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-div1069" type="section" level="1" n="337">
          <head xml:id="echoid-head417" xml:space="preserve">In Sectionem X. Propoſit. XXXXIX.
            <lb/>
          XXXXX. & XXXXXI.</head>
          <head xml:id="echoid-head418" xml:space="preserve">LEMMA XVI.</head>
          <p style="it">
            <s xml:id="echoid-s12426" xml:space="preserve">S I rectæ lineæ A B bifariam ſectæ in C vtrinque addantur æquales
              <lb/>
            portiones A D, & </s>
            <s xml:id="echoid-s12427" xml:space="preserve">B E, dico rectangulum ſub tota D E, & </s>
            <s xml:id="echoid-s12428" xml:space="preserve">
              <lb/>
            ſub intermedia A B æquale eſſe differentiæ quadratorum ex A E, & </s>
            <s xml:id="echoid-s12429" xml:space="preserve">
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            ex A D.</s>
            <s xml:id="echoid-s12430" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s12431" xml:space="preserve">Apponatur F D æqualis D
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            A, vel B E: </s>
            <s xml:id="echoid-s12432" xml:space="preserve">& </s>
            <s xml:id="echoid-s12433" xml:space="preserve">quia F D æ-
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            qualis eſt B E addita communi
              <lb/>
            B D, erit F B æqualis D E,
              <lb/>
            & </s>
            <s xml:id="echoid-s12434" xml:space="preserve">ideo rectangulum F B A æ-
              <lb/>
            quale erit rectangulo ſub D E,
              <lb/>
            & </s>
            <s xml:id="echoid-s12435" xml:space="preserve">ſub A B, ſed quadratum
              <lb/>
            B D æquale eſt quadrato D A cum rectangulo F B A, (eo quod F A ſecta eſt
              <lb/>
            bifariam in D, & </s>
            <s xml:id="echoid-s12436" xml:space="preserve">ei in directum additur A B), ergo quadratum D B æquale
              <lb/>
            eſt quadrato D A vna cum rectangulo ſub D E, & </s>
            <s xml:id="echoid-s12437" xml:space="preserve">ſub A B, & </s>
            <s xml:id="echoid-s12438" xml:space="preserve">propterea re-
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            ctangulum ſub D E, & </s>
            <s xml:id="echoid-s12439" xml:space="preserve">ſub A B contentum æquale eſt differentiæ quadrati B D,
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            ſeu A E à quadrato D A, quod erat oſtendendum.</s>
            <s xml:id="echoid-s12440" xml:space="preserve"/>
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          <head xml:id="echoid-head419" xml:space="preserve">LEMMA XVII.</head>
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            <s xml:id="echoid-s12441" xml:space="preserve">IN hyperbola, & </s>
            <s xml:id="echoid-s12442" xml:space="preserve">ellypſi, cuius centrum D, axis A C, erectus A
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            F, præſectæ A H, G C, & </s>
            <s xml:id="echoid-s12443" xml:space="preserve">in ea diameter I L, cuius erectus
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