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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        <div xml:id="echoid-div693" type="section" level="1" n="229">
          <head xml:id="echoid-head289" xml:space="preserve">Notæ in Propoſit. XXI.</head>
          <p style="it">
            <s xml:id="echoid-s7622" xml:space="preserve">QVoniam G B ad B I, ſuppoſita eſt vt H E ad E K, &</s>
            <s xml:id="echoid-s7623" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7624" xml:space="preserve">Quia L B
              <lb/>
              <note position="left" xlink:label="note-0241-01" xlink:href="note-0241-01a" xml:space="preserve">a</note>
            ad B G ex bypotheſi erat, vt M E ad E H, & </s>
            <s xml:id="echoid-s7625" xml:space="preserve">inuertendo G B ad B I
              <lb/>
            erat vt H E ad E K; </s>
            <s xml:id="echoid-s7626" xml:space="preserve">ergo ex æqualitate L B ad B I erit vt M E
              <lb/>
            ad E K; </s>
            <s xml:id="echoid-s7627" xml:space="preserve">& </s>
            <s xml:id="echoid-s7628" xml:space="preserve">per conuerſionem rationis B L ad L I erit vt E M ad M K.</s>
            <s xml:id="echoid-s7629" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s7630" xml:space="preserve">Et propter ſimilitudinem duarum ſectionum N L ad A I, nempe L O
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              <note position="left" xlink:label="note-0241-02" xlink:href="note-0241-02a" xml:space="preserve">b</note>
            ad O I eſt, vt P M ad F K, nempe M Q ad Q K, &</s>
            <s xml:id="echoid-s7631" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7632" xml:space="preserve">Quoniam duæ ſe-
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            ctiones N B, & </s>
            <s xml:id="echoid-s7633" xml:space="preserve">P E ſimiles ſuppoſitæ ſunt, & </s>
            <s xml:id="echoid-s7634" xml:space="preserve">axiũ abſciſſæ L B, M E, nec non
              <lb/>
            I B, K E ad latera recta B G,
              <lb/>
              <figure xlink:label="fig-0241-02" xlink:href="fig-0241-02a" number="275">
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                <caption xml:id="echoid-caption1" xml:space="preserve">Cc 2</caption>
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            & </s>
            <s xml:id="echoid-s7635" xml:space="preserve">H E proportionales ſunt;</s>
            <s xml:id="echoid-s7636" xml:space="preserve"> igitur N L ad A I eandem
              <note position="right" xlink:label="note-0241-03" xlink:href="note-0241-03a" xml:space="preserve">ex 12.
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              huius.</note>
            portionem habebit, quàm P M ad D K: </s>
            <s xml:id="echoid-s7637" xml:space="preserve">& </s>
            <s xml:id="echoid-s7638" xml:space="preserve">quia triangula N L O, & </s>
            <s xml:id="echoid-s7639" xml:space="preserve">A I O ſimilia ſunt pro- pter parallelas N L, & </s>
            <s xml:id="echoid-s7640" xml:space="preserve">I A, pariterque triangula P M Q,& </s>
            <s xml:id="echoid-s7641" xml:space="preserve">D K Q ſimilia ſunt; </s>
            <s xml:id="echoid-s7642" xml:space="preserve">igitur L O ad O I erit vt N L ad I A; </s>
            <s xml:id="echoid-s7643" xml:space="preserve">pariterque M Q ad Q K erit vt P M ad D I, ſeu vt N L ad A I: </s>
            <s xml:id="echoid-s7644" xml:space="preserve">& </s>
            <s xml:id="echoid-s7645" xml:space="preserve">propterea L O ad O I erit vt M Q ad QK.</s>
            <s xml:id="echoid-s7646" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s7647" xml:space="preserve">Et ex æqualitate L O ad
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            L B erit vt Q M ad M E, ſed
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            L B ad L N eſt vt M E ad
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            M P, cum ex ſuppoſitione
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            ſectiones ſint ſimiles, &</s>
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