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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[301.] PROPOSITIO XXXIV.
Page: 354 (315)
[302.] PROPOSITIO XXXV. & XXXVI.
Page: 355 (316)
[303.] In Sectionem VI.
Page: 356 (317)
[304.] LEMMA II.
Page: 357 (318)
[305.] LEMMA III.
Page: 357 (318)
[306.] LEMMA IV.
Page: 357 (318)
[307.] LEMMA V.
Page: 358 (319)
[308.] Notæ in Propof. XXXIII. & XXXIV.
Page: 359 (320)
[309.] Notæ in Propoſit. XXXV.
Page: 360 (321)
[310.] SECTIO SEPTIMA Continens Propoſit. XXXVIII. XXXIX. & XXXX. PROPOSITIO XXXVIII.
Page: 362 (323)
[311.] PROPOSITIO XXXIX.
Page: 363 (324)
[312.] PROPOSITIO XXXX.
Page: 364 (325)
[313.] In Sectionem VII. Propoſit: XXXVIII. XXXIX. & XXXX. LEMMA VI.
Page: 366 (327)
[314.] LEMMA VII.
Page: 366 (327)
[315.] LEMMA VIII.
Page: 367 (328)
[316.] LEMMA IX.
Page: 367 (328)
[317.] Notæ in Propoſit. XXXVIII. XXXIX.
Page: 369 (330)
[318.] Notæ in Propoſit. XXXX.
Page: 369 (330)
[319.] SECTIO OCTAVA Continens Propoſit. XXXXIIII. XXXXV. & XXXXVI.
Page: 372 (333)
[320.] PROPOSITIO XXXXVI.
Page: 374 (335)
[321.] In Sectionem VIII. Propoſit. XXXXIIII. XXXXV. & XXXXVI. LEMM A.X.
Page: 375 (336)
[322.] LEMM A XI.
Page: 375 (336)
[323.] LEMM A XII.
Page: 376 (337)
[324.] Notæ in Propoſit. XXXXIV. & XXXXV.
Page: 378 (339)
[325.] Notæ in Propoſit. XXXXVI.
Page: 378 (339)
[326.] SECTIO NONA Continens Propoſit. XXXXI. XXXXVII. & XXXXVIII.
Page: 380 (341)
[327.] PROPOSITIO XXXXI.
Page: 382 (343)
[328.] PROPOSITIO XXXXVII.
Page: 383 (344)
[329.] PROPOSITIO XXXXVIII.
Page: 386 (347)
[330.] In Sectionem IX. Propoſit. XXXXI. XXXXVII. & XXXXVIII. LEMMA. XIII.
Page: 388 (349)
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            pendicularis ad E D, & </s>
            <s xml:id="echoid-s13277" xml:space="preserve">D I eſt quoque perpendicularis ad A E, & </s>
            <s xml:id="echoid-s13278" xml:space="preserve">iam
              <lb/>
            ſe mutuo ſecuerunt in M, ergo E M O erit etiam perpendicularis, que-
              <lb/>
            madmodum oſtendimus in expoſitione, quàm confecimus de proprieta-
              <lb/>
            tibus triangulorum, & </s>
            <s xml:id="echoid-s13279" xml:space="preserve">cuius demonſtratio iam quidem præceſſit in ſupe-
              <lb/>
              <figure xlink:label="fig-0435-01" xlink:href="fig-0435-01a" number="503">
                <image file="0435-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0435-01"/>
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            riori propoſitione; </s>
            <s xml:id="echoid-s13280" xml:space="preserve">Similiter quoque erit F P perpendicularis ſuper C A,
              <lb/>
            & </s>
            <s xml:id="echoid-s13281" xml:space="preserve">quia duo anguli, qui ſunt apud L, & </s>
            <s xml:id="echoid-s13282" xml:space="preserve">B ſunt recti, erit D L parallela
              <lb/>
            ipſi A B, & </s>
            <s xml:id="echoid-s13283" xml:space="preserve">pariter D I ipſi C B, igitur proportio A D ad D C eſt vt
              <lb/>
            proportio A M ad F M, immo vt proportio A O ad O P, & </s>
            <s xml:id="echoid-s13284" xml:space="preserve">proportio
              <lb/>
            C D ad D A vt proportio C N ad N E, immo vt proportio C P ad P
              <lb/>
            O, & </s>
