Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
181 35
182
183 36
184
185 37
186
187 38
188
189 39
190
191 40
192
193 41
194
195 42
196
197 43
198
199 44
200
201 45
202
203 46
204
205 47
206
207
208
209
210
< >
page |< < (39) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div160" type="section" level="1" n="53">
          <p>
            <s xml:id="echoid-s2309" xml:space="preserve">
              <pb o="39" file="0089" n="89" rhead="DE IIS QVAE VEH. IN AQVA."/>
            _neæ autem a d inter ſe æquales ſunt. </s>
            <s xml:id="echoid-s2310" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s2311" xml:space="preserve">ipſæ a η, a θ. </s>
            <s xml:id="echoid-s2312" xml:space="preserve">Sed ſunt_
              <lb/>
            _æquales a o, a q: </s>
            <s xml:id="echoid-s2313" xml:space="preserve">& </s>
            <s xml:id="echoid-s2314" xml:space="preserve">earum dimidiæ a t a n. </s>
            <s xml:id="echoid-s2315" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s2316" xml:space="preserve">reliquæ t η, n θ_
              <lb/>
            _boc eſt p g, m y. </s>
            <s xml:id="echoid-s2317" xml:space="preserve">ut autem p g ad g h, ita m y ad y c; </s>
            <s xml:id="echoid-s2318" xml:space="preserve">& </s>
            <s xml:id="echoid-s2319" xml:space="preserve">permutan_
              <lb/>
              <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">34. primi</note>
            _do, ut p g ad m y, ita g s ad y c. </s>
            <s xml:id="echoid-s2320" xml:space="preserve">quare g s, y c æquales ſunt: </s>
            <s xml:id="echoid-s2321" xml:space="preserve">&_</s>
            <s xml:id="echoid-s2322" xml:space="preserve">
              <lb/>
            _ipſarum dimidiæ b s, b c: </s>
            <s xml:id="echoid-s2323" xml:space="preserve">ex quibus ſequitur ut & </s>
            <s xml:id="echoid-s2324" xml:space="preserve">reliquæ s r, c r_:
              <lb/>
            </s>
            <s xml:id="echoid-s2325" xml:space="preserve">_& </s>
            <s xml:id="echoid-s2326" xml:space="preserve">idcirco p z, m u & </s>
            <s xml:id="echoid-s2327" xml:space="preserve">u n, z t inter ſe ſunt æquales_.</s>
            <s xml:id="echoid-s2328" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2329" xml:space="preserve">Quoniam igitur m u minor eſt, quàm dupla u n.</s>
            <s xml:id="echoid-s2330" xml:space="preserve">] _Eſt_
              <lb/>
              <note position="right" xlink:label="note-0089-02" xlink:href="note-0089-02a" xml:space="preserve">L</note>
            _enim m h ipſius h n dupla, & </s>
            <s xml:id="echoid-s2331" xml:space="preserve">m u minor ipſa m h. </s>
            <s xml:id="echoid-s2332" xml:space="preserve">ergo m u minor_
              <lb/>
            _eſt, quàm dupla h n; </s>
            <s xml:id="echoid-s2333" xml:space="preserve">& </s>
            <s xml:id="echoid-s2334" xml:space="preserve">multo minor, quàm dupla ipſius u n_.</s>
            <s xml:id="echoid-s2335" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2336" xml:space="preserve">Non ergo manebit portio, ſed reuoluetur, ita ut baſis ip
              <lb/>
              <note position="right" xlink:label="note-0089-03" xlink:href="note-0089-03a" xml:space="preserve">M</note>
            ſius humidi ſuperſiciem nullo modo contingat. </s>
            <s xml:id="echoid-s2337" xml:space="preserve">quoniam
              <lb/>
            nunc in uno puncto contingens ſurſum fertur ex parte a.</s>
            <s xml:id="echoid-s2338" xml:space="preserve">]
              <lb/>
            _Tranſlatio ſic habet. </s>
            <s xml:id="echoid-s2339" xml:space="preserve">non ergo manet portio ſed inclinabitur, ut ba_-
