Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
< >
page |< < of 213 > >|
ARCHIMEDIS
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="53">
          <p>
            <s 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:space="preserve">] _Hoc nos ſu_-
              <lb/>
            _pra demonstrauimus_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="5">
            <note position="right" xlink:label="note-0087-08" xlink:href="note-0087-08a" xml:space="preserve">E</note>
          </div>
          <p>
            <s xml:space="preserve">Aequalis eſt ergo a n ipſi n q.</s>
            <s xml:space="preserve">] _Cum enim q a ad a n ſit_,
              <lb/>
              <anchor type="note" xlink:label="note-0088-01a" xlink:href="note-0088-01"/>
            _ut l a ad a d; </s>
            <s xml:space="preserve">diuidendo, conuertendoq; </s>
            <s xml:space="preserve">erit an ad n q, ut a d ad_
              <lb/>
            _d l. </s>
            <s xml:space="preserve">eſt autem a d æqualis ipſi d l, quoniam d b ponitur diameter_
              <lb/>
            _portionis. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">a n ipſi n q eſt æqualis_.
              <lb/>
            </s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="6">
            <note position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">F</note>
          </div>
          <note position="left" xml:space="preserve">14. quinti</note>
          <p>
            <s xml:space="preserve">Et a q ipſi m y æquidiſtans.</s>
            <s xml:space="preserve">] _Ex quinta ſecundi libri coni_-
              <lb/>
              <anchor type="note" xlink:label="note-0088-03a" xlink:href="note-0088-03"/>
            _corum. </s>
            <s xml:space="preserve">Apollonij_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="7">
            <note position="left" xlink:label="note-0088-03" xlink:href="note-0088-03a" xml:space="preserve">G</note>
          </div>
          <p>
            <s xml:space="preserve">Etſecetur b d in punctis k r, ut dictum eſt.</s>
            <s xml:space="preserve">] _In prima_
              <lb/>
              <anchor type="note" xlink:label="note-0088-04a" xlink:href="note-0088-04"/>
            _parte huius propoſitionis. </s>
            <s xml:space="preserve">ſecetur autem in K ita, ut b k ſit dupla ip_-
              <lb/>
            _ſius k d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in r, ut K r ſit æqualis ei, quæ uſque ad axcm_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="8">
            <note position="left" xlink:label="note-0088-04" xlink:href="note-0088-04a" xml:space="preserve">H</note>
          </div>
          <p>
            <s xml:space="preserve">Quòd cũ in portionibus æqualibus, & </s>
            <s xml:space="preserve">ſimilibus, a p o l,
              <lb/>
              <anchor type="note" xlink:label="note-0088-05a" xlink:href="note-0088-05"/>
            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:space="preserve">& </s>
            <s xml:space="preserve">anguli, qui ad y g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">lineæ y b, g b inter ſe æquales erũt.</s>
            <s xml:space="preserve">]
              <lb/>
            _Secet linea a q diametrum d b in θ, & </s>
            <s xml:space="preserve">a o ſecet in η. </s>
            <s xml:space="preserve">Itaque quo_-
              <lb/>
            _niam in portionibus æqualibus, & </s>
            <s xml:space="preserve">ſimilibus a p o l, a m q l ab ex_-
              <lb/>
            _tremitatibus baſium_
              <lb/>
              <anchor type="figure" xlink:label="fig-0088-01a" xlink:href="fig-0088-01"/>
            _ducũtur a o, a q, quæ_
              <lb/>
            _æquales angulos con_
              <lb/>
            _tinent cum ipſis baſi_
              <lb/>
            _bus: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">anguli ad d_
              <lb/>
            _utrique ſunt recti_:
              <lb/>
            </s>
            <s xml:space="preserve">_erũt & </s>
            <s xml:space="preserve">reliqui a η d_,
              <lb/>
            _a θ d inter ſe æqua_-
              <lb/>
            _les. </s>
            <s xml:space="preserve">linea autem p g_
              <lb/>
            _æquidiſtat lineæ a o_: </s>
            <s xml:space="preserve">
              <lb/>
            _itémq; </s>
            <s xml:space="preserve">m y ipſi a q_: </s>
            <s xml:space="preserve">
              <lb/>
            _& </s>
            <s xml:space="preserve">p s, m c ipſis a d_. </s>
            <s 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:space="preserve">& </s>
            <s xml:space="preserve">ut a d ad a η, ita a d ad a θ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando. </s>
            <s xml:space="preserve">li_-
              <lb/>
              <anchor type="note" xlink:label="note-0088-06a" xlink:href="note-0088-06"/>
            </s>
          </p>
        </div>
      </text>
    </echo>