Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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              <pb o="20" file="0051" n="51" rhead="DE IIS QVAE VEH. IN AQVA."/>
            pla. </s>
            <s xml:id="echoid-s1152" xml:space="preserve">ex quo fit ut pr, rh, fg inter ſe ſint æquales; </s>
            <s xml:id="echoid-s1153" xml:space="preserve">itémq; </s>
            <s xml:id="echoid-s1154" xml:space="preserve">æquales
              <lb/>
            rg, pf. </s>
            <s xml:id="echoid-s1155" xml:space="preserve">eſt enim pg utrique r p, gf communis. </s>
            <s xml:id="echoid-s1156" xml:space="preserve">Quoniam igitur
              <lb/>
            hb ad bg est, ut
              <lb/>
              <figure xlink:label="fig-0051-01" xlink:href="fig-0051-01a" number="31">
                <image file="0051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0051-01"/>
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            gb ad bf; </s>
            <s xml:id="echoid-s1157" xml:space="preserve">per c
              <gap/>
              <lb/>
            uerſionem ratio-
              <lb/>
            mis erit b h ad
              <lb/>
            h g, ut b g ad gf.
              <lb/>
            </s>
            <s xml:id="echoid-s1158" xml:space="preserve">eſt autem q h ad
              <lb/>
            h b, ut h o ad gb. </s>
            <s xml:id="echoid-s1159" xml:space="preserve">
              <lb/>
            nam ex 35 primi
              <lb/>
            libri conicorum,
              <lb/>
            cum linea qm có
              <lb/>
            tingat ſectionem
              <lb/>
            in punctom; </s>
            <s xml:id="echoid-s1160" xml:space="preserve">erút
              <lb/>
            h b, bq æquales; </s>
            <s xml:id="echoid-s1161" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s1162" xml:space="preserve">gh ipſius h b
              <lb/>
            dupla. </s>
            <s xml:id="echoid-s1163" xml:space="preserve">ergo ex æ-
              <lb/>
            quali q h ad hg,
              <lb/>
            ut ho ad g f; </s>
            <s xml:id="echoid-s1164" xml:space="preserve">hoc
              <lb/>
            eſt ad hr: </s>
            <s xml:id="echoid-s1165" xml:space="preserve">& </s>
            <s xml:id="echoid-s1166" xml:space="preserve">per
              <lb/>
            mutando q h ad
              <lb/>
            h o, ut g h ad h r. </s>
            <s xml:id="echoid-s1167" xml:space="preserve">
              <lb/>
            rurſus per conuerſionem rationis h q ad qo, ut h g ad g r; </s>
            <s xml:id="echoid-s1168" xml:space="preserve">hoc eſt
              <lb/>
            p f: </s>
            <s xml:id="echoid-s1169" xml:space="preserve">& </s>
            <s xml:id="echoid-s1170" xml:space="preserve">propterea ad ipſam cn, quod demonstrandum fuerat.</s>
            <s xml:id="echoid-s1171" xml:space="preserve"/>
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            <s xml:id="echoid-s1172" xml:space="preserve">His igitur explicatis, iam adid, quod propoſitum fue
              <lb/>
            rat, accedamus. </s>
            <s xml:id="echoid-s1173" xml:space="preserve">Itaque dico primum nc ad c k eandem
              <lb/>
            proportionem babere, quam h g ad g b.</s>
            <s xml:id="echoid-s1174" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1175" xml:space="preserve">Quoniam enim h q ad qo eſt, ut h g ad c n, hoc eſt ad a o ipſi
              <lb/>
            cn æqualem; </s>
            <s xml:id="echoid-s1176" xml:space="preserve">erit reliqua gq ad reliquam q a, ut h q ad q o: </s>
            <s xml:id="echoid-s1177" xml:space="preserve">& </s>
            <s xml:id="echoid-s1178" xml:space="preserve">
              <lb/>
            ob eam cauſſam lineæ a c g l productæ ex ijs, quæ ſupra demonſtra
              <lb/>
            uimus in linea q m conueniunt. </s>
            <s xml:id="echoid-s1179" xml:space="preserve">Rurſus gq ad qa eſt, ut h q </s>
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