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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[191.] PROPOSITIO XII.
Page: 193 (155)
[192.] PROPOSITIO XIII.
Page: 194 (156)
[193.] PROPOSITIO XIV.
Page: 195 (157)
[194.] MONITVM.
Page: 196 (158)
[195.] LEMMA II.
Page: 196 (158)
[196.] COROLLARIVM.
Page: 197 (159)
[197.] LEMMA III.
Page: 197 (159)
[198.] LEMMA IV.
Page: 198 (160)
[199.] COROLLARIVM.
Page: 198 (160)
[200.] LEMMAV.
Page: 199 (161)
[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)
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          <head xml:id="echoid-head353" xml:space="preserve">Notæ in Propoſit. XXIX.</head>
          <p style="it">
            <s xml:id="echoid-s10731" xml:space="preserve">QVoniam in hyperbola differentia quadratorum ex axi A C, & </s>
            <s xml:id="echoid-s10732" xml:space="preserve">ex axi Q
              <lb/>
              <note position="right" xlink:label="note-0333-01" xlink:href="note-0333-01a" xml:space="preserve">12. huius.</note>
            R æqualis eſt differentiæ inter quadratum I L à quadrato eius coniugatæ
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            N O; </s>
            <s xml:id="echoid-s10733" xml:space="preserve">eſtque Q R media proportionalis inter ſiguræ latera A C, & </s>
            <s xml:id="echoid-s10734" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0333-02" xlink:href="note-0333-02a" xml:space="preserve">16. lib. 1.</note>
            A F; </s>
            <s xml:id="echoid-s10735" xml:space="preserve">ergo rectangulum C A F ſub extremis contentum æquale eſt quadrato in-
              <lb/>
            termediæ Q R: </s>
            <s xml:id="echoid-s10736" xml:space="preserve">Et propterea differentia inter quadratum A C, & </s>
            <s xml:id="echoid-s10737" xml:space="preserve">rectangu-
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            lum C A F æqualis erit differentiæ inter quadratum A C à quadrato Q R.
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            pari ratione erit differentia quadrati I L à rectangulo L I P æqualis differen-
              <lb/>
            tiæ quadrati I L à quadrato N O; </s>
            <s xml:id="echoid-s10739" xml:space="preserve">& </s>
            <s xml:id="echoid-s10740" xml:space="preserve">propterea in hyperbole differentia qua-
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            drati axis A C à rectangulo ſub figuræ lateribus contentum C A F æqualis
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            eſt differentiæ quadrati diametri I L à rectangulo L I P ſub lateribus figuræ
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            eius.</s>
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          <head xml:id="echoid-head354" xml:space="preserve">Notæ in Propoſit. XXX.</head>
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            <s xml:id="echoid-s10742" xml:space="preserve">QVoniam in ellipſi quadratorum ex A C, & </s>
            <s xml:id="echoid-s10743" xml:space="preserve">ex Q R ſumma æqualis eſt
              <lb/>
              <note position="right" xlink:label="note-0333-03" xlink:href="note-0333-03a" xml:space="preserve">Prop. 13.
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              huius.
                <lb/>
              ex 15.
                <lb/>
              lib. 1.</note>
            ſummæ quadratorum ex I L, & </s>
            <s xml:id="echoid-s10744" xml:space="preserve">ex N O: </s>
            <s xml:id="echoid-s10745" xml:space="preserve">eſtque rectangulum C A F
              <lb/>
            æquale quadrato Q R, & </s>
            <s xml:id="echoid-s10746" xml:space="preserve">rectangulum L I P æquale quadrato N O
              <lb/>
            (vt in præcedenti nota dictum eſt) igitur in ellipſi quadratum axis A C, & </s>
            <s xml:id="echoid-s10747" xml:space="preserve">
              <lb/>
            rectangulum C A F ſub eius lateribus cõtentum ſimul ſumpta æqualia ſunt qua-
              <lb/>
            drato ex I L cum rectangulo figuræ eius L I P.</s>
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