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
171 133
172 134
173 135
174 136
175 137
176 138
177 139
178 140
179 141
180 142
181 143
182 144
183 145
184 146
185 147
186 148
187 149
188 150
189 151
190 152
191 153
192 154
193 155
194 156
195 157
196 158
197 159
198 160
199 161
200 162
< >
page |< < (194) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div671" type="section" level="1" n="223">
          <p>
            <s xml:id="echoid-s7336" xml:space="preserve">
              <pb o="194" file="0232" n="232" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0232-01" xlink:href="fig-0232-01a" number="262">
                <image file="0232-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0232-01"/>
              </figure>
            ad E K, nempe P M ad D K potentia, nempe M Q ad Q K, & </s>
            <s xml:id="echoid-s7337" xml:space="preserve">per con-
              <lb/>
            uerſionem rationis O L ad L I erit, vt Q M ad M K: </s>
            <s xml:id="echoid-s7338" xml:space="preserve">eſtque I L ad L B,
              <lb/>
            vt K M ad M E; </s>
            <s xml:id="echoid-s7339" xml:space="preserve">ergo O L ad L B eſt, vt Q M ad M E, & </s>
            <s xml:id="echoid-s7340" xml:space="preserve">L B ad L N
              <lb/>
            eſt, vt E M ad M P (propter ſimilitudinem duarum ſectionum) ergo ex
              <lb/>
              <note position="right" xlink:label="note-0232-01" xlink:href="note-0232-01a" xml:space="preserve">c</note>
              <note position="left" xlink:label="note-0232-02" xlink:href="note-0232-02a" xml:space="preserve">Defin. 2.</note>
            æqualitate O L ad L N erit, vt Q M ad M P; </s>
            <s xml:id="echoid-s7341" xml:space="preserve">ſuntque M, & </s>
            <s xml:id="echoid-s7342" xml:space="preserve">L duo an-
              <lb/>
            guli recti; </s>
            <s xml:id="echoid-s7343" xml:space="preserve">ergo N L O ſimile eſt P M Q; </s>
            <s xml:id="echoid-s7344" xml:space="preserve">& </s>
            <s xml:id="echoid-s7345" xml:space="preserve">per R, S ſemipartitiones ip-
              <lb/>
            ſarum N A, D P ducamus ipſas T V, X Y parallelas duobus axibus, & </s>
            <s xml:id="echoid-s7346" xml:space="preserve">
              <lb/>
            ex duobus punctis V, Y, educamus perpendiculares V Z, Y a ſuper duos
              <lb/>
            axes. </s>
            <s xml:id="echoid-s7347" xml:space="preserve">Et quia N O ad O A eſt, vt P Q ad Q D comparando antecedẽ-
              <lb/>
            tes ad ſemiſſes differentiarum terminorum vel ad ſemiſummas eorũ fiet N
              <lb/>
              <note position="right" xlink:label="note-0232-03" xlink:href="note-0232-03a" xml:space="preserve">d</note>
            O ad R O, nempe N L ad L T, quæ eſt æqualis ipſi V Z, nempe L B
              <lb/>
            ad B Z longitudine (19. </s>
            <s xml:id="echoid-s7348" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s7349" xml:space="preserve">vt P Q ad Q S, nempe P M ad X M æ-
              <lb/>
            qualem ipſi Y a, nempe longitudine, vt M E ad E a (19. </s>
            <s xml:id="echoid-s7350" xml:space="preserve">ex 1) igitur
              <lb/>
              <note position="left" xlink:label="note-0232-04" xlink:href="note-0232-04a" xml:space="preserve">20. lib. 1.</note>
            comparando differentias terminorum ad antecedentes, erit Z L ad L B,
              <lb/>
            vt a M ad M E, & </s>
            <s xml:id="echoid-s7351" xml:space="preserve">L B ad L O eſt, vt M E ad M Q; </s>
            <s xml:id="echoid-s7352" xml:space="preserve">ergo ex æqualitate
              <lb/>
            L Z ad L O, nempe N b ad N O eſt, vt M a ad M Q, nempe P c ad P Q
              <lb/>
              <note position="left" xlink:label="note-0232-05" xlink:href="note-0232-05a" xml:space="preserve">Ibidem.</note>
            crat autem prius N R ad N O, vt S P ad P Q, & </s>
            <s xml:id="echoid-s7353" xml:space="preserve">comparando ſemisũ-
              <lb/>
              <note position="right" xlink:label="note-0232-06" xlink:href="note-0232-06a" xml:space="preserve">e</note>
            mas, vel ſemidifferentias terminorum ad eorundem differentias O R ad
              <lb/>
            R b erit, vt Q S ad S c, & </s>
            <s xml:id="echoid-s7354" xml:space="preserve">R b ad R V eſt, vt S c ad S Y; </s>
            <s xml:id="echoid-s7355" xml:space="preserve">quia
              <lb/>
            duo triangula V R b, Y S c ſunt ſimilia; </s>
            <s xml:id="echoid-s7356" xml:space="preserve">ergo R O ad R V eandem pro-
              <lb/>
            portionem habet, quàm Q S ad S Y; </s>
            <s xml:id="echoid-s7357" xml:space="preserve">ſed tangens in V perueniens ad L O
              <lb/>
              <note position="right" xlink:label="note-0232-07" xlink:href="note-0232-07a" xml:space="preserve">f</note>
            æqualis eſt O R, cui parallela eſt; </s>
            <s xml:id="echoid-s7358" xml:space="preserve">quia cadit inter duas lineas parallelas;
              <lb/>
            </s>
            <s xml:id="echoid-s7359" xml:space="preserve">& </s>
            <s xml:id="echoid-s7360" xml:space="preserve">ſimiliter tangens in Y parallela eſt S Q, & </s>
            <s xml:id="echoid-s7361" xml:space="preserve">ei æqualis; </s>
            <s xml:id="echoid-s7362" xml:space="preserve">ergo V R ab-
              <lb/>
            ſciſſa ad tangentem eſt, vt abſciſſa S Y ad eius tangentem, & </s>
            <s xml:id="echoid-s7363" xml:space="preserve">angulus Q
              <lb/>
            æqualis eſt angulo O; </s>
            <s xml:id="echoid-s7364" xml:space="preserve">igitur duo ſegmenta N V A, P Y D ſunt ſimilia
              <lb/>
            (16. </s>
            <s xml:id="echoid-s7365" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s7366" xml:space="preserve">& </s>
            <s xml:id="echoid-s7367" xml:space="preserve">pariter duo ſegmenta A B C, D E F, atque duo ſegmen-
              <lb/>
              <note position="right" xlink:label="note-0232-08" xlink:href="note-0232-08a" xml:space="preserve">g</note>
            ta N B, P E ſunt ſimilia inter ſe, & </s>
            <s xml:id="echoid-s7368" xml:space="preserve">ſimiliter poſita.</s>
            <s xml:id="echoid-s7369" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7370" xml:space="preserve">Deinde ponamus aliud ſegmentum P d. </s>
            <s xml:id="echoid-s7371" xml:space="preserve">Dico non eſſe ſimile alicui
              <lb/>
              <note position="right" xlink:label="note-0232-09" xlink:href="note-0232-09a" xml:space="preserve">h</note>
            prædictorum ſegmentorum, quia non abſcinduntur à duabus ordinationi-
              <lb/>
            bus vnius axis (18. </s>
            <s xml:id="echoid-s7372" xml:space="preserve">ex 6.)</s>
            <s xml:id="echoid-s7373" xml:space="preserve">. </s>
            <s xml:id="echoid-s7374" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s7375" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum