Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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              <pb file="0052" n="52" rhead="ARCHIMEDIS"/>
            q o; </s>
            <s xml:id="echoid-s1180" xml:space="preserve">uidelicet ut h g ad f p: </s>
            <s xml:id="echoid-s1181" xml:space="preserve">quod proxime demonſtr atum eſt. </s>
            <s xml:id="echoid-s1182" xml:space="preserve">At
              <lb/>
              <note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">2. lem:</note>
            ueroipſi g q æquales ſunt duæ lineæ ſimul ſumptæ qb, hoc eſt h b,
              <lb/>
              <note position="left" xlink:label="note-0052-02" xlink:href="note-0052-02a" xml:space="preserve">4. lem.</note>
            & </s>
            <s xml:id="echoid-s1183" xml:space="preserve">b g: </s>
            <s xml:id="echoid-s1184" xml:space="preserve">atque ipſi q a æqualis eſt h f. </s>
            <s xml:id="echoid-s1185" xml:space="preserve">Sienim ab æqualibus h b,
              <lb/>
            bq, æqualia fb,
              <lb/>
              <figure xlink:label="fig-0052-01" xlink:href="fig-0052-01a" number="32">
                <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0052-01"/>
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            ba demantur, re
              <lb/>
            manentia æqua-
              <lb/>
            lia erunt. </s>
            <s xml:id="echoid-s1186" xml:space="preserve">ergo
              <lb/>
            dempta h g ex
              <lb/>
            duabus lineis h
              <lb/>
            b, h g, relinqui-
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            tur dupla ipſius
              <lb/>
            b g; </s>
            <s xml:id="echoid-s1187" xml:space="preserve">hoc eſt o h:
              <lb/>
            </s>
            <s xml:id="echoid-s1188" xml:space="preserve">& </s>
            <s xml:id="echoid-s1189" xml:space="preserve">dempta p f ex
              <lb/>
            f h, reliqua est
              <lb/>
            b p. </s>
            <s xml:id="echoid-s1190" xml:space="preserve">quare o h
              <lb/>
              <note position="left" xlink:label="note-0052-03" xlink:href="note-0052-03a" xml:space="preserve">19. quinti</note>
            ad h p, eſt ut g q
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            ad q a. </s>
            <s xml:id="echoid-s1191" xml:space="preserve">Sed ut
              <lb/>
            g q ad q a, ita
              <lb/>
            h q ad q o; </s>
            <s xml:id="echoid-s1192" xml:space="preserve">hoc
              <lb/>
            eſt h g ad n c:
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            </s>
            <s xml:id="echoid-s1193" xml:space="preserve">& </s>
            <s xml:id="echoid-s1194" xml:space="preserve">ut o h ad h p,
              <lb/>
              <note position="left" xlink:label="note-0052-04" xlink:href="note-0052-04a" xml:space="preserve">15. quin-
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              ti.</note>
            ita g b ad c k. </s>
            <s xml:id="echoid-s1195" xml:space="preserve">eſt
              <lb/>
            cnim o h dupla
              <lb/>
            g b, & </s>
            <s xml:id="echoid-s1196" xml:space="preserve">h p item
              <lb/>
            dupla gf; </s>
            <s xml:id="echoid-s1197" xml:space="preserve">hoc eſt
              <lb/>
            c k. </s>
            <s xml:id="echoid-s1198" xml:space="preserve">eandem igitur proportionem habet h g ad n c, qnam g b ad
              <lb/>
            c k: </s>
            <s xml:id="echoid-s1199" xml:space="preserve">& </s>
            <s xml:id="echoid-s1200" xml:space="preserve">permutando n c ad c k eandem habet, quam b g ad g b.</s>
            <s xml:id="echoid-s1201" xml:space="preserve"/>
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            <s xml:id="echoid-s1202" xml:space="preserve">Sumatur deinde aliud quod uis punctum in ſectum in ſectione,
              <lb/>
            quod ſit s: </s>
            <s xml:id="echoid-s1203" xml:space="preserve">& </s>
            <s xml:id="echoid-s1204" xml:space="preserve">per s duæ lineæ ducantur: </s>
            <s xml:id="echoid-s1205" xml:space="preserve">st quidem
              <lb/>
            æquidistans ipſi db, diametrumque in puncto t ſecans;
              <lb/>
            </s>
            <s xml:id="echoid-s1206" xml:space="preserve">s u uero æquidistans ac, & </s>
            <s xml:id="echoid-s1207" xml:space="preserve">ſecans c e in u. </s>
            <s xml:id="echoid-s1208" xml:space="preserve">Dico u c
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            ad ck maiorem proportionem habere, quamtg ad gb.</s>
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