Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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              <pb file="0050" n="50" rhead="ARCHIMEDIS"/>
            nea h m ad li-
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            neam fc. </s>
            <s xml:id="echoid-s1125" xml:space="preserve">at uero
              <lb/>
            ut h m ad f c, ita
              <lb/>
            o h ad a f: </s>
            <s xml:id="echoid-s1126" xml:space="preserve">& </s>
            <s xml:id="echoid-s1127" xml:space="preserve">ut
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            quadratum h m
              <lb/>
            ad quadratú g l,
              <lb/>
            ita linea h b ad
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            b g; </s>
            <s xml:id="echoid-s1128" xml:space="preserve">hoc est b g
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            ad b f. </s>
            <s xml:id="echoid-s1129" xml:space="preserve">ex quibus
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            ſequitur o h ad
              <lb/>
            a f ita eſſe, ut b g
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            ad b f: </s>
            <s xml:id="echoid-s1130" xml:space="preserve">& </s>
            <s xml:id="echoid-s1131" xml:space="preserve">permu
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            tando oh ad b g,
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            ut a f ad f b. </s>
            <s xml:id="echoid-s1132" xml:space="preserve">ſed
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            eſt a f dupla ip-
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            ſius fb: </s>
            <s xml:id="echoid-s1133" xml:space="preserve">ſunt eni
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            a b, b f æquales
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            ex 35 primi libri
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            conicorum. </s>
            <s xml:id="echoid-s1134" xml:space="preserve">ergo
              <lb/>
            & </s>
            <s xml:id="echoid-s1135" xml:space="preserve">h o ipſius g b
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            eſt dupla. </s>
            <s xml:id="echoid-s1136" xml:space="preserve">quod demonſtrare oportebat.</s>
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          <head xml:id="echoid-head39" xml:space="preserve">LEMMA IIII.</head>
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            <s xml:id="echoid-s1138" xml:space="preserve">Iiſdem manentibus, & </s>
            <s xml:id="echoid-s1139" xml:space="preserve">à puncto m ducta m q uſque
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            ad diametrum, quæ ſectionem in puncto m conting at;
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            <s xml:id="echoid-s1140" xml:space="preserve">Dico h q ad q o eandem proportionem habere, quam
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            habet g h ad c n.</s>
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            <s xml:id="echoid-s1142" xml:space="preserve">F_IAT_ enim h r æqualis g f. </s>
            <s xml:id="echoid-s1143" xml:space="preserve">& </s>
            <s xml:id="echoid-s1144" xml:space="preserve">cumtriangula a f c, o p n ſimi
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            lia ſint, & </s>
            <s xml:id="echoid-s1145" xml:space="preserve">p n ſit æqualis f c; </s>
            <s xml:id="echoid-s1146" xml:space="preserve">eodem modo demonſtrabimus p o, f a
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            inter ſe æquales eſſe. </s>
            <s xml:id="echoid-s1147" xml:space="preserve">quare p o ipſius f b dupla erit. </s>
            <s xml:id="echoid-s1148" xml:space="preserve">Sed eſt h o du
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            pla g b. </s>
            <s xml:id="echoid-s1149" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s1150" xml:space="preserve">reliqua p h reliquæ f g; </s>
            <s xml:id="echoid-s1151" xml:space="preserve">uidelicet ipſius r h eſt </s>
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