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 |< < (259) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div814" type="section" level="1" n="248">
          <p style="it">
            <s xml:id="echoid-s9745" xml:space="preserve">
              <pb o="259" file="0297" n="297" rhead="Conicor. Lib. VI."/>
              <figure xlink:label="fig-0297-01" xlink:href="fig-0297-01a" number="344">
                <image file="0297-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0297-01"/>
              </figure>
            lum H I K ad quadratum I K, vt H I ad I K ſeu vt C A ad A D; </s>
            <s xml:id="echoid-s9746" xml:space="preserve">eſtque
              <lb/>
            rectangulum C I A æquale rectangulo H I K; </s>
            <s xml:id="echoid-s9747" xml:space="preserve">igitur rectangulum C I A ad qua-
              <lb/>
            dratum I K eandem proportionem habet, quàm C A ad A D; </s>
            <s xml:id="echoid-s9748" xml:space="preserve">componitur verò
              <lb/>
            proportio rectanguli C I A ad quadratum I K ex duabus proportionibus laterum
              <lb/>
            C I ad I K, & </s>
            <s xml:id="echoid-s9749" xml:space="preserve">A I ad I K: </s>
            <s xml:id="echoid-s9750" xml:space="preserve">& </s>
            <s xml:id="echoid-s9751" xml:space="preserve">propter parallelas N O, I K, atque K N, & </s>
            <s xml:id="echoid-s9752" xml:space="preserve">
              <lb/>
            C I, & </s>
            <s xml:id="echoid-s9753" xml:space="preserve">latus commune C O K duo triangula C I K, & </s>
            <s xml:id="echoid-s9754" xml:space="preserve">K O N ſimilia ſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s9755" xml:space="preserve">igitur K N ad N O eſt, vt C I ad I K; </s>
            <s xml:id="echoid-s9756" xml:space="preserve">& </s>
            <s xml:id="echoid-s9757" xml:space="preserve">quia in parallelogrammo I N la-
              <lb/>
            tera oppoſita ſunt æqualia K N ad N A eandem proportionem habebit quàm A I
              <lb/>
            ad I K; </s>
            <s xml:id="echoid-s9758" xml:space="preserve">quapropter duæ rationes K N ad N O, & </s>
            <s xml:id="echoid-s9759" xml:space="preserve">K N ad N A componunt
              <lb/>
            proportionem quadrati K N ad rectangulum A N O, quæ eadem eſt proportioni
              <lb/>
            rectanguli C I A ad quadratum I K; </s>
            <s xml:id="echoid-s9760" xml:space="preserve">& </s>
            <s xml:id="echoid-s9761" xml:space="preserve">propterea quadratum K N ad rectan-
              <lb/>
            gulum A N O eandem proportionem habebit, quàm A G ad A D. </s>
            <s xml:id="echoid-s9762" xml:space="preserve">Si igitur
              <lb/>
            fiat conus, cuius vertex K baſis circulus diametro A O deſcriptus, cuius pla-
              <lb/>
            num perpendiculare ſit ad planum A K C; </s>
            <s xml:id="echoid-s9763" xml:space="preserve">atque per rectam A C æquidiſtan-
              <lb/>
            tem ipſi K N planum ducatur perpendiculare ad idem planum A K C genera-
              <lb/>
            bitur ellipſis, cuius axis tranſuerſus erit A C, & </s>
            <s xml:id="echoid-s9764" xml:space="preserve">latus rectum A D. </s>
            <s xml:id="echoid-s9765" xml:space="preserve">Textus
              <lb/>
            igitur corrigi debere ex dictis manifeſtum eſt.</s>
            <s xml:id="echoid-s9766" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9767" xml:space="preserve">Et quia angulus H K C nempe A O K æqualis eſt H A C, & </s>
            <s xml:id="echoid-s9768" xml:space="preserve">angulus
              <lb/>
              <note position="left" xlink:label="note-0297-01" xlink:href="note-0297-01a" xml:space="preserve">C</note>
            C H A æqualis eſt C K A remanet angulus H C A æqualis O A K erit
              <lb/>
            H C A ſimile F E G ſimile quoque O K A; </s>
            <s xml:id="echoid-s9769" xml:space="preserve">ergo, &</s>
            <s xml:id="echoid-s9770" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9771" xml:space="preserve">Quoniam ex con-
              <lb/>
            ſtructione ſegmentum A H C capax eſt anguli æqualis angulo F erit angulus A
              <lb/>
            H C æqualis angulo F; </s>
            <s xml:id="echoid-s9772" xml:space="preserve">& </s>
            <s xml:id="echoid-s9773" xml:space="preserve">quia peripheria A H C ſecta eſt bifariam in H; </s>
            <s xml:id="echoid-s9774" xml:space="preserve">ergo
              <lb/>
            ſubtenſa latera A H, & </s>
            <s xml:id="echoid-s9775" xml:space="preserve">H C æqualia ſunt: </s>
            <s xml:id="echoid-s9776" xml:space="preserve">& </s>
            <s xml:id="echoid-s9777" xml:space="preserve">propterea triangulum A H C
              <lb/>
            iſoſcelium, & </s>
            <s xml:id="echoid-s9778" xml:space="preserve">ſimile erit triangulo E F G; </s>
            <s xml:id="echoid-s9779" xml:space="preserve">propterea quod anguli verticales æ-
              <lb/>
            quales ſunt inter ſe; </s>
            <s xml:id="echoid-s9780" xml:space="preserve">ſunt verò duo anguli A H C, & </s>
            <s xml:id="echoid-s9781" xml:space="preserve">A K C in eodem circuli
              <lb/>
            ſegmento; </s>
            <s xml:id="echoid-s9782" xml:space="preserve">ergo æquales ſunt inter ſe; </s>
            <s xml:id="echoid-s9783" xml:space="preserve">pariterque duo anguli C A H, & </s>
            <s xml:id="echoid-s9784" xml:space="preserve">C K H
              <lb/>
            in eodem circuli ſegmento conſtituti, æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s9785" xml:space="preserve">propter </s>
          </p>
        </div>
      </text>
    </echo>
Impressum