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-div1106" type="section" level="1" n="348">
          <pb o="386" file="0424" n="425" rhead="Archimedis"/>
        </div>
        <div xml:id="echoid-div1107" type="section" level="1" n="349">
          <head xml:id="echoid-head441" xml:space="preserve">PROPOSITIO I.</head>
          <p>
            <s xml:id="echoid-s12929" xml:space="preserve">SI mutuo ſe tangant duo circuli, vt duo circuli A E B, C E
              <lb/>
            D in E, fuerintque eorum diametri parallelæ, vt ſunt duæ
              <lb/>
            diametri A B, C D, & </s>
            <s xml:id="echoid-s12930" xml:space="preserve">iungantur duo puncta B, D, & </s>
            <s xml:id="echoid-s12931" xml:space="preserve">conta-
              <lb/>
            ctus E [lineis] D E, B D, erit linea B E recta.</s>
            <s xml:id="echoid-s12932" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12933" xml:space="preserve">Sint duo centra G, F, & </s>
            <s xml:id="echoid-s12934" xml:space="preserve">iunga-
              <lb/>
              <figure xlink:label="fig-0424-01" xlink:href="fig-0424-01a" number="487">
                <image file="0424-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0424-01"/>
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            mus G F, & </s>
            <s xml:id="echoid-s12935" xml:space="preserve">producamus ad E, & </s>
            <s xml:id="echoid-s12936" xml:space="preserve">
              <lb/>
            educamus D H parallelam ipſi G F.
              <lb/>
            </s>
            <s xml:id="echoid-s12937" xml:space="preserve">Et quia H F æqualis eſt ipſi G D,
              <lb/>
            ſuntque G D, E G æquales, ergo
              <lb/>
            ex æqualibus F B, F E remanebunt
              <lb/>
            G F, nempe D H, & </s>
            <s xml:id="echoid-s12938" xml:space="preserve">H B, quæ
              <lb/>
            erunt æquales, atque duo anguli H
              <lb/>
            D B, H B D æquales. </s>
            <s xml:id="echoid-s12939" xml:space="preserve">Et quia
              <lb/>
            duo anguli E G D, E F B ſunt re-
              <lb/>
            cti, atq; </s>
            <s xml:id="echoid-s12940" xml:space="preserve">duo anguli E G D, D H
              <lb/>
            B ſunt æquales, remanebunt duo
              <lb/>
            anguli G E D, G D E, qui inter ſe, & </s>
            <s xml:id="echoid-s12941" xml:space="preserve">duobus angulis H D B, H B D
              <lb/>
            æquales erunt; </s>
            <s xml:id="echoid-s12942" xml:space="preserve">ergo angulus E D G æqualis eſt angulo D B F, & </s>
            <s xml:id="echoid-s12943" xml:space="preserve">com-
              <lb/>
            prehenſus angulus G D B eſt communis, ergo erunt duo anguli G D B,
              <lb/>
            F B D (qui ſunt pares duobus rectis) æquales duobus angulis G D B,
              <lb/>
            G D E: </s>
            <s xml:id="echoid-s12944" xml:space="preserve">igitur ipſi quoque ſunt æquales duobus rectis, ergo linea E D
              <lb/>
            B eſt recta, & </s>
            <s xml:id="echoid-s12945" xml:space="preserve">hoc eſt, quod voluimus.</s>
            <s xml:id="echoid-s12946" xml:space="preserve"/>
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        <div xml:id="echoid-div1109" type="section" level="1" n="350">
          <head xml:id="echoid-head442" xml:space="preserve">SCHOLIVM ALMOCHTASSO.</head>
          <p>
            <s xml:id="echoid-s12947" xml:space="preserve">DIcit Doctor; </s>
            <s xml:id="echoid-s12948" xml:space="preserve">Et quidem dici poteſt cum duo anguli H D B, H B
              <lb/>
            D ſint æquales, & </s>
            <s xml:id="echoid-s12949" xml:space="preserve">angulus D H B rectus, quod erit angulus B D
              <lb/>
            H ſemirectus, & </s>
            <s xml:id="echoid-s12950" xml:space="preserve">ſimiliter angulus E D G, & </s>
            <s xml:id="echoid-s12951" xml:space="preserve">angulus G D H rectus,
              <lb/>
            ergo tres anguli ſunt æquales duobus rectis, igitur linea E D B eſt re-
              <lb/>
            cta. </s>
            <s xml:id="echoid-s12952" xml:space="preserve">Idem ſequitur, ſi illi duo circuli ſe mutuo exterius contigerint.</s>
            <s xml:id="echoid-s12953" xml:space="preserve"/>
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        <div xml:id="echoid-div1110" type="section" level="1" n="351">
          <head xml:id="echoid-head443" xml:space="preserve">Notæ in Propoſit. I.</head>
          <p style="it">
            <s xml:id="echoid-s12954" xml:space="preserve">HAEc eſt vna earum Propoſitionum, quas Pappus in quodam libro antiquo
              <lb/>
            reperit, qui, vt deduximus ex Eutocio, ab Archimede conſcriptus diu
              <lb/>
            apud Arabes latuit. </s>
            <s xml:id="echoid-s12955" xml:space="preserve">Hæc aſſumitur in propoſit. </s>
            <s xml:id="echoid-s12956" xml:space="preserve">14. </s>
            <s xml:id="echoid-s12957" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12958" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12959" xml:space="preserve">Collect. </s>
            <s xml:id="echoid-s12960" xml:space="preserve">Pappi, eam-
              <lb/>
            que ſupplet Commandinus, ſed extat expreſſe lib. </s>
            <s xml:id="echoid-s12961" xml:space="preserve">7. </s>
            <s xml:id="echoid-s12962" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s12963" xml:space="preserve">110. </s>
            <s xml:id="echoid-s12964" xml:space="preserve">eiuſdem
              <lb/>
            Pappi, eſtque demonſtratio vniuer ſaliſſima comprehendens caſum neglectum
              <lb/>
            in hac demonſtratione, ſcilicet quando duo circuli ſeſe exterius contingunt, &</s>
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