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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[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
[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)
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            <s xml:id="echoid-s3335" xml:space="preserve">
              <pb o="80" file="0118" n="118" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0118-01" xlink:href="fig-0118-01a" number="99">
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            & </s>
            <s xml:id="echoid-s3336" xml:space="preserve">quia A H cadit infra A G ad partes axis cum D A, ad quam illa perpen-
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            dicularis eſt, extendatur vltra axim A E, nec poſsit inter tangentem A G, & </s>
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            ſectionem conicam A B, aliqua recta linea intercipi; </s>
            <s xml:id="echoid-s3338" xml:space="preserve">igitur A H cadit intra
              <lb/>
            coniſectionem, & </s>
            <s xml:id="echoid-s3339" xml:space="preserve">angulus E A H eſt acutus.</s>
            <s xml:id="echoid-s3340" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s3341" xml:space="preserve">Quoniam ex D non educitur ad ſectionem A C vllus breuiſecans, & </s>
            <s xml:id="echoid-s3342" xml:space="preserve">c.
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            <s xml:id="echoid-s3343" xml:space="preserve">
              <note position="right" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">b</note>
            Sequitur quidem ex hac hypotheſi, quod menſura E A non ſit maior ſemierecto
              <lb/>
              <note position="left" xlink:label="note-0118-02" xlink:href="note-0118-02a" xml:space="preserve">Ex 49. 50.
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              huius.</note>
            aut ſi maior eſt, ſit quoque perpendicularis D E maior Trutina F, ex conuerſa
              <lb/>
            propoſitione 51. </s>
            <s xml:id="echoid-s3344" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3345" xml:space="preserve">huius per deductionem ad inconueniens.</s>
            <s xml:id="echoid-s3346" xml:space="preserve"/>
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            <s xml:id="echoid-s3347" xml:space="preserve">Quare ſi centro D interuallo D B, &</s>
            <s xml:id="echoid-s3348" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3349" xml:space="preserve">Circulus enim B I L H A ra-
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              <note position="right" xlink:label="note-0118-03" xlink:href="note-0118-03a" xml:space="preserve">c</note>
            dio D B deſcriptus tranſibit per verticem A cum radius D B poſitus ſit æqualis
              <lb/>
            D A, cumque angulus D B I ſit acutus, ex Lemmate nono, cadet neceſſario B
              <lb/>
            I intra circulum B I L.</s>
            <s xml:id="echoid-s3350" xml:space="preserve"/>
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            <s xml:id="echoid-s3351" xml:space="preserve">Ig tur circulus ſecat coniſectionem, &</s>
            <s xml:id="echoid-s3352" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3353" xml:space="preserve">Quia B I cadit extra coniſe-
              <lb/>
              <note position="right" xlink:label="note-0118-04" xlink:href="note-0118-04a" xml:space="preserve">d</note>
            ctionem, quàm tangit, & </s>
            <s xml:id="echoid-s3354" xml:space="preserve">intra circulum B L A, vt dictum eſt, è contra re-
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            cta A H cadit intra eandem coniſectionem, & </s>
            <s xml:id="echoid-s3355" xml:space="preserve">extra ipſum circulum, quem,
              <lb/>
            tangit, cum H A perpendicularis ſit ad circuli radium D A; </s>
            <s xml:id="echoid-s3356" xml:space="preserve">igitur circulus B
              <lb/>
            I L A fertur extra coniſectionem ad partes B I, & </s>
            <s xml:id="echoid-s3357" xml:space="preserve">intra eandem ad partes A
              <lb/>
            H; </s>
            <s xml:id="echoid-s3358" xml:space="preserve">quare neceſſario coniſectionem ſecat.</s>
            <s xml:id="echoid-s3359" xml:space="preserve"/>
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            <s xml:id="echoid-s3360" xml:space="preserve">Patet, vt dictum eſt, quod D L G ſit acutus, &</s>
            <s xml:id="echoid-s3361" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3362" xml:space="preserve">Hoc enim ſequitur ex
              <lb/>
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            nono Lemmate præmiſſo, reſpicit enim angulus D L G verticem A; </s>
            <s xml:id="echoid-s3363" xml:space="preserve">& </s>
            <s xml:id="echoid-s3364" xml:space="preserve">ideo eſt
              <lb/>
            acutus, & </s>
            <s xml:id="echoid-s3365" xml:space="preserve">cadit neceſſario recta L G intra circulum B L A radio D L deſcri-
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            ptum ad partes L A; </s>
            <s xml:id="echoid-s3366" xml:space="preserve">& </s>
            <s xml:id="echoid-s3367" xml:space="preserve">portio circuli L H A cadit intra coniſectionem L A;
              <lb/>
            </s>
            <s xml:id="echoid-s3368" xml:space="preserve">igitur recta L G cadit intra coniſectionem L A, ſed cadit extra eandem ſectio-
              <lb/>
              <note position="left" xlink:label="note-0118-06" xlink:href="note-0118-06a" xml:space="preserve">35. 36.
                <lb/>
              lib. 1.</note>
            nem, cum contingat eam in L, quod eſt abſurdum.</s>
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