              <lb/>
            _ſis ipſius nec ſecundum unum tang at ſuperficiem humidi, quoniam_
              <lb/>
            _nunc ſecundum unum tacta ipſa reclinatur. </s>
            <s xml:id="echoid-s2340" xml:space="preserve">Quæ nos ex alijs Ar_-
              <lb/>
            _chimedis locis, & </s>
            <s xml:id="echoid-s2341" xml:space="preserve">perſpicuitatis cauſſa in eum modum corrigenda_
              <lb/>
            _duximus. </s>
            <s xml:id="echoid-s2342" xml:space="preserve">In ſexta enim propoſitione huius ita ſcribit, ut habetur in_
              <lb/>
            _tranſlatione. </s>
            <s xml:id="echoid-s2343" xml:space="preserve">reuoluetur ergo ſolidum a p o l, & </s>
            <s xml:id="echoid-s2344" xml:space="preserve">baſis ipſius nó tan_
              <lb/>
            _get ſuperficiem humidi ſecundum unum ſignum. </s>
            <s xml:id="echoid-s2345" xml:space="preserve">Rurſus in ſeptima_
              <lb/>
            _propoſitione. </s>
            <s xml:id="echoid-s2346" xml:space="preserve">manifeſtum igitur, quòd reuoluetur ſolidum ita ut ba_-
              <lb/>
            _ſis ipſius nec ſecundum unum ſignum contingat ſuperficiem humidi_,
              <lb/>
            _quoniam nunc ſecundum unum tangens deorſum fertur ex parte l_.
              <lb/>
            </s>
            <s xml:id="echoid-s2347" xml:space="preserve">_At uero portionem ſurſum ferri ex parte a manifeſte constat. </s>
            <s xml:id="echoid-s2348" xml:space="preserve">nam_
              <lb/>
            _cumperpendicularis ad ſuperficiem humidi, quæ tranſit per ω ad_
              <lb/>
            _partes a cadat, & </s>
            <s xml:id="echoid-s2349" xml:space="preserve">quæ per e ad partes l, neceſſe eſt ut centrum ω_
              <lb/>
            _ſurſum, e uero deorſum feratur_.</s>
            <s xml:id="echoid-s2350" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2351" xml:space="preserve">Perſpicuum eſtigitur portionem conſiſtere ita, ut axis
              <lb/>
              <note position="right" xlink:label="note-0089-04" xlink:href="note-0089-04a" xml:space="preserve">N</note>
            cum ſuperficie humidi faciat angulum maiorem angu-
              <lb/>
            10 χ.</s>
            <s xml:id="echoid-s2352" xml:space="preserve">] _Iuncta enim a x producatur, ut diametrum b d ſe_-
              <lb/>
            _cet in λ, & </s>
            <s xml:id="echoid-s2353" xml:space="preserve">ab o puncto ipſi æquidistans ducatur o χ. </s>
            <s xml:id="echoid-s2354" xml:space="preserve">con_-
              <lb/>
            _tinget eaſectionem in o, ut in prima figura: </s>
            <s xml:id="echoid-s2355" xml:space="preserve">atque erit angu_-
              <lb/>
              <note position="right" xlink:label="note-0089-05" xlink:href="note-0089-05a" xml:space="preserve">29. primi</note>
            _lus ad χ angulo ad λ æqualis. </s>
            <s xml:id="echoid-s2356" xml:space="preserve">Sed angulus ad y æqualis est_
              <lb/>
            _angulo ad θ: </s>
            <s xml:id="echoid-s2357" xml:space="preserve">& </s>
            <s xml:id="echoid-s2358" xml:space="preserve">angulus a θ d maior angulo a λ d; </s>
            <s xml:id="echoid-s2359" xml:space="preserve">quod ex_-
              <lb/>
              <note position="right" xlink:label="note-0089-06" xlink:href="note-0089-06a" xml:space="preserve">16. primi</note>
            _traipſum cadat. </s>
            <s xml:id="echoid-s2360" xml:space="preserve">ergo angulus ad y eo, qui ad χ maior erit_.</s>
            <s xml:id="echoid-s2361" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum