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

Table of contents

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[181.] Notæ in Propoſit. III.
Page: 187 (149)
[182.] Notæ in Propoſit. VI.
Page: 187 (149)
[183.] Notæ in Propoſit. VII.
Page: 187 (149)
[184.] Notæ in Propoſit. IX.
Page: 188 (150)
[185.] LEMMAI.
Page: 188 (150)
[186.] SECTIO TERTIA Continens Propoſit. V. & VIII. PROPOSITIO V.
Page: 190 (152)
[187.] PROPOSITIO VIII.
Page: 191 (153)
[188.] Notæ in Propoſit. V.
Page: 192 (154)
[189.] Notæ in Propoſit. VIII.
Page: 192 (154)
[190.] SECTIO QVARTA Continens Propoſit. XI. XII. XIII. & XIV. PROPOSITIO XI.
Page: 192 (154)
[191.] PROPOSITIO XII.
Page: 193 (155)
[192.] PROPOSITIO XIII.
Page: 194 (156)
[193.] PROPOSITIO XIV.
Page: 195 (157)
[194.] MONITVM.
Page: 196 (158)
[195.] LEMMA II.
Page: 196 (158)
[196.] COROLLARIVM.
Page: 197 (159)
[197.] LEMMA III.
Page: 197 (159)
[198.] LEMMA IV.
Page: 198 (160)
[199.] COROLLARIVM.
Page: 198 (160)
[200.] LEMMAV.
Page: 199 (161)
[201.] COROLLARIVM I.
Page: 199 (161)
[202.] COROLLARIVM II.
Page: 199 (161)
[203.] Notæ in Propoſit. XI.
Page: 203 (165)
[204.] Notæ in Propoſit. XII.
Page: 204 (166)
[205.] Notæ in Propoſit. XIII.
Page: 205 (167)
[206.] Notæ in Propoſit. XIV.
Page: 206 (168)
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
Page: 206 (168)
[208.] PROPOSITIO Præmiſſa VI.
Page: 209 (171)
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
Page: 209 (171)
[210.] Notæ in Propoſit. Præmiſſ. VI.
Page: 212 (174)
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            <s xml:id="echoid-s5467" xml:space="preserve">Quoniam facta conuenienti ſuperpoſitione axis A M ſuper axim D
              <lb/>
            O, cadet quoque ſectio A B ſuper ſectionem D E: </s>
            <s xml:id="echoid-s5468" xml:space="preserve">ſi enim non cadit ſu-
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            per illam, ſumatur (ſi fieri poteſt) eius punctum B, extra ſectionem.
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            <s xml:id="echoid-s5469" xml:space="preserve">D E cadens; </s>
            <s xml:id="echoid-s5470" xml:space="preserve">& </s>
            <s xml:id="echoid-s5471" xml:space="preserve">producatur ad axim perpendicularis B L vſque ad P: </s>
            <s xml:id="echoid-s5472" xml:space="preserve">& </s>
            <s xml:id="echoid-s5473" xml:space="preserve">
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            perficiatur planum A P applicatum comparatum; </s>
            <s xml:id="echoid-s5474" xml:space="preserve">& </s>
            <s xml:id="echoid-s5475" xml:space="preserve">ſecetur D N æqua-
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            lis A L, & </s>
            <s xml:id="echoid-s5476" xml:space="preserve">erigatur per N ad axim perpendicularis N E, & </s>
            <s xml:id="echoid-s5477" xml:space="preserve">producatur
              <lb/>
            vſque ad R, perficiendo planum D R applicatum comparatum; </s>
            <s xml:id="echoid-s5478" xml:space="preserve">Et quia
              <lb/>
            A I æqualis eſt D K, & </s>
            <s xml:id="echoid-s5479" xml:space="preserve">A L æqualis D N: </s>
            <s xml:id="echoid-s5480" xml:space="preserve">erit planum I L, æquale pla-
              <lb/>
            no K N; </s>
            <s xml:id="echoid-s5481" xml:space="preserve">cumque G I, H K ſint duæ figuræ ſimiles, & </s>
            <s xml:id="echoid-s5482" xml:space="preserve">æquales, pariter-
              <lb/>
              <note position="right" xlink:label="note-0178-01" xlink:href="note-0178-01a" xml:space="preserve">b</note>
            que I P, K R; </s>
            <s xml:id="echoid-s5483" xml:space="preserve">ergo duo plana A P, D R ſunt æqualia: </s>
            <s xml:id="echoid-s5484" xml:space="preserve">& </s>
            <s xml:id="echoid-s5485" xml:space="preserve">propterea E
              <lb/>
            N, B L, quæ illa ſpatia poſſunt (13. </s>
            <s xml:id="echoid-s5486" xml:space="preserve">14. </s>
            <s xml:id="echoid-s5487" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5488" xml:space="preserve">ſunt æquales. </s>
            <s xml:id="echoid-s5489" xml:space="preserve">Si autem
              <lb/>
              <note position="left" xlink:label="note-0178-02" xlink:href="note-0178-02a" xml:space="preserve">12. 13.
