Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of handwritten notes

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            <s xml:id="echoid-s1151" xml:space="preserve">
              <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
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            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
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            hb ad bg est, ut
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              <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/>
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            uerſionem ratio-
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            mis erit b h ad
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            h g, ut b g ad gf.
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            </s>
            <s xml:id="echoid-s1158" xml:space="preserve">eſt autem q h ad
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            h b, ut h o ad gb. </s>
            <s xml:id="echoid-s1159" xml:space="preserve">
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            nam ex 35 primi
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            libri conicorum,
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            cum linea qm có
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            tingat ſectionem
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            in punctom; </s>
            <s xml:id="echoid-s1160" xml:space="preserve">erút
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            h b, bq æquales; </s>
            <s xml:id="echoid-s1161" xml:space="preserve">
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            & </s>
            <s xml:id="echoid-s1162" xml:space="preserve">gh ipſius h b
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            dupla. </s>
            <s xml:id="echoid-s1163" xml:space="preserve">ergo ex æ-
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            quali q h ad hg,
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            ut ho ad g f; </s>
            <s xml:id="echoid-s1164" xml:space="preserve">hoc
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            eſt ad hr: </s>
            <s xml:id="echoid-s1165" xml:space="preserve">& </s>
            <s xml:id="echoid-s1166" xml:space="preserve">per
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            mutando q h ad
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            h o, ut g h ad h r. </s>
            <s xml:id="echoid-s1167" xml:space="preserve">
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            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
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            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
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            rat, accedamus. </s>
            <s xml:id="echoid-s1173" xml:space="preserve">Itaque dico primum nc ad c k eandem
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            proportionem babere, quam h g ad g b.</s>
            <s xml:id="echoid-s1174" xml:space="preserve"/>
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            <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
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            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">
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            ob eam cauſſam lineæ a c g l productæ ex ijs, quæ ſupra demonſtra
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            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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