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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[221.] SECTIO SEPTIMA Continens Propoſit. XVIII. & XIX.
Page: 229 (191)
[222.] Notæ in Propoſit. XVIII. & XIX.
Page: 230 (192)
[223.] SECTIO OCTAVA Continens Propoſit. XX. & XXI. Apollonij. PROPOSITIO XX.
Page: 231 (193)
[224.] PROPOSITIO XXI.
Page: 233 (195)
[225.] PROPOSITIO XXII.
Page: 235 (197)
[226.] PROPOSITIO XXIII.
Page: 236 (198)
[227.] PROPOSITIO XXIV.
Page: 236 (198)
[228.] Notæ in Propoſit. XX.
Page: 237 (199)
[229.] Notæ in Propoſit. XXI.
Page: 241 (203)
[230.] Notæ in Propoſit. XXII.
Page: 243 (205)
[231.] Notæ in Propoſit. XXIII.
Page: 244 (206)
[232.] Notæ in Propoſit. XXIV.
Page: 245 (207)
[233.] SECTIO NONA Continens Propoſit. XXV.
Page: 245 (207)
[234.] Notæ in Propoſit. XXV.
Page: 246 (208)
[235.] LEMMA IX.
Page: 267 (229)
[236.] SECTIO DECIMA Continens Propoſit. XXVI. XXVII. & XXVIII. PROPOSITIO XXVI.
Page: 275 (237)
[237.] PROPOSITIO XXVII.
Page: 276 (238)
[238.] PROPOSITIO XXVIII.
Page: 278 (240)
[239.] Notæ in Propoſit. XXVI.
Page: 279 (241)
[240.] Notæ in Propoſit. XXVII.
Page: 280 (242)
[241.] Notæ in Propoſit. XXVIII.
Page: 284 (246)
[242.] LEMMAX.
Page: 284 (246)
[243.] SECTIO VNDECIMA Continens Propoſit. XXIX. XXX. & XXXI. PROPOSTIO XXIX.
Page: 285 (247)
[244.] PROPOSITIO XXX.
Page: 286 (248)
[245.] PROPOSITIO XXXI.
Page: 289 (251)
[246.] Notæ in Propoſit. XXIX.
Page: 291 (253)
[247.] Notæ in Propoſit. XXX.
Page: 292 (254)
[248.] Notæ in Propoſit. XXXI.
Page: 296 (258)
[249.] LIBRI SEXTI FINIS.
Page: 308 (270)
[250.] DEFINITIONES. I.
Page: 309 (271)
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              <pb o="394" file="0432" n="433" rhead="Archimedis"/>
            & </s>
            <s xml:id="echoid-s13187" xml:space="preserve">circulus I H L tangat circulum A B C in H, & </s>
            <s xml:id="echoid-s13188" xml:space="preserve">circulum A D E in
              <lb/>
            L, & </s>
            <s xml:id="echoid-s13189" xml:space="preserve">perpendicularem in I. </s>
            <s xml:id="echoid-s13190" xml:space="preserve">Dico eſſe æqualem circulo, qui eſt in al-
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            tera parte. </s>
            <s xml:id="echoid-s13191" xml:space="preserve">Hoc modo, Educamus I M parallelam ipſi A C, & </s>
            <s xml:id="echoid-s13192" xml:space="preserve">iungamus
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            A H, quæ tranſibit per M, quemadmodum demonſtrauit Archimedes,
              <lb/>
              <note position="left" xlink:label="note-0432-01" xlink:href="note-0432-01a" xml:space="preserve">Prop. I.
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              huius.</note>
              <figure xlink:label="fig-0432-01" xlink:href="fig-0432-01a" number="500">
                <image file="0432-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0432-01"/>
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            & </s>
            <s xml:id="echoid-s13193" xml:space="preserve">producamus eam quouſque occurrat perpendiculari N G in N, & </s>
            <s xml:id="echoid-s13194" xml:space="preserve">
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            iungamus I A, quæ tranſibit per L, & </s>
            <s xml:id="echoid-s13195" xml:space="preserve">producamus illam ad O, & </s>
            <s xml:id="echoid-s13196" xml:space="preserve">iun-
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            gamus C O, O N, quæ erit linea recta, & </s>
            <s xml:id="echoid-s13197" xml:space="preserve">iungamus M E, quæ tranſi-
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            bit per L, & </s>
            <s xml:id="echoid-s13198" xml:space="preserve">iungamus C H, quæ tranſibit per I; </s>
            <s xml:id="echoid-s13199" xml:space="preserve">& </s>
            <s xml:id="echoid-s13200" xml:space="preserve">linea C O N pa-
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            a eſt lineæ E M, & </s>
            <s xml:id="echoid-s13201" xml:space="preserve">proportio A N ad N M, nempe proportio A
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            G ad I M eſt vt C A ad C E, ergo rectangulum A G in C E æquale
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            eſt rectangulo C A in I M; </s>
            <s xml:id="echoid-s13202" xml:space="preserve">& </s>
            <s xml:id="echoid-s13203" xml:space="preserve">quia G D eſt perpendicularis in duobus
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            circulis C D F, E D A ſuper duas diametros C F, E A, erit rectangu-
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            lum C G in G F æquale quadrato G D, & </s>
            <s xml:id="echoid-s13204" xml:space="preserve">rectangulum A G in G E
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            æquale etiam eſt illi, ergo rectangulum C G in G F æquale eſt rectan-
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            lo A G in G E, & </s>
            <s xml:id="echoid-s13205" xml:space="preserve">proportio C G ad G A eſt vt proportio E G ad G
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            F, immo vt proportio C E ad F A reſiduam; </s>
            <s xml:id="echoid-s13206" xml:space="preserve">ergo rectangulum C G in
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            F A, eſt æquale rectangulo C A in I M cui æquale eſt rectangulum G
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            A in C E. </s>
            <s xml:id="echoid-s13207" xml:space="preserve">Et ſi fuerit in altera parte circulus modo præfato eadem ra-
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            tione oſtendemus, quod reſtangulum C A in diametrum illius circuli
              <lb/>
            æquale ſit rectangulo C G in A F, & </s>
            <s xml:id="echoid-s13208" xml:space="preserve">oſtendetur quod duæ diametri duo-
              <lb/>
            rum circulorum ſint æquales.</s>
            <s xml:id="echoid-s13209" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1130" type="section" level="1" n="362">
          <head xml:id="echoid-head454" xml:space="preserve">SCHOLIVM SECVNDVM ALKAVHI.</head>
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            <s xml:id="echoid-s13210" xml:space="preserve">POrrò ſecunda eſt hæc. </s>
            <s xml:id="echoid-s13211" xml:space="preserve">Dicit quod ſi duo ſemicirculi non
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            ſint tangentes, nec ſe mutuo ſecantes, ſed ſeparati, & </s>
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            perpendicularis tranſeat per concurſum duarum linearum </s>
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