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              lib. I.</note>
            ſuperponatur axis axi cadet B L ſuper E N, eoquod duo anguli N, & </s>
            <s xml:id="echoid-s5490" xml:space="preserve">L
              <lb/>
            ſunt æquales; </s>
            <s xml:id="echoid-s5491" xml:space="preserve">igitur B cadit ſuper E, quod prius cadere non concedeba-
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            tur: </s>
            <s xml:id="echoid-s5492" xml:space="preserve">& </s>
            <s xml:id="echoid-s5493" xml:space="preserve">hoc eſt abſurdum. </s>
            <s xml:id="echoid-s5494" xml:space="preserve">Quapropter ſectio ſectioni æqualis eſt.</s>
            <s xml:id="echoid-s5495" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5496" xml:space="preserve">Deinde ponamus duas ſe-
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                <image file="0178-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0178-02"/>
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            ctiones æquales, vtique con-
              <lb/>
            gruet ſectio A B ſectioni D E,
              <lb/>
            & </s>
            <s xml:id="echoid-s5497" xml:space="preserve">axis A L axi D N, quia ſi
              <lb/>
            non cadit ſuper illum, eſſent
              <lb/>
              <note position="right" xlink:label="note-0178-03" xlink:href="note-0178-03a" xml:space="preserve">c</note>
            in hyperbola duo axes, & </s>
            <s xml:id="echoid-s5498" xml:space="preserve">in
              <lb/>
            ellipſi tres axes, quod eſt ab-
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            ſurdum (52. </s>
            <s xml:id="echoid-s5499" xml:space="preserve">53. </s>
            <s xml:id="echoid-s5500" xml:space="preserve">ex 2.) </s>
            <s xml:id="echoid-s5501" xml:space="preserve">Et fi-
              <lb/>
              <note position="left" xlink:label="note-0178-04" xlink:href="note-0178-04a" xml:space="preserve">48. lib. 2.</note>
            at A L æqualis D N, & </s>
            <s xml:id="echoid-s5502" xml:space="preserve">reli-
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            qua perficiantur, vt prius ca-
              <lb/>
            dent duo puncta L, B ſuper
              <lb/>
            N, E; </s>
            <s xml:id="echoid-s5503" xml:space="preserve">ideoque B L æqualis
              <lb/>
              <note position="right" xlink:label="note-0178-05" xlink:href="note-0178-05a" xml:space="preserve">d</note>
            erit E N; </s>
            <s xml:id="echoid-s5504" xml:space="preserve">& </s>
            <s xml:id="echoid-s5505" xml:space="preserve">poterunt æqua-
              <lb/>
            lia rectangula A P, D R applicata ad æquales A L, D N (13. </s>
            <s xml:id="echoid-s5506" xml:space="preserve">14. </s>
            <s xml:id="echoid-s5507" xml:space="preserve">ex 1.)
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              <note position="left" xlink:label="note-0178-06" xlink:href="note-0178-06a" xml:space="preserve">12. 13.
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              lib. 1.</note>
            ergo L P æqualis eſt N R. </s>
            <s xml:id="echoid-s5509" xml:space="preserve">Similiter ponatur A M æqualis D O, & </s>
            <s xml:id="echoid-s5510" xml:space="preserve">edu-
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            cantur C M Q, F O S duæ ordinationes, oſtendetur, quod M Q æqua-
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            lis eſt O S, & </s>
            <s xml:id="echoid-s5511" xml:space="preserve">L M æqualis N O; </s>
            <s xml:id="echoid-s5512" xml:space="preserve">& </s>
            <s xml:id="echoid-s5513" xml:space="preserve">propterea duo plana P Q, R S ſunt
              <lb/>
            æqualia, & </s>
            <s xml:id="echoid-s5514" xml:space="preserve">ſimilia; </s>
            <s xml:id="echoid-s5515" xml:space="preserve">igitur duo plana G P, H R ſunt æqualia, & </s>
            <s xml:id="echoid-s5516" xml:space="preserve">ſimilia,
              <lb/>
            & </s>
            <s xml:id="echoid-s5517" xml:space="preserve">L P oſtenſa eſt æqualis N R: </s>
            <s xml:id="echoid-s5518" xml:space="preserve">ergo G L æqualis eſt H N, & </s>
            <s xml:id="echoid-s5519" xml:space="preserve">A L æ-
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            qualis D N; </s>
            <s xml:id="echoid-s5520" xml:space="preserve">& </s>
            <s xml:id="echoid-s5521" xml:space="preserve">propterea G A æqualis eſt D H, & </s>
            <s xml:id="echoid-s5522" xml:space="preserve">A I æqualis D K.</s>
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