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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            <s xml:id="echoid-s11493" xml:space="preserve">
              <pb o="325" file="0363" n="364" rhead="Conicor. Lib. VII."/>
            tionem, quàm C M in M A quater ſumptum vna cum quadrato C A,
              <lb/>
            nempe quàm quadratum C m ad quadratum A C; </s>
            <s xml:id="echoid-s11494" xml:space="preserve">ideoque M H in H
              <lb/>
            A ad quadrarum H A minorem proportionem habet quàm quadratum.
              <lb/>
            </s>
            <s xml:id="echoid-s11495" xml:space="preserve">C m ad quadratum A C. </s>
            <s xml:id="echoid-s11496" xml:space="preserve">Et permutando M H in H A ad quadratum. </s>
            <s xml:id="echoid-s11497" xml:space="preserve">
              <lb/>
            C m, ſeu ad quadratum ex ſumma ipſarum G M; </s>
            <s xml:id="echoid-s11498" xml:space="preserve">& </s>
            <s xml:id="echoid-s11499" xml:space="preserve">M H, ad quod
              <lb/>
            habet eandem proportionem quàm quadratum C A ad quadratum ſum-
              <lb/>
            mæ P Q, & </s>
            <s xml:id="echoid-s11500" xml:space="preserve">P R (17. </s>
            <s xml:id="echoid-s11501" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s11502" xml:space="preserve">habebit minorem proportionem, quàm
              <lb/>
            quadratum A H ad quadratum A C, ſeu quàm quadratum A C ad qua-
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            dratum ſummæ ipſarum A C, & </s>
            <s xml:id="echoid-s11503" xml:space="preserve">A F; </s>
            <s xml:id="echoid-s11504" xml:space="preserve">igitur ſumma ipſarum A C, & </s>
            <s xml:id="echoid-s11505" xml:space="preserve">
              <lb/>
            A F minor eſt quàm ſumma ipſarum P Q, & </s>
            <s xml:id="echoid-s11506" xml:space="preserve">P R. </s>
            <s xml:id="echoid-s11507" xml:space="preserve">Et quia M H maior
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            eſt quarta parte ſummæ ipſarum M G, & </s>
            <s xml:id="echoid-s11508" xml:space="preserve">M H; </s>
            <s xml:id="echoid-s11509" xml:space="preserve">ergo quadruplum C m
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            in M H maius eſt quadrato C m, & </s>
            <s xml:id="echoid-s11510" xml:space="preserve">ponatur V u æqualis A V; </s>
            <s xml:id="echoid-s11511" xml:space="preserve">igitur
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            quadruplũ V M in C m ad quadruplum M H in C m, ſcilicet V M ad
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            M H minorem proportionem habebit, quàm quadruplum V M in C m
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            ad quadratum C m: </s>
            <s xml:id="echoid-s11512" xml:space="preserve">& </s>
            <s xml:id="echoid-s11513" xml:space="preserve">componendo V H ad H M, nempe V H in H
              <lb/>
            A ad M H in H A minorem proportionem habebit, quàm V M in C m
              <lb/>
            quater ſumptum, vel u m in m C bis ſumptum cum quadrato C m (eo
              <lb/>
            quod u m dupla eſt ipſius V M quæ omnia ſimul ad idem quadratum C
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            m minorem proportionem habet, quàm quadratum C u. </s>
            <s xml:id="echoid-s11514" xml:space="preserve">Ergo V H in
              <lb/>
            H A ad quadratum C u, ſcilicet quadratum A C ad quadratum ſummæ
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            ipſarum S T, & </s>
            <s xml:id="echoid-s11515" xml:space="preserve">S Z (17. </s>
            <s xml:id="echoid-s11516" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s11517" xml:space="preserve">) minorem proportionem habet quàm
              <lb/>
            M H in H A ad quadratum C m, ſeu qnàm quadratum A C ad quadra-
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            tum ſummæ ipſarum P Q, P R (17. </s>
            <s xml:id="echoid-s11518" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s11519" xml:space="preserve">quapropter P Q, & </s>
            <s xml:id="echoid-s11520" xml:space="preserve">P R ſi-
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            mul ſumptæ minores ſunt, quàm S T, & </s>
            <s xml:id="echoid-s11521" xml:space="preserve">S Z ſimul ſumptæ.</s>
            <s xml:id="echoid-s11522" xml:space="preserve"/>
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        <div xml:id="echoid-div987" type="section" level="1" n="312">
          <head xml:id="echoid-head387" xml:space="preserve">PROPOSITIO XXXX.</head>
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            <s xml:id="echoid-s11523" xml:space="preserve">S It A C minor triente ipſius A F, erit A H minor dimidio
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            ipſius H G, & </s>
            <s xml:id="echoid-s11524" xml:space="preserve">ponatur M H æqualis dimidio H G, & </s>
            <s xml:id="echoid-s11525" xml:space="preserve">du-
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              <figure xlink:label="fig-0363-01" xlink:href="fig-0363-01a" number="431">
                <image file="0363-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0363-01"/>
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