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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          <p style="it">
            <s xml:id="echoid-s13308" xml:space="preserve">
              <pb o="398" file="0436" n="437" rhead="Archimedis"/>
            ſuper oſtendit perpendicularem E O æqualem eſſe circuli diametro E F. </s>
            <s xml:id="echoid-s13309" xml:space="preserve">Itaque
              <lb/>
            in quadrato ſpatio E O P F, circuli diameter E F, ſiue O P media proportio-
              <lb/>
            nalis erit inter A O, & </s>
            <s xml:id="echoid-s13310" xml:space="preserve">P C. </s>
            <s xml:id="echoid-s13311" xml:space="preserve">Zuam ergo proportionem habent tres continuè
              <lb/>
            proportionales in eadem ratione A D ad D C ſimul ſumptæ ad illarum inter-
              <lb/>
              <figure xlink:label="fig-0436-01" xlink:href="fig-0436-01a" number="504">
                <image file="0436-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0436-01"/>
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            mediam, eandem habebit diameter maioris ſemicirculi A C ad O P, ſiue E F.
              <lb/>
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            <s xml:id="echoid-s13312" xml:space="preserve">Zuæ deinde Pappus demonſtrat perpendiculares à centris circulorum in collate-
              <lb/>
            ralibus ſpatijs prædicti Arbeli exiſtentium eſſe multiplices diametrorum eorum
              <lb/>
            circulorum à quibus educuntur ſecundum ſeriem natur alem numerorum ab vni-
              <lb/>
            tate creſcentium, proprietas quidem eſt admirabilis, de qua in hac propoſitio-
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            ne Archimedis altum ſilentium, quod forte temporum iniuriæ tribuendum
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            eſt.</s>
            <s xml:id="echoid-s13313" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s13314" xml:space="preserve">Poſſent in hiſce duabus propoſitionibus non pauca problemata ſuperaddi, quo-
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            modo nimirum in prædicto ſpatio à tribus ſemicirculis comprehenſo circuli in-
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            numerabiles deſcribi debeant, & </s>
            <s xml:id="echoid-s13315" xml:space="preserve">alia quamplurima facilia, quæ lectorum ſa-
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            gacitati relinquuntur.</s>
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          <head xml:id="echoid-head458" xml:space="preserve">PROPOSITIO VII.</head>
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            <s xml:id="echoid-s13317" xml:space="preserve">SI circulus circa quadratum deſcriptus fuerit, & </s>
            <s xml:id="echoid-s13318" xml:space="preserve">alius intra
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            illum, vtique erit circumſcriptus duplus inſcripti.</s>
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            <s xml:id="echoid-s13320" xml:space="preserve">Sit itaque circulus compre-
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            hendens quadratum A B, cir-
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            culus A B, & </s>
            <s xml:id="echoid-s13321" xml:space="preserve">inſcriptus C D,
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            & </s>
            <s xml:id="echoid-s13322" xml:space="preserve">ſit diameter quadrati A B, & </s>
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            eſt diameter circuli circumſcri-
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            pti, & </s>
            <s xml:id="echoid-s13324" xml:space="preserve">educamus C D diame-
              <lb/>
            trum circuli inſcripti parallelam
              <lb/>
            ipſi A E, quæ eſt ei æqualis.
              <lb/>
            </s>
            <s xml:id="echoid-s13325" xml:space="preserve">Et quia quadratum A B duplum
              <lb/>
            eſt quadrati A E, ſiue D C, & </s>
            <s xml:id="echoid-s13326" xml:space="preserve">
              <lb/>
            proportio quadratorum ex </s>
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