Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
121 5
122
123 6
124
125 7
126
127 8
128
129 9
130
131 10
132
133 11
134
135 12
136
137 13
138
139 14
140
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
< >
page |< < 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-s2264" xml:space="preserve">
              <pb file="0088" n="88" rhead="ARCHIMEDIS"/>
            ductæ ſunt à baſibus ad portiones lineæ a n, a q, quæ angu
              <lb/>
            los æquales continent cum ipſis baſibus, eandem propor-
              <lb/>
            tionem habebit q a ad a n, quam l a ad a d.</s>
            <s xml:id="echoid-s2265" xml:space="preserve">] _Hoc nos ſu_-
              <lb/>
            _pra demonstrauimus_.</s>
            <s xml:id="echoid-s2266" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2267" xml:space="preserve">Aequalis eſt ergo a n ipſi n q.</s>
            <s xml:id="echoid-s2268" xml:space="preserve">] _Cum enim q a ad a n ſit_,
              <lb/>
              <note position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">F</note>
            _ut l a ad a d; </s>
            <s xml:id="echoid-s2269" xml:space="preserve">diuidendo, conuertendoq; </s>
            <s xml:id="echoid-s2270" xml:space="preserve">erit an ad n q, ut a d ad_
              <lb/>
            _d l. </s>
            <s xml:id="echoid-s2271" xml:space="preserve">eſt autem a d æqualis ipſi d l, quoniam d b ponitur diameter_
              <lb/>
            _portionis. </s>
            <s xml:id="echoid-s2272" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s2273" xml:space="preserve">a n ipſi n q eſt æqualis_.
              <lb/>
            </s>
            <s xml:id="echoid-s2274" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">14. quinti</note>
          <p>
            <s xml:id="echoid-s2275" xml:space="preserve">Et a q ipſi m y æquidiſtans.</s>
            <s xml:id="echoid-s2276" xml:space="preserve">] _Ex quinta ſecundi libri coni_-
              <lb/>
              <note position="left" xlink:label="note-0088-03" xlink:href="note-0088-03a" xml:space="preserve">G</note>
            _corum. </s>
            <s xml:id="echoid-s2277" xml:space="preserve">Apollonij_.</s>
            <s xml:id="echoid-s2278" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2279" xml:space="preserve">Etſecetur b d in punctis k r, ut dictum eſt.</s>
            <s xml:id="echoid-s2280" xml:space="preserve">] _In prima_
              <lb/>
              <note position="left" xlink:label="note-0088-04" xlink:href="note-0088-04a" xml:space="preserve">H</note>
            _parte huius propoſitionis. </s>
            <s xml:id="echoid-s2281" xml:space="preserve">ſecetur autem in K ita, ut b k ſit dupla ip_-
              <lb/>
            _ſius k d; </s>
            <s xml:id="echoid-s2282" xml:space="preserve">& </s>
            <s xml:id="echoid-s2283" xml:space="preserve">in r, ut K r ſit æqualis ei, quæ uſque ad axcm_.</s>
            <s xml:id="echoid-s2284" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2285" xml:space="preserve">Quòd cũ in portionibus æqualibus, & </s>
            <s xml:id="echoid-s2286" xml:space="preserve">ſimilibus, a p o l,
              <lb/>
              <note position="left" xlink:label="note-0088-05" xlink:href="note-0088-05a" xml:space="preserve">K</note>
            a m q l ab extremitatibus baſium ductæ ſint a o, a q, ita ut
              <lb/>
            portiones ablatæ faciant cum diametris angulos æquales:
              <lb/>
            </s>
            <s xml:id="echoid-s2287" xml:space="preserve">& </s>
            <s xml:id="echoid-s2288" xml:space="preserve">anguli, qui ad y g: </s>
            <s xml:id="echoid-s2289" xml:space="preserve">& </s>
            <s xml:id="echoid-s2290" xml:space="preserve">lineæ y b, g b inter ſe æquales erũt.</s>
            <s xml:id="echoid-s2291" xml:space="preserve">]
              <lb/>
            _Secet linea a q diametrum d b in θ, & </s>
            <s xml:id="echoid-s2292" xml:space="preserve">a o ſecet in η. </s>
            <s xml:id="echoid-s2293" xml:space="preserve">Itaque quo_-
              <lb/>
            _niam in portionibus æqualibus, & </s>
            <s xml:id="echoid-s2294" xml:space="preserve">ſimilibus a p o l, a m q l ab ex_-
              <lb/>
            _tremitatibus baſium_
              <lb/>
              <figure xlink:label="fig-0088-01" xlink:href="fig-0088-01a" number="54">
                <image file="0088-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0088-01"/>
              </figure>
            _ducũtur a o, a q, quæ_
              <lb/>
            _æquales angulos con_
              <lb/>
            _tinent cum ipſis baſi_
              <lb/>
            _bus: </s>
            <s xml:id="echoid-s2295" xml:space="preserve">& </s>
            <s xml:id="echoid-s2296" xml:space="preserve">anguli ad d_
              <lb/>
            _utrique ſunt recti_:
              <lb/>
            </s>
            <s xml:id="echoid-s2297" xml:space="preserve">_erũt & </s>
            <s xml:id="echoid-s2298" xml:space="preserve">reliqui a η d_,
              <lb/>
            _a θ d inter ſe æqua_-
              <lb/>
            _les. </s>
            <s xml:id="echoid-s2299" xml:space="preserve">linea autem p g_
              <lb/>
            _æquidiſtat lineæ a o_: </s>
            <s xml:id="echoid-s2300" xml:space="preserve">
              <lb/>
            _itémq; </s>
            <s xml:id="echoid-s2301" xml:space="preserve">m y ipſi a q_: </s>
            <s xml:id="echoid-s2302" xml:space="preserve">
              <lb/>
            _& </s>
            <s xml:id="echoid-s2303" xml:space="preserve">p s, m c ipſis a d_. </s>
            <s xml:id="echoid-s2304" xml:space="preserve">
              <lb/>
            _triágula igitur p g s_,
              <lb/>
            _m y c triãgulis a η d_
              <lb/>
            _a θ d, atque inter ſe_
              <lb/>
            _ſunt ſimilia: </s>
            <s xml:id="echoid-s2305" xml:space="preserve">& </s>
            <s xml:id="echoid-s2306" xml:space="preserve">ut a d ad a η, ita a d ad a θ: </s>
            <s xml:id="echoid-s2307" xml:space="preserve">& </s>
            <s xml:id="echoid-s2308" xml:space="preserve">permutando. </s>
            <s xml:id="echoid-s2309" xml:space="preserve">li_-
              <lb/>
              <note position="left" xlink:label="note-0088-06" xlink:href="note-0088-06a" xml:space="preserve">4. ſexti.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum