Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
161 25
162
163 26
164
165 27
166
167 28
168
169 29
170
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="69">
          <pb file="0126" n="126" rhead="FED. COMMANDINI"/>
          <p>
            <s xml:space="preserve">Itaque quoniam duæ lineæ K l, l m ſe ſe tangentes, duabus
              <lb/>
            lineis ſe ſe tangentibus a b, b c æquidiſtant; </s>
            <s xml:space="preserve">nec ſunt in eo-
              <lb/>
            dem plano: </s>
            <s xml:space="preserve">angulus
              <emph style="sc">K</emph>
            l m æqualis eſt angulo a b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita an
              <lb/>
              <anchor type="note" xlink:label="note-0126-01a" xlink:href="note-0126-01"/>
            gulus l m
              <emph style="sc">K</emph>
            , angulo b c a, & </s>
            <s xml:space="preserve">m
              <emph style="sc">K</emph>
            lipſi c a b æqualis prob abi
              <lb/>
            tur. </s>
            <s xml:space="preserve">triangulum ergo
              <emph style="sc">K</emph>
            l m eſt æquale, & </s>
            <s xml:space="preserve">ſimile triang ulo
              <lb/>
            a b c. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">triangulo d e f. </s>
            <s xml:space="preserve">Ducatur linea c g o, & </s>
            <s xml:space="preserve">per ip
              <lb/>
            ſam, & </s>
            <s xml:space="preserve">per c f ducatur planum ſecans priſma, cuius & </s>
            <s xml:space="preserve">paral
              <lb/>
            lelogrammi a e communis ſectio ſit o p q. </s>
            <s xml:space="preserve">tranſibit linea
              <lb/>
            f q per h, & </s>
            <s xml:space="preserve">m p per n. </s>
            <s xml:space="preserve">nam cum plana æquidiſtantia ſecen
              <lb/>
            tur à plano c q, communes eorum ſectiones c g o, m p, f q
              <lb/>
            ſibi ipſis æquidiſtabunt. </s>
            <s xml:space="preserve">Sed & </s>
            <s xml:space="preserve">æquidiſtant a b,
              <emph style="sc">K</emph>
            l, d e. </s>
            <s xml:space="preserve">an-
              <lb/>
            guli ergo a o c,
              <emph style="sc">K</emph>
            p m, d q f inter ſe æquales ſunt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſunt
              <lb/>
              <anchor type="note" xlink:label="note-0126-02a" xlink:href="note-0126-02"/>
            æquales qui ad puncta a k d conſtituuntur. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">reliqui
              <lb/>
            reliquis æquales; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangula a c o, _K_ m p, d f q inter ſe ſimi
              <lb/>
            lia erunt. </s>
            <s xml:space="preserve">Vtigitur ca ad a o, ita fd ad d q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando
              <lb/>
              <anchor type="note" xlink:label="note-0126-03a" xlink:href="note-0126-03"/>
            ut c a ad fd, ita a o ad d q. </s>
            <s xml:space="preserve">eſt autem c a æqualis fd. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">
              <lb/>
            a o ipſi d q. </s>
            <s xml:space="preserve">eadem quoque ratione & </s>
            <s xml:space="preserve">a o ipſi _K_ p æqualis
              <lb/>
            demonſtrabitur. </s>
            <s xml:space="preserve">Itaque ſi triangula, a b c, d e f æqualia & </s>
            <s xml:space="preserve">
              <lb/>
            ſimilia inter ſe aptétur,
              <lb/>
              <anchor type="figure" xlink:label="fig-0126-01a" xlink:href="fig-0126-01"/>
            cadet linea f q in lineam
              <lb/>
            c g o. </s>
            <s xml:space="preserve">Sed & </s>
            <s xml:space="preserve">centrũ gra
              <lb/>
              <anchor type="note" xlink:label="note-0126-04a" xlink:href="note-0126-04"/>
            uitatis h in g centrũ ca-
              <lb/>
            det. </s>
            <s xml:space="preserve">trãſibit igitur linea
              <lb/>
            f q per h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">planum per
              <lb/>
            c o & </s>
            <s xml:space="preserve">c f ductũ per axẽ
              <lb/>
            g h ducetur: </s>
            <s xml:space="preserve">idcircoq; </s>
            <s xml:space="preserve">li
              <lb/>
            neam m p etiã per n trã
              <lb/>
            ſire neceſſe erit. </s>
            <s xml:space="preserve">Quo-
              <lb/>
            niam ergo ſh, c g æqua-
              <lb/>
            les ſunt, & </s>
            <s xml:space="preserve">æquidiſtãtes:
              <lb/>
            </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">h q, g o; </s>
            <s xml:space="preserve">rectæ li-
              <lb/>
            neæ, quæ ipſas cónectũt
              <lb/>
            c m f, g n h, o p q æqua-
              <lb/>
            les & </s>
            <s xml:space="preserve">æquidiſtãtes erũt.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>