Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
171 30
172
173 31
174
175 32
176
177 33
178
179 34
180
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="65">
          <p>
            <s xml:space="preserve">
              <pb file="0120" n="120" rhead="FED. COMMANDINI"/>
            triangulum m k φ triangulo n k φ. </s>
            <s xml:space="preserve">ergo anguli l z k, o z k,
              <lb/>
            m φ k, n φ k æquales ſunt, ac recti. </s>
            <s xml:space="preserve">quòd cum etiam recti
              <lb/>
            ſint, qui ad k; </s>
            <s xml:space="preserve">æquidiſtabunt lineæ l o, m n axi b d. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita.
              <lb/>
            </s>
            <s xml:space="preserve">
              <anchor type="note" xlink:label="note-0120-01a" xlink:href="note-0120-01"/>
            demonſtrabuntur l m, o n ipſi a c æquidiſtare. </s>
            <s xml:space="preserve">Rurſus ſi
              <lb/>
            iungantur a l, l b, b m, m c, c n, n d, d o, o a: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">bifariam di
              <lb/>
            uidantur: </s>
            <s xml:space="preserve">à centro autem k ad diuiſiones ductæ lineæ pro-
              <lb/>
            trahantur uſque ad ſectionem in puncta p q r s t u x y: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">po
              <lb/>
            ſtremo p y, q x, r u, s t, q r, p s, y t, x u coniungantur. </s>
            <s xml:space="preserve">Simili-
              <lb/>
            ter oſtendemus lineas
              <lb/>
              <anchor type="figure" xlink:label="fig-0120-01a" xlink:href="fig-0120-01"/>
            p y, q x, r u, s t axi b d æ-
              <lb/>
            quidiſtantes eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">q r,
              <lb/>
            p s, y t, x u æquidiſtan-
              <lb/>
            tesipſi a c. </s>
            <s xml:space="preserve">Itaque dico
              <lb/>
            harum figurarum in el-
              <lb/>
            lipſi deſcriptarum cen-
              <lb/>
            trum grauitatis eſſe pũ-
              <lb/>
            ctum k, idem quod & </s>
            <s xml:space="preserve">el
              <lb/>
            lipſis centrum. </s>
            <s xml:space="preserve">quadri-
              <lb/>
            lateri enim a b c d cen-
              <lb/>
            trum eſt k, ex decima e-
              <lb/>
            iuſdem libri Archime-
              <lb/>
            dis, quippe cũ in eo om
              <lb/>
            nes diametri cõueniãt.
              <lb/>
            </s>
            <s xml:space="preserve">Sed in figura alb m c n
              <lb/>
              <anchor type="note" xlink:label="note-0120-02a" xlink:href="note-0120-02"/>
            d o, quoniam trianguli
              <lb/>
            alb centrum grauitatis
              <lb/>
              <anchor type="note" xlink:label="note-0120-03a" xlink:href="note-0120-03"/>
            eſt in linea l e: </s>
            <s xml:space="preserve">trapezijq́; </s>
            <s xml:space="preserve">a b m o centrum in linea e k: </s>
            <s xml:space="preserve">trape
              <lb/>
            zij o m c d in k g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">trianguli c n d in ipſa g n: </s>
            <s xml:space="preserve">erit magnitu
              <lb/>
            dinis ex his omnibus conſtantis, uidelicet totius figuræ cen
              <lb/>
            trum grauitatis in linea l n: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">o b eandem cauſſam in linea
              <lb/>
            o m. </s>
            <s xml:space="preserve">eſt enim trianguli a o d centrum in linea o h: </s>
            <s xml:space="preserve">trapezij
              <lb/>
            a l n d in h k: </s>
            <s xml:space="preserve">trapezij l b c n in k f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">trianguli b m c in fm.
              <lb/>
            </s>
            <s xml:space="preserve">cum ergo figuræ a l b m c n d o centrum grauitatis ſit in li-
              <lb/>
            nea l n, & </s>
            <s xml:space="preserve">in linea o m; </s>
            <s xml:space="preserve">erit centrum ipſius punctum k, in</s>
          </p>
        </div>
      </text>
    </echo>