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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[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
[141.] PROPOSITIO XXXIII. XXXIV.
Page: 163 (125)
[142.] PROPOSITIO XXXV.
Page: 163 (125)
[143.] PROPOSITIO XXXVI.
Page: 164 (126)
[144.] PROPOSITIO XXXVII. XLVI.
Page: 164 (126)
[145.] PROPOSITIO XXXVIII.
Page: 165 (127)
[146.] PR OPOSITIO XXXIX.
Page: 166 (128)
[147.] PROPOSITIO XXXX.
Page: 166 (128)
[148.] PROPOSITIO XXXXVII.
Page: 166 (128)
[149.] PROPOSITIO XXXXVIII.
Page: 167 (129)
[150.] Notæ in Propoſit. XXXII.
Page: 167 (129)
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              <pb o="104" file="0142" n="142" rhead="104 Apollonij Pergæi"/>
            nem: </s>
            <s xml:id="echoid-s4203" xml:space="preserve">Dico, quod circumpherentia Z γ ſecat tangentem rectam lineam
              <lb/>
            x A, & </s>
            <s xml:id="echoid-s4204" xml:space="preserve">coniſectionem B G in puncto A.</s>
            <s xml:id="echoid-s4205" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4206" xml:space="preserve">Quoniam perpendicularis D E ponitur ma-
              <lb/>
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                <image file="0142-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0142-01"/>
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            ior trutina L; </s>
            <s xml:id="echoid-s4207" xml:space="preserve">ergo quilibet ramus D A cadit
              <lb/>
              <note position="left" xlink:label="note-0142-01" xlink:href="note-0142-01a" xml:space="preserve">51. 52.
                <lb/>
              huius.</note>
            ſupra breuiſsimam ex puncto A ad axim B E
              <lb/>
            ductam: </s>
            <s xml:id="echoid-s4208" xml:space="preserve">efficit vero breuiſsima cum tangente
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            A x angulum rectum; </s>
            <s xml:id="echoid-s4209" xml:space="preserve">ergo angulus D A x eſt
              <lb/>
              <note position="left" xlink:label="note-0142-02" xlink:href="note-0142-02a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            acutus; </s>
            <s xml:id="echoid-s4210" xml:space="preserve">& </s>
            <s xml:id="echoid-s4211" xml:space="preserve">propterea recta A x cadit intracir-
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            culum A Z; </s>
            <s xml:id="echoid-s4212" xml:space="preserve">ſed A x cadit extra coniſectio-
              <lb/>
              <note position="left" xlink:label="note-0142-03" xlink:href="note-0142-03a" xml:space="preserve">35. 36.
                <lb/>
              Lib. 1.</note>
            nem B A, quàm contingit; </s>
            <s xml:id="echoid-s4213" xml:space="preserve">ergo circumferen-
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            tia Z A cadit extra ſectionem B A, & </s>
            <s xml:id="echoid-s4214" xml:space="preserve">extra
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            tangentem A x: </s>
            <s xml:id="echoid-s4215" xml:space="preserve">poſtea ducatur quilibet ramus
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            D G infra ramum D A ſecans circumferentiã
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            circuli in r: </s>
            <s xml:id="echoid-s4216" xml:space="preserve">& </s>
            <s xml:id="echoid-s4217" xml:space="preserve">quia ramus D A propinquior
              <lb/>
            eſt vertici B, quàm D G, erit D A minor,
              <lb/>
              <note position="left" xlink:label="note-0142-04" xlink:href="note-0142-04a" xml:space="preserve">64. 65.
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              huius.</note>
            quàm D G; </s>
            <s xml:id="echoid-s4218" xml:space="preserve">eſtque D γ æqualis D A (cum ſint ambo radij eiuſdem circuli) ergo
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            D γ minor erit, quàm D G: </s>
            <s xml:id="echoid-s4219" xml:space="preserve">& </s>
            <s xml:id="echoid-s4220" xml:space="preserve">propterea quodlibet punctum γ peripheriæ cir-
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            cularis infra punctum A poſitum cadet intra coniſectionem B G; </s>
            <s xml:id="echoid-s4221" xml:space="preserve">& </s>
            <s xml:id="echoid-s4222" xml:space="preserve">ideo cir-
              <lb/>
            cumferentia Z A γ ſecat tangentẽ, & </s>
            <s xml:id="echoid-s4223" xml:space="preserve">coniſectionẽ in A, quod erat propoſitum.</s>
            <s xml:id="echoid-s4224" xml:space="preserve"/>
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            <s xml:id="echoid-s4225" xml:space="preserve">Iſdem poſitis, ſit perpendicularis D E æqualis Trutinæ L, & </s>
            <s xml:id="echoid-s4226" xml:space="preserve">ſit D
              <lb/>
              <note position="left" xlink:label="note-0142-05" xlink:href="note-0142-05a" xml:space="preserve">PR. 10.
