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

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            ſarum in vna ſectionum ad homologa abſciſſa alterius eſt eadem ( 12. </s>
            <s xml:id="echoid-s6876" xml:space="preserve">ex
              <lb/>
            6. </s>
            <s xml:id="echoid-s6877" xml:space="preserve">), & </s>
            <s xml:id="echoid-s6878" xml:space="preserve">anguli compræhenſi à potentibus, & </s>
            <s xml:id="echoid-s6879" xml:space="preserve">abſciſſis ſunt æquales; </s>
            <s xml:id="echoid-s6880" xml:space="preserve">quia
              <lb/>
            æquales ſunt duobus angulis R A L, S C N æqualibus, & </s>
            <s xml:id="echoid-s6881" xml:space="preserve">propterea duo
              <lb/>
              <note position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            ſegmenta ſunt ſimilia.</s>
            <s xml:id="echoid-s6882" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6883" xml:space="preserve">Poſtea oſtendetur, quod ſi duo ſegmenta fuerint ſimilia, erit
              <lb/>
            angulus F æqualis E, & </s>
            <s xml:id="echoid-s6884" xml:space="preserve">A M ad A E, vt O C ad C F.</s>
            <s xml:id="echoid-s6885" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6886" xml:space="preserve">Quia propter ſimilitudinem duorum ſegmentorum continebunt poten-
              <lb/>
              <note position="right" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">d</note>
            tes cum ſuis abſciſſis angulos æquales, & </s>
            <s xml:id="echoid-s6887" xml:space="preserve">erit proportio potentium ad ab-
              <lb/>
              <note position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            ſciſſas eadem, & </s>
            <s xml:id="echoid-s6888" xml:space="preserve">proportio abſciſſarum, in vna earum ad ſua homologa in
              <lb/>
            altera, erit eadem. </s>
            <s xml:id="echoid-s6889" xml:space="preserve">Et quia V a in a E ad quadratũ a A eandem propor-
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              <figure xlink:label="fig-0218-01" xlink:href="fig-0218-01a" number="243">
                <image file="0218-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0218-01"/>
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            tionem habet, quàm Y c in c F ad quadratum c C, & </s>
            <s xml:id="echoid-s6890" xml:space="preserve">duo anguli a, & </s>
            <s xml:id="echoid-s6891" xml:space="preserve">c
              <lb/>
            ſunt recti; </s>
            <s xml:id="echoid-s6892" xml:space="preserve">atque angulus C, nempe O æqualis eſt A, nempe M, propter
              <lb/>
            ſimilitudinem ſegmentorum: </s>
            <s xml:id="echoid-s6893" xml:space="preserve">ergo triangulum A E V ſimile eſt C F Y,
              <lb/>
            & </s>
            <s xml:id="echoid-s6894" xml:space="preserve">angulus V æqualis eſt angulo Y; </s>
            <s xml:id="echoid-s6895" xml:space="preserve">pariterque angulus E æqualis eſt F,
              <lb/>
            & </s>
            <s xml:id="echoid-s6896" xml:space="preserve">A V ad A E eandem proportionem habet, quàm Y C ad C F. </s>
            <s xml:id="echoid-s6897" xml:space="preserve">Po-
              <lb/>
            namus iam P A ad duplam A E, vt Q C ad duplam C F; </s>
            <s xml:id="echoid-s6898" xml:space="preserve">ergo ex æqua-
              <lb/>
            litate A T diameter ad A P erectum eius eſt, vt C X diameter ad C Q
              <lb/>
            erectum eius ( 53. </s>
            <s xml:id="echoid-s6899" xml:space="preserve">54. </s>
            <s xml:id="echoid-s6900" xml:space="preserve">ex I. </s>
            <s xml:id="echoid-s6901" xml:space="preserve">) & </s>
            <s xml:id="echoid-s6902" xml:space="preserve">T M in M A ad quadratum M G eandẽ
              <lb/>
              <note position="left" xlink:label="note-0218-04" xlink:href="note-0218-04a" xml:space="preserve">21. lib. I.</note>
            proportionem habet, quàm X O in O C ad quadratum O I: </s>
            <s xml:id="echoid-s6903" xml:space="preserve">at ſuppoſi-
              <lb/>
            tum eſt quadratum A M ad quadratum M G, vt quadratum C O ad qua-
              <lb/>
            dratum O I; </s>
            <s xml:id="echoid-s6904" xml:space="preserve">ergo ex æqualitate T M in M A ad quadratum A M, nem-
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            pe T M ad M A, eandem proportionem habet, quàm X O in O C </s>
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