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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            differentia I L, & </s>
            <s xml:id="echoid-s10675" xml:space="preserve">N O maior ſit, quàm differentia quarumlibet duarum
              <lb/>
            coniugatarum ab axi remotiorum. </s>
            <s xml:id="echoid-s10676" xml:space="preserve">Et hoc erat oſtendendum.</s>
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        <div xml:id="echoid-div904" type="section" level="1" n="281">
          <head xml:id="echoid-head351" xml:space="preserve">Notæ in Propoſit. XII.</head>
          <p style="it">
            <s xml:id="echoid-s10678" xml:space="preserve">IN eiſdem figuris, quia quadratum A C ad quadratum ſui coniugati in
              <lb/>
              <note position="left" xlink:label="note-0331-01" xlink:href="note-0331-01a" xml:space="preserve">a</note>
            propoſitione 12. </s>
            <s xml:id="echoid-s10679" xml:space="preserve">& </s>
            <s xml:id="echoid-s10680" xml:space="preserve">25. </s>
            <s xml:id="echoid-s10681" xml:space="preserve">nempe A C ad A F erectum ipſius eſt vt præ-
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            ſecta C G ad Interceptam G A, ſeu C H: </s>
            <s xml:id="echoid-s10682" xml:space="preserve">ergo quadratum A C in hy-
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            perbola ad differentiam quadratorum axium ipſius, & </s>
            <s xml:id="echoid-s10683" xml:space="preserve">in ellipſi ad illo-
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            rum ſnmmam eſt, vt C G ad H G, &</s>
            <s xml:id="echoid-s10684" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10685" xml:space="preserve">Ideſt. </s>
            <s xml:id="echoid-s10686" xml:space="preserve">Quia quadratum A C ad
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            quadratum axis ei coniugati Q R, ſiue C A ad eius erectum A F eandem pro-
              <lb/>
              <note position="right" xlink:label="note-0331-02" xlink:href="note-0331-02a" xml:space="preserve">Defin. 1.
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              & 2.
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              huius.</note>
            portionem habet, quàm præſecta C G ad Interceptam G A, vel ad C H, & </s>
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              <lb/>
            comparando antecedentes ad terminorum differentias in hyperbola, & </s>
            <s xml:id="echoid-s10688" xml:space="preserve">ad ter-
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            minorum ſummas in ellipſi, quadratum C A ad differentiam quadratorum ex axi
              <lb/>
            A C, & </s>
            <s xml:id="echoid-s10689" xml:space="preserve">ex axi Q R habebit in hyperbola eandem proportionem, quàm C G
              <lb/>
            ad differentiam inter C G, & </s>
            <s xml:id="echoid-s10690" xml:space="preserve">C H: </s>
            <s xml:id="echoid-s10691" xml:space="preserve">in ellipſi verò quadratum A C ad ſum-
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            mam quadratorum ex A C, & </s>
            <s xml:id="echoid-s10692" xml:space="preserve">ex Q R eandem proportionem habebit, quàm
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            C G ad ſummam ipſius C G cum C H.</s>
            <s xml:id="echoid-s10693" xml:space="preserve"/>
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            <s xml:id="echoid-s10694" xml:space="preserve">Et quia iam demonſtratum eſt, quod quadratum C A ad quadratum
              <lb/>
              <note position="left" xlink:label="note-0331-03" xlink:href="note-0331-03a" xml:space="preserve">b</note>
            I L ſit, vt C G ad E H, &</s>
            <s xml:id="echoid-s10695" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10696" xml:space="preserve">Relicta abſtruſa complicatione propoſitionum
              <lb/>
            Arabici Interpretis diſtinctiori methodo, ſicuti in præcedenti ſectione factum eſt
              <lb/>
              <note position="right" xlink:label="note-0331-04" xlink:href="note-0331-04a" xml:space="preserve">6. huius.</note>
            propoſitiones declarabimus. </s>
            <s xml:id="echoid-s10697" xml:space="preserve">Quoniam in hyperbola quadratum I L ad quadra-
              <lb/>
            tum N O eandem proportionem habet, quàm H E ad E G comparando antece-
              <lb/>
            dentes ad terminorum differentias, quadratum I L ad differentiam quadrati
              <lb/>
            I L à quadrato N O eandem proportionem habebit, quàm H E ad ipſarum H
              <lb/>
            E, & </s>
            <s xml:id="echoid-s10698" xml:space="preserve">E G differentiam; </s>
            <s xml:id="echoid-s10699" xml:space="preserve">ſed quadratum A C ad quadratum I L eſt vt C G
              <lb/>
            ad H E (veluti in propoſitione 8. </s>
            <s xml:id="echoid-s10700" xml:space="preserve">oſtenſum eſt) ergo ex æqualitate quadratum
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            A C ad quadratorum ex I L, & </s>
            <s xml:id="echoid-s10701" xml:space="preserve">ex N O differentiam eandem </s>
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