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

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              <pb o="220" file="0258" n="258" rhead="Apollonij Pergæi"/>
            pter parallelas G H, B A, eſt an-
              <lb/>
              <figure xlink:label="fig-0258-01" xlink:href="fig-0258-01a" number="300">
                <image file="0258-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0258-01"/>
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            gulus G H A, ſeu E H N æqualis
              <lb/>
            angulo B A I; </s>
            <s xml:id="echoid-s8281" xml:space="preserve">ſed anguli B A I,
              <lb/>
            & </s>
            <s xml:id="echoid-s8282" xml:space="preserve">A E F vnicum rectum com-
              <lb/>
            plent; </s>
            <s xml:id="echoid-s8283" xml:space="preserve">ergo duo anguli N H E, & </s>
            <s xml:id="echoid-s8284" xml:space="preserve">
              <lb/>
            N E H ſimul ſumpti vni recto æ-
              <lb/>
            quales ſunt, & </s>
            <s xml:id="echoid-s8285" xml:space="preserve">propterea in trian-
              <lb/>
            gulo E N H reliquus angulus N
              <lb/>
            rectus erit: </s>
            <s xml:id="echoid-s8286" xml:space="preserve">erat quoque angulus
              <lb/>
            I G H rectus; </s>
            <s xml:id="echoid-s8287" xml:space="preserve">igitur I G (qui eſt
              <lb/>
              <note position="left" xlink:label="note-0258-01" xlink:href="note-0258-01a" xml:space="preserve">31. lib. 5.</note>
            ramus breuiſſimus cum ſit perpen-
              <lb/>
            dicularis ad tangentem G H) eſt
              <lb/>
            æquidiſtans rectæ lineæ E F; </s>
            <s xml:id="echoid-s8288" xml:space="preserve">quod erat propoſitum.</s>
            <s xml:id="echoid-s8289" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8290" xml:space="preserve">Facile deducitur, quod ſi angulus A E F fuerit rectus in parabola, & </s>
            <s xml:id="echoid-s8291" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0258-02" xlink:href="note-0258-02a" xml:space="preserve">SCHO-
                <lb/>
              LIVM.</note>
            non fuerit ſemirecto minor in hyperbole facta eadem conſtructione quilibet
              <lb/>
            ramus breuiſſimus I G æquidiſtans erit rectæ lineæ diuidenti angulũ A E F.</s>
            <s xml:id="echoid-s8292" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8293" xml:space="preserve">Nam angulus A I G ab axi, & </s>
            <s xml:id="echoid-s8294" xml:space="preserve">ramo breuiſſimo contentus eſt acutus, ſed an-
              <lb/>
            gulus F E A in parabola eſt re-
              <lb/>
              <figure xlink:label="fig-0258-02" xlink:href="fig-0258-02a" number="301">
                <image file="0258-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0258-02"/>
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              <note position="left" xlink:label="note-0258-03" xlink:href="note-0258-03a" xml:space="preserve">13. 14. 15.
                <lb/>
              lib. 5.</note>
            ctus; </s>
            <s xml:id="echoid-s8295" xml:space="preserve">ergo recta linea I G paralle-
              <lb/>
            la eſt alicui rectæ lineæ diuidenti
              <lb/>
            angulum A E F, in hyperbela ve-
              <lb/>
            rò factus eſt angulus A E D æqua-
              <lb/>
            lis angulo A E F, qui ſemirecto
              <lb/>
            minor non eſt; </s>
            <s xml:id="echoid-s8296" xml:space="preserve">propterea erit totus
              <lb/>
            angulus D E F rectus, aut obtu-
              <lb/>
            ſus; </s>
            <s xml:id="echoid-s8297" xml:space="preserve">ergo in triangulo E M N ex-
              <lb/>
            ternus angulus F N M maior in-
              <lb/>
            terno, & </s>
            <s xml:id="echoid-s8298" xml:space="preserve">oppoſito angulo E recto,
              <lb/>
            vel obtuſo, erit quoque obtuſus, & </s>
            <s xml:id="echoid-s8299" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0258-04" xlink:href="note-0258-04a" xml:space="preserve">31. lib. 5.</note>
            angulus I G N rectus eſt; </s>
            <s xml:id="echoid-s8300" xml:space="preserve">igitur I
              <lb/>
            G, F N ſe viciſſim ſecabunt vltra punctum E, & </s>
            <s xml:id="echoid-s8301" xml:space="preserve">ideo I G parallela erit rectæ
              <lb/>
            lineæ diuidenti angulum A E F. </s>
            <s xml:id="echoid-s8302" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s8303" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8304" xml:space="preserve">Sint duæ parabolæ, vel duæ hyperbo-
              <lb/>
              <figure xlink:label="fig-0258-03" xlink:href="fig-0258-03a" number="302">
                <image file="0258-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0258-03"/>
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              <note position="left" xlink:label="note-0258-05" xlink:href="note-0258-05a" xml:space="preserve">PROP. 7.
                <lb/>
              Addit.</note>
            læ æquales, & </s>
            <s xml:id="echoid-s8305" xml:space="preserve">ſimiliter poſitæ H B D,
              <lb/>
            & </s>
            <s xml:id="echoid-s8306" xml:space="preserve">I F G circa communem axim A H I:
              <lb/>
            </s>
            <s xml:id="echoid-s8307" xml:space="preserve">intercepta axis portio erit diſtantia ſectio-
              <lb/>
            num omnium maxima, & </s>
            <s xml:id="echoid-s8308" xml:space="preserve">ei propinquior
              <lb/>
            remotiore maior erit.</s>
            <s xml:id="echoid-s8309" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s8310" xml:space="preserve">Sint centra E, & </s>
            <s xml:id="echoid-s8311" xml:space="preserve">K, asymptoti P E O,
              <lb/>
            Q K R, & </s>
            <s xml:id="echoid-s8312" xml:space="preserve">à vertice H, & </s>
            <s xml:id="echoid-s8313" xml:space="preserve">à quibuslibet
              <lb/>
            punctis interiores ſectionis B D eleuentur
              <lb/>
              <note position="left" xlink:label="note-0258-06" xlink:href="note-0258-06a" xml:space="preserve">8. 9. 10. 30.
                <lb/>
              lib. 5.</note>
            lineæ breuiſſimæ, ſeu perpendiculares ad rectas
              <lb/>
            curuam B D contingentes in eiſdem punctis,
              <lb/>
            quæ ſint H A, B A, & </s>
            <s xml:id="echoid-s8314" xml:space="preserve">D C, quæ ſecent re-
              <lb/>
            liquam ſectionem in punctis I, F, & </s>
            <s xml:id="echoid-s8315" xml:space="preserve">G.</s>
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