id="echoid-s7130" xml:space="preserve">C O ductæ ſint re-
              <lb/>
              <figure xlink:label="fig-0226-01" xlink:href="fig-0226-01a" number="254">
                <image file="0226-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0226-01"/>
              </figure>
            ctæ lineæ contingentes A E, & </s>
            <s xml:id="echoid-s7131" xml:space="preserve">C F, efficientes cum axibus angulos A E B, & </s>
            <s xml:id="echoid-s7132" xml:space="preserve">
              <lb/>
            C F D æquales, ſintque H G, & </s>
            <s xml:id="echoid-s7133" xml:space="preserve">K I ordinatim ad diametros applicatæ, ſcili-
              <lb/>
            cet æquidiſtantes contingentibus verticalibus; </s>
            <s xml:id="echoid-s7134" xml:space="preserve">& </s>
            <s xml:id="echoid-s7135" xml:space="preserve">habeat abſciſſa M A ad portio-
              <lb/>
            nem contingentis A E eandem proportionem, quàm abſcißa O C habet ad por-
              <lb/>
            tionem contingentis C F; </s>
            <s xml:id="echoid-s7136" xml:space="preserve">Dico ſegmenta H A G, & </s>
            <s xml:id="echoid-s7137" xml:space="preserve">K C I ſimlia eſſe inter ſe.</s>
            <s xml:id="echoid-s7138" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7139" xml:space="preserve">Ergo Y c C ſimile eſt V a A, &</s>
            <s xml:id="echoid-s7140" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7141" xml:space="preserve">Quoniam duæ ordinatim ad axes ap-
              <lb/>
              <note position="right" xlink:label="note-0226-02" xlink:href="note-0226-02a" xml:space="preserve">b</note>
            plicatæ A a, & </s>
            <s xml:id="echoid-s7142" xml:space="preserve">C c perpendiculares ſunt ad axes, erunt in triangulis A a E,
              <lb/>
            & </s>
            <s xml:id="echoid-s7143" xml:space="preserve">C c F duo anguli a, & </s>
            <s xml:id="echoid-s7144" xml:space="preserve">c recti: </s>
            <s xml:id="echoid-s7145" xml:space="preserve">atque ex hypotheſi duo reliqui anguli E, & </s>
            <s xml:id="echoid-s7146" xml:space="preserve">
              <lb/>
            F æquales quoque ſunt; </s>
            <s xml:id="echoid-s7147" xml:space="preserve">igitur tertius angulus a A E æqualis eſt tertio angulo c
              <lb/>
            C F, cumque in duobus triangulis V A E, atque γ C F ab eorum verticibus A,
              <lb/>
            & </s>
            <s xml:id="echoid-s7148" xml:space="preserve">C ducuntur ad baſes V E, & </s>
            <s xml:id="echoid-s7149" xml:space="preserve">γ F duæ rectæ lineæ A a, & </s>
            <s xml:id="echoid-s7150" xml:space="preserve">C c continentes
              <lb/>
            cum baſibus angulos æquales, nempe rectos, & </s>
            <s xml:id="echoid-s7151" xml:space="preserve">rectangulum V a E ad quadra-
              <lb/>
            tum a A eandem proportionem habet, quàm rectangulum γ c F ad quadratum
              <lb/>
            c C, vt in textu oſtenſum eſt: </s>
            <s xml:id="echoid-s7152" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s7153" xml:space="preserve">duo anguli a A E, & </s>
            <s xml:id="echoid-s7154" xml:space="preserve">c C F æquales oſten-
              <lb/>
              <note position="left" xlink:label="note-0226-03" xlink:href="note-0226-03a" xml:space="preserve">ex 37.
                <lb/>
              lib. 1.</note>
            ſi ſunt inter ſe; </s>
            <s xml:id="echoid-s7155" xml:space="preserve">igitur erunt triangula V A E, & </s>
            <s xml:id="echoid-s7156" xml:space="preserve">γ C F ſimilia inter ſe; </s>
            <s xml:id="echoid-s7157" xml:space="preserve">ergo
              <lb/>
              <note position="left" xlink:label="note-0226-04" xlink:href="note-0226-04a" xml:space="preserve">Propoſ. 6
                <lb/>
              præmiſſ.</note>
            angulus V æqualis eſt angulo γ, atque angulus E A V æqualis erit angulo F </s>
          </p>
        </div>
      </text>
    </echo>
Impressum