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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[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)
[211.] SECTIO SEXTA Continens Propoſit. XV. XVI. & XVII. PROPOSITIO XV.
Page: 213 (175)
[212.] PROPOSITIO XVI.
Page: 215 (177)
[213.] PROPOSITIO XVII.
Page: 216 (178)
[214.] Notæ in Propoſit. XV.
Page: 219 (181)
[215.] MONITVM.
Page: 221 (183)
[216.] LEMMA VI.
Page: 221 (183)
[217.] LEMMA VII.
Page: 222 (184)
[218.] LEMMA VIII.
Page: 224 (186)
[219.] Notæ in Propoſit. XVI.
Page: 225 (187)
[220.] Notæ in Propoſit. XVII.
Page: 226 (188)
[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)
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            minimo remotiore minor eſt. </s>
            <s xml:id="echoid-s904" xml:space="preserve">Quadratum autem menſuræ mi-
              <lb/>
            nus eſt quadrato cuiuslibet rami aſſignati (4) in parabola qui-
              <lb/>
            dem quadrato ſuæ abſciſſæ (5) & </s>
            <s xml:id="echoid-s905" xml:space="preserve">in hyperbola (6) & </s>
            <s xml:id="echoid-s906" xml:space="preserve">ellipſi
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            exemplari applicato ad abſciſſam illius rami.</s>
            <s xml:id="echoid-s907" xml:space="preserve"/>
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        <div xml:id="echoid-div43" type="section" level="1" n="37">
          <head xml:id="echoid-head62" xml:space="preserve">PROPOSITIO IV.</head>
          <p>
            <s xml:id="echoid-s908" xml:space="preserve">SIt ſectio A B C, & </s>
            <s xml:id="echoid-s909" xml:space="preserve">axis eius C E, & </s>
            <s xml:id="echoid-s910" xml:space="preserve">inclinatus, ſiue tranſuerſa D C
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            centrum G, atque erectum C F, & </s>
            <s xml:id="echoid-s911" xml:space="preserve">ex C E ſecetur C I æqualis C H
              <lb/>
              <figure xlink:label="fig-0046-01" xlink:href="fig-0046-01a" number="13">
                <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-01"/>
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            (quæ ſit ſemiſſis erecti) & </s>
            <s xml:id="echoid-s912" xml:space="preserve">ex puncto
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            originis I educantur rami I B perpen-
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            dicularis, & </s>
            <s xml:id="echoid-s913" xml:space="preserve">I K, I L, I A, & </s>
            <s xml:id="echoid-s914" xml:space="preserve">per H, I
              <lb/>
            in hyperbola, & </s>
            <s xml:id="echoid-s915" xml:space="preserve">ellipſi ducatur H I P,
              <lb/>
            & </s>
            <s xml:id="echoid-s916" xml:space="preserve">per H, G recta H G T, ad quam ex
              <lb/>
            A, B, K, L extendantur A P E T, B I S,
              <lb/>
            K N R, L M O Q perpendiculares ſuper
              <lb/>
            C E. </s>
            <s xml:id="echoid-s917" xml:space="preserve">Dico, quod C I, comparata mi-
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            nor eſt, quam I L, & </s>
            <s xml:id="echoid-s918" xml:space="preserve">
              <lb/>
            I L, quam I K, & </s>
            <s xml:id="echoid-s919" xml:space="preserve">I K,
              <lb/>
            quam I B, & </s>
            <s xml:id="echoid-s920" xml:space="preserve">maximus
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            ramorum in ellipſi eſt
              <lb/>
            I D, & </s>
            <s xml:id="echoid-s921" xml:space="preserve">quod quadra-
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            tum menſuræ I C mi-
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            nus eſt quadrato I L,
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            in parabola quidem
              <lb/>
            quadrato C M, & </s>
            <s xml:id="echoid-s922" xml:space="preserve">in
              <lb/>
            hyperbola, & </s>
            <s xml:id="echoid-s923" xml:space="preserve">ellipſi
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            exemplari applicato
              <lb/>
            ad C M. </s>
            <s xml:id="echoid-s924" xml:space="preserve">Quoniam in
              <lb/>
            parabola L M poteſt
              <lb/>
              <note position="right" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">a</note>
            duplum M C in C H, nempè C I (12. </s>
            <s xml:id="echoid-s925" xml:space="preserve">ex primo) & </s>
            <s xml:id="echoid-s926" xml:space="preserve">quadratum I L ęqua-
              <lb/>
            le eſt aggregato duorum quadratorum L M, & </s>
            <s xml:id="echoid-s927" xml:space="preserve">M I, quadratum itaque L
              <lb/>
            I æquale eſt quadrato M I, & </s>
            <s xml:id="echoid-s928" xml:space="preserve">M C in C I bis, quæ ſunt æqualia duobus
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            quadratis C I, M C. </s>
            <s xml:id="echoid-s929" xml:space="preserve">Quadratum igitur C I minus eſt quadrato L I qua-
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            drato ipſius M C, quæ eſt eius abſciſſa, & </s>
            <s xml:id="echoid-s930" xml:space="preserve">pariter oſtendetur, quod qua-
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            dratum C I minus eſt quadrato I K quadrato N C, & </s>
            <s xml:id="echoid-s931" xml:space="preserve">minus quadrato I
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            B quadrato C I, & </s>
            <s xml:id="echoid-s932" xml:space="preserve">minus quadrato A I quadrato E C.</s>
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          <head xml:id="echoid-head63" xml:space="preserve">PROPOSITIO V. & VI.</head>
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            <s xml:id="echoid-s934" xml:space="preserve">AT verò in hyperbola, & </s>
            <s xml:id="echoid-s935" xml:space="preserve">ellipſi producantur ex Q, O, H lineæ pa-
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            rallelæ ipſi M C, & </s>
            <s xml:id="echoid-s936" xml:space="preserve">quia I C ex hypotheſi æqualis eſt H C, erit I
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              <note position="right" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">a</note>
            M æqualis M O, quadratum itaque I M duplum eſt trianguli I M O, & </s>
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              <lb/>
              <note position="right" xlink:label="note-0046-03" xlink:href="note-0046-03a" xml:space="preserve">b</note>
            quadratum L M duplum eſt trapezij C M Q H (prima ex 5.) </s>
            <s xml:id="echoid-s938" xml:space="preserve">ergo </s>
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