            <s xml:id="echoid-s13285" xml:space="preserve">erat A D ſexquialtera D C, ergo A O eſt ſexquialtera O P, & </s>
            <s xml:id="echoid-s13286" xml:space="preserve">
              <lb/>
            O P ſexquialtera C P, ergo tres lineæ A O, O P, P C ſunt proportio-
              <lb/>
            nales: </s>
            <s xml:id="echoid-s13287" xml:space="preserve">& </s>
            <s xml:id="echoid-s13288" xml:space="preserve">in eadem menſura, in qua eſt P C quatuor, erit O P ſex, & </s>
            <s xml:id="echoid-s13289" xml:space="preserve">
              <lb/>
            A O nouem, & </s>
            <s xml:id="echoid-s13290" xml:space="preserve">C A nouendecim, & </s>
            <s xml:id="echoid-s13291" xml:space="preserve">quia P O æ qualis eſt E F, erit
              <lb/>
            proportio A C ad E F vt nouendecim ad ſex, igitur reperimus dictam
              <lb/>
            proportionem. </s>
            <s xml:id="echoid-s13292" xml:space="preserve">Etiam ſi fuerit A D ad D C qualiſcumque vt ſexquiter-
              <lb/>
            tia, aut ſexquiquarta, aut alia, erit iudicium, & </s>
            <s xml:id="echoid-s13293" xml:space="preserve">ratio, vti dictum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s13294" xml:space="preserve">Et hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13295" xml:space="preserve"/>
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        <div xml:id="echoid-div1136" type="section" level="1" n="365">
          <head xml:id="echoid-head457" xml:space="preserve">Notæ in Propoſit. VI.</head>
          <p style="it">
            <s xml:id="echoid-s13296" xml:space="preserve">HAEc propoſitio nil prorſus differre videtur à 16. </s>
            <s xml:id="echoid-s13297" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s13298" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13299" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13300" xml:space="preserve">Pappi
              <lb/>
            Alex. </s>
            <s xml:id="echoid-s13301" xml:space="preserve">eſt tamen pars illius, & </s>
            <s xml:id="echoid-s13302" xml:space="preserve">particulariter demonſtrata, quod quidem
              <lb/>
            peccatum alicui expoſitori tribui debet; </s>
            <s xml:id="echoid-s13303" xml:space="preserve">nunquam enim Archimedes propoſitionẽ
              <lb/>
            illam, quam vniuerſaltſſimè demonſtrare potuißet, exemplis numericis tam
              <lb/>
            pueriliter oſtendiſſet. </s>
            <s xml:id="echoid-s13304" xml:space="preserve">Pappus igitur quærit menſuram diametri illius circuli,
              <lb/>
            qui in loco inter tres circunferentias circulares interijcitur, quod Arbelon ap-
              <lb/>
            pellatur, & </s>
            <s xml:id="echoid-s13305" xml:space="preserve">oſtendit quidem diametrum ſemicirculi maioris A C ſecari in duo-
              <lb/>
            bus punctis O, & </s>
            <s xml:id="echoid-s13306" xml:space="preserve">P à perpendicularibus cadentibus à terminis E, & </s>
            <s xml:id="echoid-s13307" xml:space="preserve">F dia-
              <lb/>
            metri circuli in Arbelo inſcripti, ac diuidi in tria ſegmenta A O, O P, P C
              <lb/>
            continue proportionalia in eadem ratione, quàm habet A D ad D C, & </s>
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