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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            reliquæ verò lineæ referuntur ad hoc latus.</s>
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          <head xml:id="echoid-head320" xml:space="preserve">VII.</head>
          <p>
            <s xml:id="echoid-s10149" xml:space="preserve">Inſuper vocabo duas diametros coniugatas, & </s>
            <s xml:id="echoid-s10150" xml:space="preserve">æquales in elli-
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            pſi, ÆQVALES.</s>
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          <p>
            <s xml:id="echoid-s10152" xml:space="preserve">Et ſi quidem ad vtraſque partes axis ſectionis duæ diame-
              <lb/>
            tri educantur, quæ ad ſua erecta eandem proportionem ha-
              <lb/>
            beant, vtique vocabo c
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            as ÆQVALES.</s>
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          <head xml:id="echoid-head321" xml:space="preserve">VIII.</head>
          <p>
            <s xml:id="echoid-s10154" xml:space="preserve">Diametros verò æquales ad vtraſque partes duarum axium elli-
              <lb/>
            pſis cadentes, voco Homologas illius axis: </s>
            <s xml:id="echoid-s10155" xml:space="preserve">ſuntque homo-
              <lb/>
            logæ diametri in ellipſi tranſuerſa ad tranſuerſam, & </s>
            <s xml:id="echoid-s10156" xml:space="preserve">recta
              <lb/>
            ad rectam.</s>
            <s xml:id="echoid-s10157" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div848" type="section" level="1" n="258">
          <head xml:id="echoid-head322" xml:space="preserve">NOTÆ.</head>
          <p style="it">
            <s xml:id="echoid-s10158" xml:space="preserve">I. </s>
            <s xml:id="echoid-s10159" xml:space="preserve">P Rima definitio breuiſſimè exponi poteſt hac ratione. </s>
            <s xml:id="echoid-s10160" xml:space="preserve">Si axis tranſuerſus
              <lb/>
            interius in hyperbola diuidatur, aut exterius in ellipſi, ſecundum pro-
              <lb/>
            portionem figuræ, ſegmentum homologum axis tranſuerſi vocabo Præſectum, vt
              <lb/>
            ſi fuerit hyperbole, vel ellipſis A B, cuius axis tranſuerſus A C, centrum D,
              <lb/>
            latus rectũ A F, & </s>
            <s xml:id="echoid-s10161" xml:space="preserve">in hyperbola ſecetur C A inter vertices A, & </s>
            <s xml:id="echoid-s10162" xml:space="preserve">C; </s>
            <s xml:id="echoid-s10163" xml:space="preserve">in ellipſi
              <lb/>
            verò ſecetur exterius in puncto G, ita vt ſumma, vel differentia ipſarum G A,
              <lb/>
            & </s>
            <s xml:id="echoid-s10164" xml:space="preserve">axis C A, ideſt C G ad G A habeat proportionem figuræ ſcilicet eandem,
              <lb/>
            quàm habet latus tranſuerſum C A ad latus rectum A F; </s>
            <s xml:id="echoid-s10165" xml:space="preserve">tunc quidem vocatur
              <lb/>
            recta linea C G Præſecta.</s>
            <s xml:id="echoid-s10166" xml:space="preserve"/>
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            <s xml:id="echoid-s10167" xml:space="preserve">II. </s>
            <s xml:id="echoid-s10168" xml:space="preserve">Atque G A vocatur Intercepta.</s>
            <s xml:id="echoid-s10169" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10170" xml:space="preserve">III. </s>
            <s xml:id="echoid-s10171" xml:space="preserve">Punctum verò A extremum
              <lb/>
              <figure xlink:label="fig-0310-01" xlink:href="fig-0310-01a" number="357">
                <image file="0310-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0310-01"/>
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            interceptæ G A, & </s>
            <s xml:id="echoid-s10172" xml:space="preserve">diametri C A
              <lb/>
            vocabitur terminus communis dua-
              <lb/>
            rum linearum, ſcilicet axis C A, & </s>
            <s xml:id="echoid-s10173" xml:space="preserve">
              <lb/>
            additæ, vel ablatæ A G.</s>
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            <s xml:id="echoid-s10175" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s10176" xml:space="preserve">Punctum verò G, in quo axis
              <lb/>
            A C interius, vel exterius diuiditur
              <lb/>
            ſecundum proportionem figuræ voca-
              <lb/>
            tur terminus diuidens; </s>
            <s xml:id="echoid-s10177" xml:space="preserve">Si verò ſece-
              <lb/>
            tur C H æqualis A G vocabitur etiã
              <lb/>
            C H intercepta, & </s>
            <s xml:id="echoid-s10178" xml:space="preserve">A H præſecta,
              <lb/>
            atque C terminus communis, & </s>
            <s xml:id="echoid-s10179" xml:space="preserve">H
              <lb/>
            terminus diuidens.</s>
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            <s xml:id="echoid-s10181" xml:space="preserve">V. </s>
            <s xml:id="echoid-s10182" xml:space="preserve">Si diameter I L ſecuerit biſa-
              <lb/>
            riam ſubtenſam A B à ſectionis ver
              <lb/>
            tice A eductam, atque à termino </s>
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