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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            differentia duorum laterum figuræ ſui homologi; </s>
            <s xml:id="echoid-s10815" xml:space="preserve">pariterque pro-
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            ximioris axi homologi differentia duorum laterum figuræ eius
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            maior eſt, quàm differentia duorum laterum figuræ remotioris.</s>
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          <head xml:id="echoid-head359" xml:space="preserve">PROPOSITIO XXI. & XXVIII.</head>
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            <s xml:id="echoid-s10817" xml:space="preserve">SIt itaque ſectio A B P, & </s>
            <s xml:id="echoid-s10818" xml:space="preserve">duo axes coniugati eius A C, Q
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            R, centrum D; </s>
            <s xml:id="echoid-s10819" xml:space="preserve">ſintque I L, N O duæ aliæ diametri con-
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            iugatæ; </s>
            <s xml:id="echoid-s10820" xml:space="preserve">pariterque S T, V X, & </s>
            <s xml:id="echoid-s10821" xml:space="preserve">educamus ad axim C A M
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            perpendiculares B E, P M. </s>
            <s xml:id="echoid-s10822" xml:space="preserve">Dico quod ſi fuerit A C æqualis
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            Q R; </s>
            <s xml:id="echoid-s10823" xml:space="preserve">erit quoque I L æqualis ipſi N O, & </s>
            <s xml:id="echoid-s10824" xml:space="preserve">S T ipſi V X. </s>
            <s xml:id="echoid-s10825" xml:space="preserve">Si
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            verò fuerit eorum aliquis reliquo major, vtique eius homologa
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            diameter maior quoque erit ſua coniugata, & </s>
            <s xml:id="echoid-s10826" xml:space="preserve">ſimiliter in reli-
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            quis propoſitionibus.</s>
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            <s xml:id="echoid-s10828" xml:space="preserve">Sit prius alter axis A C maior in prima figura, ſed Q R in ſecunda;
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            <s xml:id="echoid-s10829" xml:space="preserve">ſintque A G, C H duæ interceptæ diametri A C. </s>
            <s xml:id="echoid-s10830" xml:space="preserve">Et quia quadratum
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            A C ad quadratum Q R, nempe A C ad eius erectum eſt vt A H ad H
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            C, ſeu ad A G; </s>
            <s xml:id="echoid-s10831" xml:space="preserve">& </s>
            <s xml:id="echoid-s10832" xml:space="preserve">habet H A ad A G maiorem proportionem in prima
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              huius.</note>
            figura, & </s>
            <s xml:id="echoid-s10833" xml:space="preserve">minorem in ſecunda, quàm H E ad E G, quæ oſtenſa eſt
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            ( 6. </s>
            <s xml:id="echoid-s10834" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10835" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s10836" xml:space="preserve">) vt quadratum I L ad
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            quadratum N O, nempe I L ad eius
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            erectum. </s>
            <s xml:id="echoid-s10837" xml:space="preserve">Et ſimiliter proportio illa
              <lb/>
            maior, aut minor eſt, quam H M ad
              <lb/>
            M G, quæ eſt vt quadratum S T ad
              <lb/>
            quadratum V X; </s>
            <s xml:id="echoid-s10838" xml:space="preserve">igitur A C ad Q R,
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            ſiue ad erectum ipſius A C in prima
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            maiorem proportionem habet, & </s>
            <s xml:id="echoid-s10839" xml:space="preserve">in
              <lb/>
            ſecunda minorem, quàm I L ad N O,
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            ſiue ad erectum ipſius I L, ſiue quàm
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            S T ad V X, vel ad erectum ipſius
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            S T; </s>
            <s xml:id="echoid-s10840" xml:space="preserve">ſed quia H E ad E G in prima
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            figura maiorem proportionem, & </s>
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            ſecunda minorem, quàm H M ad M
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            G habebit I L ad N O maiorem pro-
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            portionem in prima, & </s>
            <s xml:id="echoid-s10842" xml:space="preserve">minorem in
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            ſecunda, quàm S T ad V X, cum-
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            que H E in prima figura ſit maior, & </s>
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            in ſecunda minor, quàm E G, pari-
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            terque H M, quàm M G, erit I L in
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            prima maior, & </s>
            <s xml:id="echoid-s10844" xml:space="preserve">in ſecunda minor,
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            quàm N O, ſimiliterque S T, quàm
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            V X.</s>
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