                <lb/>
              Addit.</note>
            A ſingularis ille ramus breuiſecans, qui ex concurſu D ad ſectionem
              <lb/>
            B G duci poteſt; </s>
            <s xml:id="echoid-s4227" xml:space="preserve">perficiaturque conſtructio, vt antea factum eſt; </s>
            <s xml:id="echoid-s4228" xml:space="preserve">Dico,
              <lb/>
              <note position="left" xlink:label="note-0142-06" xlink:href="note-0142-06a" xml:space="preserve">51. 52.
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              huius.</note>
            circulum Z A γ ſecare coniſectionem in A, & </s>
            <s xml:id="echoid-s4229" xml:space="preserve">contingere rectam Ax.</s>
            <s xml:id="echoid-s4230" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s4231" xml:space="preserve">Ducatur quilibet ramus D F ſupra breuiſe-
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                <image file="0142-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0142-02"/>
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            cantem D A, ſecans circuli peripheriam in Z,
              <lb/>
            & </s>
            <s xml:id="echoid-s4232" xml:space="preserve">quilibet alius ramus D G infra D A ſecans
              <lb/>
            eandem peripheriam in γ. </s>
            <s xml:id="echoid-s4233" xml:space="preserve">Et quia ex con-
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            curſu D ad ſectionem B G vnicus tantum bre-
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              <note position="left" xlink:label="note-0142-07" xlink:href="note-0142-07a" xml:space="preserve">Ibidem.</note>
            uiſecans D A duci poteſt; </s>
            <s xml:id="echoid-s4234" xml:space="preserve">igitur ramus D F
              <lb/>
            propinquio
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            r vertici B minor eſt remotiore D
              <lb/>
              <note position="left" xlink:label="note-0142-08" xlink:href="note-0142-08a" xml:space="preserve">67. huius.</note>
            A, & </s>
            <s xml:id="echoid-s4235" xml:space="preserve">D A propinquior vertici B minor eſt
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            remotiore D G: </s>
            <s xml:id="echoid-s4236" xml:space="preserve">ſuntque rectæ D Z, D γ æ-
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            quales eidem D A (cum ſint radij eiuſdem,
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            circuli) ergo D Z maior eſt, quàm D F, & </s>
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            D γ minor, quàm D G; </s>
            <s xml:id="echoid-s4238" xml:space="preserve">& </s>
            <s xml:id="echoid-s4239" xml:space="preserve">propterea quodli-
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            bet punctum Z circuli ſupra A ſumptum ca-
              <lb/>
            dit extra coniſectionem B F A, & </s>
            <s xml:id="echoid-s4240" xml:space="preserve">quodlibet
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            infimum punctum γ eiuſdem circuli cadit intra eandem coniſectionem A G;
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            <s xml:id="echoid-s4241" xml:space="preserve">quapropter circumferentia circuli Z A γ ſecat coniſectionem B A G in A. </s>
            <s xml:id="echoid-s4242" xml:space="preserve">Po-
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            ſtea quia recta A x contingens ſectionem in A perpendicularis eſt ad breuiſe-
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            cantem D A, cum I A ſit breuiſsima; </s>
            <s xml:id="echoid-s4243" xml:space="preserve">igitur recta linea x A, quæ perpendicu-
              <lb/>
              <note position="left" xlink:label="note-0142-09" xlink:href="note-0142-09a" xml:space="preserve">29. 30.
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              huius.</note>
            laris eſt ad radium D A, continget circulum Z Y γ. </s>
            <s xml:id="echoid-s4244" xml:space="preserve">Quapropter circulus Z
              <lb/>
            A γ ſecant coniſectionem B A G in A, & </s>
            <s xml:id="echoid-s4245" xml:space="preserve">tangit eandem rectam lineam A x,
              <lb/>
            quàm contingit ſectio conica B A G, & </s>
            <s xml:id="echoid-s4246" xml:space="preserve">in eodem puncto A, quod erat oſtendendũ.</s>
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