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-div1132" type="section" level="1" n="363">
          <p style="it">
            <s xml:id="echoid-s13249" xml:space="preserve">
              <pb o="396" file="0434" n="435" rhead="Archimedis"/>
            demonſtrationis ſpectes; </s>
            <s xml:id="echoid-s13250" xml:space="preserve">differunt tamen in concluſione, quæ demonſtranda pro-
              <lb/>
              <figure xlink:label="fig-0434-01" xlink:href="fig-0434-01a" number="502">
                <image file="0434-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0434-01"/>
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            ponitur; </s>
            <s xml:id="echoid-s13251" xml:space="preserve">oſtendit enim Pap-
              <lb/>
            pus, ſicut, & </s>
            <s xml:id="echoid-s13252" xml:space="preserve">Archime-
              <lb/>
            des, ſemicircularis diame-
              <lb/>
            tri ſegmentum maius A C
              <lb/>
            ad circuli intercepti dia-
              <lb/>
            metrum H E habere ean-
              <lb/>
            dem proportionem, quàm
              <lb/>
            maioris circuli diameter A
              <lb/>
            B habet ad reliquum ſeg-
              <lb/>
            mentum eius B C, pari-
              <lb/>
            terque B A ad A C ean-
              <lb/>
            dem proportionem habet,
              <lb/>
            quàm C B ad reliqui circuli intercepti L M N diametrum: </s>
            <s xml:id="echoid-s13253" xml:space="preserve">ex hiſce ſequitur
              <lb/>
            concluſio Archimedea, nam ſi A C ad H E eandem rationem habet, quàm A
              <lb/>
            B ad B C, permutando B A ad A C erit vt C B ad H E igitur eadem C B ad
              <lb/>
            duas circulorum diametros H E, & </s>
            <s xml:id="echoid-s13254" xml:space="preserve">L N eandem proportionem habet, & </s>
            <s xml:id="echoid-s13255" xml:space="preserve">pro-
              <lb/>
            pterea circulorum diametri H E, & </s>
            <s xml:id="echoid-s13256" xml:space="preserve">L N æquales ſunt inter ſe. </s>
            <s xml:id="echoid-s13257" xml:space="preserve">Mirum ta-
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            men eſt hanc concluſionem, quàm præ manibus Pappus habebat, non ani-
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            maduertiſſe, demonſtrat tamen quamplurima ſymptomata pulcherrima circu-
              <lb/>
            lorum in Arbelo deſcriptorum, quæ tamen in hoc opuſculo Archimedi tributo
              <lb/>
            pariter recenſeri debebant, ſi hic liber eſſet idem antiquus ille à Pappo viſus,
              <lb/>
            in quo huiuſmodi lemmata circumferebantur: </s>
            <s xml:id="echoid-s13258" xml:space="preserve">ſed for ſan librariorum vitio, & </s>
            <s xml:id="echoid-s13259" xml:space="preserve">
              <lb/>
            incuria codex corruptiſſimus ad Arabes tranſmißus non omnes illas admirandas
              <lb/>
            propoſitiones, ſed vnius tantum particulam continebat, ſicut è contra liber ille
              <lb/>
            antiquus, in quo Pappus prædicta lemmata reperit, carebat concluſione in hi-
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            ſce lemmatibus demonſtrata. </s>
            <s xml:id="echoid-s13260" xml:space="preserve">Cæterum propoſitiones in ſcholijs additæ manifeſtæ
              <lb/>
            quidem ſunt, ſed abſque duabus prioribus poßet propoſitum facillimè demon-
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            ſtrari, Reliquæ duæ propoſitiones ſuperadditæ ad Arabibus faciles quidem
              <lb/>
            ſunt.</s>
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          <head xml:id="echoid-head456" xml:space="preserve">PROPOSITIO VI.</head>
          <p>
            <s xml:id="echoid-s13262" xml:space="preserve">SI fuerit femicirculus A B C, & </s>
            <s xml:id="echoid-s13263" xml:space="preserve">in eius diametro ſumatur
              <lb/>
            punctum D, & </s>
            <s xml:id="echoid-s13264" xml:space="preserve">fuerit A D ipſius D C ſexqui altera, & </s>
            <s xml:id="echoid-s13265" xml:space="preserve">
              <lb/>
            deſcribantur ſuper A D, D C duo ſemicirculi, & </s>
            <s xml:id="echoid-s13266" xml:space="preserve">ponatur cir-
              <lb/>
            culus E F inter tres ſemicirculos tangens eos, & </s>
            <s xml:id="echoid-s13267" xml:space="preserve">educatur dia-
              <lb/>
            meter E F in illo parallela diametro A C, reperiri debet pro-
              <lb/>
            portio diametri A C ad diametrum E F.</s>
            <s xml:id="echoid-s13268" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13269" xml:space="preserve">Iungamus enim duas lineas A E, E B, & </s>
            <s xml:id="echoid-s13270" xml:space="preserve">duas lineas C F, F B,
              <lb/>
            erunt C B, A B rectæ, vti dictũ eſt in prima propoſit. </s>
            <s xml:id="echoid-s13271" xml:space="preserve">Deſcribamus etiam
              <lb/>
            duas lineas F G A, E H C, oſtendeturque eſſe quoque rectas; </s>
            <s xml:id="echoid-s13272" xml:space="preserve">Simili-
              <lb/>
            ter duas lineas D E, D F, & </s>
            <s xml:id="echoid-s13273" xml:space="preserve">iungamus D I, D L, & </s>
            <s xml:id="echoid-s13274" xml:space="preserve">E M, F N, & </s>
            <s xml:id="echoid-s13275" xml:space="preserve">
              <lb/>
            producamus eas ad O, P; </s>
            <s xml:id="echoid-s13276" xml:space="preserve">Et quia in triangulo A E D, A G eſt </s>
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