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
251 213
252 214
253 215
254 216
255 217
256 218
257 219
258 220
259 221
260 222
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
< >
page |< < (180) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div641" type="section" level="1" n="213">
          <p>
            <s xml:id="echoid-s6875" xml:space="preserve">
              <pb o="180" file="0218" n="218" rhead="Apollonij Pergæi"/>
            ſarum in vna ſectionum ad homologa abſciſſa alterius eſt eadem ( 12. </s>
            <s xml:id="echoid-s6876" xml:space="preserve">ex
              <lb/>
            6. </s>
            <s xml:id="echoid-s6877" xml:space="preserve">), & </s>
            <s xml:id="echoid-s6878" xml:space="preserve">anguli compræhenſi à potentibus, & </s>
            <s xml:id="echoid-s6879" xml:space="preserve">abſciſſis ſunt æquales; </s>
            <s xml:id="echoid-s6880" xml:space="preserve">quia
              <lb/>
            æquales ſunt duobus angulis R A L, S C N æqualibus, & </s>
            <s xml:id="echoid-s6881" xml:space="preserve">propterea duo
              <lb/>
              <note position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            ſegmenta ſunt ſimilia.</s>
            <s xml:id="echoid-s6882" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6883" xml:space="preserve">Poſtea oſtendetur, quod ſi duo ſegmenta fuerint ſimilia, erit
              <lb/>
            angulus F æqualis E, & </s>
            <s xml:id="echoid-s6884" xml:space="preserve">A M ad A E, vt O C ad C F.</s>
            <s xml:id="echoid-s6885" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6886" xml:space="preserve">Quia propter ſimilitudinem duorum ſegmentorum continebunt poten-
              <lb/>
              <note position="right" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">d</note>
            tes cum ſuis abſciſſis angulos æquales, & </s>
            <s xml:id="echoid-s6887" xml:space="preserve">erit proportio potentium ad ab-
              <lb/>
              <note position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            ſciſſas eadem, & </s>
            <s xml:id="echoid-s6888" xml:space="preserve">proportio abſciſſarum, in vna earum ad ſua homologa in
              <lb/>
            altera, erit eadem. </s>
            <s xml:id="echoid-s6889" xml:space="preserve">Et quia V a in a E ad quadratũ a A eandem propor-
              <lb/>
              <figure xlink:label="fig-0218-01" xlink:href="fig-0218-01a" number="243">
                <image file="0218-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0218-01"/>
              </figure>
            tionem habet, quàm Y c in c F ad quadratum c C, & </s>
            <s xml:id="echoid-s6890" xml:space="preserve">duo anguli a, & </s>
            <s xml:id="echoid-s6891" xml:space="preserve">c
              <lb/>
            ſunt recti; </s>
            <s xml:id="echoid-s6892" xml:space="preserve">atque angulus C, nempe O æqualis eſt A, nempe M, propter
              <lb/>
            ſimilitudinem ſegmentorum: </s>
            <s xml:id="echoid-s6893" xml:space="preserve">ergo triangulum A E V ſimile eſt C F Y,
              <lb/>
            & </s>
            <s xml:id="echoid-s6894" xml:space="preserve">angulus V æqualis eſt angulo Y; </s>
            <s xml:id="echoid-s6895" xml:space="preserve">pariterque angulus E æqualis eſt F,
              <lb/>
            & </s>
            <s xml:id="echoid-s6896" xml:space="preserve">A V ad A E eandem proportionem habet, quàm Y C ad C F. </s>
            <s xml:id="echoid-s6897" xml:space="preserve">Po-
              <lb/>
            namus iam P A ad duplam A E, vt Q C ad duplam C F; </s>
            <s xml:id="echoid-s6898" xml:space="preserve">ergo ex æqua-
              <lb/>
            litate A T diameter ad A P erectum eius eſt, vt C X diameter ad C Q
              <lb/>
            erectum eius ( 53. </s>
            <s xml:id="echoid-s6899" xml:space="preserve">54. </s>
            <s xml:id="echoid-s6900" xml:space="preserve">ex I. </s>
            <s xml:id="echoid-s6901" xml:space="preserve">) & </s>
            <s xml:id="echoid-s6902" xml:space="preserve">T M in M A ad quadratum M G eandẽ
              <lb/>
              <note position="left" xlink:label="note-0218-04" xlink:href="note-0218-04a" xml:space="preserve">21. lib. I.</note>
            proportionem habet, quàm X O in O C ad quadratum O I: </s>
            <s xml:id="echoid-s6903" xml:space="preserve">at ſuppoſi-
              <lb/>
            tum eſt quadratum A M ad quadratum M G, vt quadratum C O ad qua-
              <lb/>
            dratum O I; </s>
            <s xml:id="echoid-s6904" xml:space="preserve">ergo ex æqualitate T M in M A ad quadratum A M, nem-
              <lb/>
            pe T M ad M A, eandem proportionem habet, quàm X O in O C </s>
          </p>
        </div>
      </text>
    </echo>
Impressum