Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s1210" xml:space="preserve">Producatur enim u s ad lineam qm in x: </s>
            <s xml:id="echoid-s1211" xml:space="preserve">& </s>
            <s xml:id="echoid-s1212" xml:space="preserve">à puncto x duca
              <lb/>
            tur ad diametrum x y ipſi bd æquidistans. </s>
            <s xml:id="echoid-s1213" xml:space="preserve">erit gt minor quàm
              <lb/>
            gy, quoniam u s minor eſt quàm ux: </s>
            <s xml:id="echoid-s1214" xml:space="preserve">& </s>
            <s xml:id="echoid-s1215" xml:space="preserve">ex primo lemmate yg
              <lb/>
            ad uc erit, ut h g ad n c; </s>
            <s xml:id="echoid-s1216" xml:space="preserve">uidelicet ut g b ad c k, quod proxime de
              <lb/>
            monstrauimus: </s>
            <s xml:id="echoid-s1217" xml:space="preserve">& </s>
            <s xml:id="echoid-s1218" xml:space="preserve">permutando yg ad gb, ut uc ad c k. </s>
            <s xml:id="echoid-s1219" xml:space="preserve">Sed t g
              <lb/>
            cum ſit ipſa y g minor, habet ad g b proportionem minorem, quàm
              <lb/>
            y g ad eandem. </s>
            <s xml:id="echoid-s1220" xml:space="preserve">ergo u c ad c K maiorem proportioné habet, quàm
              <lb/>
            t g ad g b. </s>
            <s xml:id="echoid-s1221" xml:space="preserve">quod demonstraſſe oportuit. </s>
            <s xml:id="echoid-s1222" xml:space="preserve">Itaque poſitione data g K
              <lb/>
            unum duntaxat erit in ſectione punctum, uidelicet m, à quo ductis
              <lb/>
            duabus lineis m e h, mno, habeat n c ad c K proportionem ean-
              <lb/>
            dem, quam h g ad g b. </s>
            <s xml:id="echoid-s1223" xml:space="preserve">nam ſi ab alijs omnibus ducantur, ſemper
              <lb/>
            ea, quæ inter a c, & </s>
            <s xml:id="echoid-s1224" xml:space="preserve">lineam ipſi æquidistantem interijcitur, ad c K
              <lb/>
            proportionem maiorem habebit, quàm quæ inter g K atque ei æqui
              <lb/>
            diſtantem, ad ipſam g b. </s>
            <s xml:id="echoid-s1225" xml:space="preserve">Conſtat igitur id, quod ab Archimede di-
              <lb/>
            ctum est; </s>
            <s xml:id="echoid-s1226" xml:space="preserve">nempe lineam pi ad p h uel eandem, quam n ω ad ω o,
              <lb/>
            uel maiorem habere proportionem.</s>
            <s xml:id="echoid-s1227" xml:space="preserve"/>
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            <s xml:id="echoid-s1228" xml:space="preserve">Quare p h ipſius h i aut dupla eſt, aut minor quàm du
              <lb/>
              <note position="right" xlink:label="note-0053-01" xlink:href="note-0053-01a" xml:space="preserve">D</note>
            pla.</s>
            <s xml:id="echoid-s1229" xml:space="preserve">] _Si quidé_
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            _minor, quàm du-_
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            _pla, ſit pt dupl. </s>
            <s xml:id="echoid-s1230" xml:space="preserve">2_
              <lb/>
            _ti. </s>
            <s xml:id="echoid-s1231" xml:space="preserve">erit centrum_
              <lb/>
            _grauitatis eius,_
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            _quod in humido_
              <lb/>
            _est, punctumt. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">ſi_
              <lb/>
            _uero p h ſit ip-_
              <lb/>
            _ſius h i dupla,_
              <lb/>
            _erit h grauitatis_
              <lb/>
            _centrum: </s>
            <s xml:id="echoid-s1233" xml:space="preserve">ductâq;_
              <lb/>
            </s>
            <s xml:id="echoid-s1234" xml:space="preserve">_h f, & </s>
            <s xml:id="echoid-s1235" xml:space="preserve">producta_
              <lb/>
            _ad centrum eius,_
              <lb/>
            _quod est extra humidum, uidelicct ad g, alia ſimiliter demonstra-_
              <lb/>
            _buntur. </s>
            <s xml:id="echoid-s1236" xml:space="preserve">atque idem intelligendum est in propoſitione, quæ ſe_-
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            _quitur._</s>
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            <s xml:id="echoid-s1238" xml:space="preserve">Reuoluetur ergo ſolidum a p o l, & </s>
            <s xml:id="echoid-s1239" xml:space="preserve">baſis ipſius nullo
              <lb/>
              <note position="right" xlink:label="note-0053-02" xlink:href="note-0053-02a" xml:space="preserve">E</note>
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Impressum