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
191 153
192 154
193 155
194 156
195 157
196 158
197 159
198 160
199 161
200 162
201 163
202 164
203 165
204 166
205 167
206 168
207 169
208 170
209 171
210 172
211 173
212 174
213 175
214 176
215 177
216 178
217 179
218 180
219 181
220 182
< >
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