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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        <div xml:id="echoid-div263" type="section" level="1" n="87">
          <head xml:id="echoid-head120" xml:space="preserve">SECTIO DECIMA</head>
          <head xml:id="echoid-head121" xml:space="preserve">Continens Propof. XXXXIV. XXXXV.
            <lb/>
          Apollonij.</head>
          <p>
            <s xml:id="echoid-s2890" xml:space="preserve">SI ex axe recto ellipſis ſumatur menſura ab origine, quæ ad
              <lb/>
              <note position="left" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">a</note>
            ſemiaxim rectum non habeat minorem proportionem, quàm
              <lb/>
            habet figura ſuæ tranſuerſæ, tunc quicumque ramus ſecans, ab
              <lb/>
            illa origine ad fectionem ductus, abſcindit ex axe tranſuerſo ad
              <lb/>
            verticem ſectionis lineam minorem ea, quàm abſcindit linea
              <lb/>
            breuiſsima egrediens ab eius termino in ſectione poſito ad tran-
              <lb/>
            ſuerſum axim; </s>
            <s xml:id="echoid-s2891" xml:space="preserve">ſi vero fuerit proportio ad ſemirectum minor,
              <lb/>
            tunc ramorum ſecantium vnus eſt breuiſecans; </s>
            <s xml:id="echoid-s2892" xml:space="preserve">reliqui vero, qui
              <lb/>
            ſequuntur extremum tranſuerſæ habent proprietates ſuperius ex-
              <lb/>
            poſitas, & </s>
            <s xml:id="echoid-s2893" xml:space="preserve">qui ſequuntur extremitatem recti, ſecant ex tranſuer-
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            ſa lineam maiorem ea, quàm abſcindit breuiſsima egrediens ab
              <lb/>
            eius termino.</s>
            <s xml:id="echoid-s2894" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div265" type="section" level="1" n="88">
          <head xml:id="echoid-head122" xml:space="preserve">PROPOSITIO XXXXIV.</head>
          <p>
            <s xml:id="echoid-s2895" xml:space="preserve">Sit A D dimidium axis recti, & </s>
            <s xml:id="echoid-s2896" xml:space="preserve">minoris ſectionis ellipticæ
              <lb/>
              <note position="left" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">b</note>
            A B C, & </s>
            <s xml:id="echoid-s2897" xml:space="preserve">meuſura A E, quæ ſit maior, quàm A D, & </s>
            <s xml:id="echoid-s2898" xml:space="preserve">pro-
              <lb/>
            portio illius ad iſtam non ſit minor proportione figuræ ſectionis;
              <lb/>
            </s>
            <s xml:id="echoid-s2899" xml:space="preserve">Dico, quod linea breuiſsima egrediens ab extremitate cuiuſcum-
              <lb/>
            que rami ſecantis educti ex E ad ſectionem A B C, ſecat ex
              <lb/>
            tranuerſa B C cum vertice B, vel C lineam maiorem ea, quàm
              <lb/>
            abſcindit ille ramus.</s>
            <s xml:id="echoid-s2900" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2901" xml:space="preserve">Ponatur ramus E F, & </s>
            <s xml:id="echoid-s2902" xml:space="preserve">ducamus ex F ad vtrum-
              <lb/>
              <figure xlink:label="fig-0105-01" xlink:href="fig-0105-01a" number="85">
                <image file="0105-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0105-01"/>
              </figure>
              <note position="left" xlink:label="note-0105-03" xlink:href="note-0105-03a" xml:space="preserve">c</note>
            que axim duas perpendiculares F H, F I. </s>
            <s xml:id="echoid-s2903" xml:space="preserve">Et quia
              <lb/>
            proportio E A ad A D non eſt minor proportio-
              <lb/>
            ne ſiguræ, ſed minor eſt, quàm E H ad H D, nem-
              <lb/>
            pe E F ad F G, ſeu D I ad I G, erit proportio ſigu-
              <lb/>
            ræ minor, quàm D I ad I G, & </s>
            <s xml:id="echoid-s2904" xml:space="preserve">ponamus D I ad
              <lb/>
            I K, vt eſt proportio figuræ, & </s>
            <s xml:id="echoid-s2905" xml:space="preserve">iungamus F K;
              <lb/>
            </s>
            <s xml:id="echoid-s2906" xml:space="preserve">erit ergo F K linea breuiſſima (10. </s>
            <s xml:id="echoid-s2907" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2908" xml:space="preserve">& </s>
            <s xml:id="echoid-s2909" xml:space="preserve">iam
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              <note position="right" xlink:label="note-0105-04" xlink:href="note-0105-04a" xml:space="preserve">10.
                <lb/>
              huius.</note>
            ſecat K B maiorem, quàm B G, & </s>
            <s xml:id="echoid-s2910" xml:space="preserve">G F non erit
              <lb/>
            breuiſſima; </s>
            <s xml:id="echoid-s2911" xml:space="preserve">& </s>
            <s xml:id="echoid-s2912" xml:space="preserve">hoc erat propoſitum.</s>
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