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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              <pb o="171" file="0209" n="209" rhead="Conicor. Lib. VI."/>
            Q ſimile eſt M K S,
              <lb/>
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            quare angulus G æ-
              <lb/>
            qualis eſt angulo M,
              <lb/>
            & </s>
            <s xml:id="echoid-s6557" xml:space="preserve">propterea periphe-
              <lb/>
            riæ E F Q, & </s>
            <s xml:id="echoid-s6558" xml:space="preserve">K F S,
              <lb/>
            quibus inſiſtunt, æ-
              <lb/>
            quales erunt, quod
              <lb/>
            eſt abſurdũ: </s>
            <s xml:id="echoid-s6559" xml:space="preserve">eſt enim
              <lb/>
            E F Q maior, quàm
              <lb/>
            K F S; </s>
            <s xml:id="echoid-s6560" xml:space="preserve">ergo duo triã-
              <lb/>
            gula A B C, D E F
              <lb/>
            in omnibus figuris
              <lb/>
            ſunt ſimilia. </s>
            <s xml:id="echoid-s6561" xml:space="preserve">Quod e-
              <lb/>
            rat oſtendendum.</s>
            <s xml:id="echoid-s6562" xml:space="preserve"/>
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        <div xml:id="echoid-div623" type="section" level="1" n="208">
          <head xml:id="echoid-head263" xml:space="preserve">PROPOSITIO
            <lb/>
          Præmiſſa VI.</head>
          <p>
            <s xml:id="echoid-s6563" xml:space="preserve">DEinde ſint duo anguli B, E qualeſcunque; </s>
            <s xml:id="echoid-s6564" xml:space="preserve">ſed angulus
              <lb/>
              <note position="left" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">a</note>
            A B H, vel C B H æqualis angulo D E I, aut F E I:
              <lb/>
            </s>
            <s xml:id="echoid-s6565" xml:space="preserve">& </s>
            <s xml:id="echoid-s6566" xml:space="preserve">ſupponantur reliqua omnia iam dicta.</s>
            <s xml:id="echoid-s6567" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6568" xml:space="preserve">Quia proportio C H in H A ad quadratum H B ſuppoſita eſt, vt F I
              <lb/>
            in I D ad quadratum I E, & </s>
            <s xml:id="echoid-s6569" xml:space="preserve">H C, vel H A ad H B eſt, vt F I, vel D I
              <lb/>
            ad I E; </s>
            <s xml:id="echoid-s6570" xml:space="preserve">erit etiam H A ad H B, vt I D ad I E, & </s>
            <s xml:id="echoid-s6571" xml:space="preserve">duo anguli H, I ſunt
              <lb/>
            æquales; </s>
            <s xml:id="echoid-s6572" xml:space="preserve">igitur triangulum H B A, aut H B C ſimile eſt triangulo E D
              <lb/>
            I, aut E F I, quare duo triangula A B C, D E F ſimilia ſunt; </s>
            <s xml:id="echoid-s6573" xml:space="preserve">Et hoc
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s6574" xml:space="preserve"/>
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        <div xml:id="echoid-div625" type="section" level="1" n="209">
          <head xml:id="echoid-head264" xml:space="preserve">Notæ in Propoſit. Præmiſſas
            <lb/>
          I. II. III. IV. & V.</head>
          <p style="it">
            <s xml:id="echoid-s6575" xml:space="preserve">AFferuntur in hac ſectione aliquæ propoſitiones ſimul coaceruatæ, quæ lem-
              <lb/>
            maticæ ſunt, & </s>
            <s xml:id="echoid-s6576" xml:space="preserve">vſum habent in ſequentibus propoſitionibus; </s>
            <s xml:id="echoid-s6577" xml:space="preserve">ſanè conij-
              <lb/>
            citur ex hoc titulo PRAEMISS AE rubeis characteribus inſcripto, huiuſmodi lẽ-
              <lb/>
            mata T extui Apollonij ab Arabico Interprete, vel ab aliquo alio ſuperaddita fuiſſe;
              <lb/>
            </s>
            <s xml:id="echoid-s6578" xml:space="preserve">licet Pappus Alexandrinus libro 7. </s>
            <s xml:id="echoid-s6579" xml:space="preserve">afferat eadem ferè lemmata, tanquã propria,
              <lb/>
            & </s>
            <s xml:id="echoid-s6580" xml:space="preserve">conferentia ad Apollonij ſexti libri intelligentiam.</s>
            <s xml:id="echoid-s6581" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6582" xml:space="preserve">Poteſt tamen propoſitio vniuerſalis breuius exponi hac ratione. </s>
            <s xml:id="echoid-s6583" xml:space="preserve">Si à vertici-
              <lb/>
            bus duorum triangulorum à duobus circulis compræhenſorum rectæ lineæ ductæ
              <lb/>
            efficiant cum baſibus angulos æquales; </s>
            <s xml:id="echoid-s6584" xml:space="preserve">atque eorundem ſegmentorum inter baſim,
              <lb/>
            & </s>
            <s xml:id="echoid-s6585" xml:space="preserve">peripheriam interceptorum quadrata ad rectangula ſub factis ſegmentis </s>
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