Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
211
212
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div123" type="section" level="1" n="41">
          <p style="it">
            <s xml:id="echoid-s1761" xml:space="preserve">
              <pb file="0072" n="72" rhead="ARCHIMEDIS"/>
            quindecim ad quatuor; </s>
            <s xml:id="echoid-s1762" xml:space="preserve">& </s>
            <s xml:id="echoid-s1763" xml:space="preserve">ad eam, quæ uſque ad axem maiorem pro
              <lb/>
            portionem habeat: </s>
            <s xml:id="echoid-s1764" xml:space="preserve">erit quæ uſ que ad axem minor ipſa k c.</s>
            <s xml:id="echoid-s1765" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10. quinti</note>
          <p>
            <s xml:id="echoid-s1766" xml:space="preserve">Sit ei, quæ uſque ad axem æ qualis k r.</s>
            <s xml:id="echoid-s1767" xml:space="preserve">] _Hac nos addidimus,_
              <lb/>
              <note position="left" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">G</note>
            _quæ in translatione non erant._</s>
            <s xml:id="echoid-s1768" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1769" xml:space="preserve">_Eſt autem & </s>
            <s xml:id="echoid-s1770" xml:space="preserve">s b ſeſquialtera ipſius b r.</s>
            <s xml:id="echoid-s1771" xml:space="preserve">]_ Ponitur enim
              <lb/>
              <note position="left" xlink:label="note-0072-03" xlink:href="note-0072-03a" xml:space="preserve">H</note>
            d b ſeſquialtera ipſius b k; </s>
            <s xml:id="echoid-s1772" xml:space="preserve">itémq; </s>
            <s xml:id="echoid-s1773" xml:space="preserve">d ſ ſeſquialtera k r. </s>
            <s xml:id="echoid-s1774" xml:space="preserve">quare ut to
              <lb/>
            ta d b ad totam b K, ita pars d s ad partem K r. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s1776" xml:space="preserve">reliqua
              <lb/>
              <note position="left" xlink:label="note-0072-04" xlink:href="note-0072-04a" xml:space="preserve">19. quinti</note>
            s b ad reliquim b r, ut d b ad b k.</s>
            <s xml:id="echoid-s1777" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1778" xml:space="preserve">_Quæ ſimiles ſint portioni a b l.</s>
            <s xml:id="echoid-s1779" xml:space="preserve">]_ Similes portiones coni ſe-
              <lb/>
              <note position="left" xlink:label="note-0072-05" xlink:href="note-0072-05a" xml:space="preserve">K</note>
            ctionum Apollonius it. </s>
            <s xml:id="echoid-s1780" xml:space="preserve">i diffiniuit in ſexto libro conicorum, ut ſcri-
              <lb/>
            bit Eutocius, εν οἱς α χ θεισω
              <unsure/>
            νἐν ἑηάστω παραλλήλων τῆ βάσει, ἵσωι
              <lb/>
            τὸ πλῆθος, ὰι παρὰλληλοι, καὶ αἱ βάσ{ει}ς πρ
              <unsure/>
            ὸς τὰςἀποτεμνομένας
              <lb/>
            ἀπὸ τῶν διαμέ τρων ταῖς νορυφαῖς ἐν τοῖς αὐτοῖ ς λὄγοιςεἰσἰ, καὶἁι
              <lb/>
            ἀποτεμνόμεναι πρ
              <unsure/>
            ὸς τάς ἀποτεμνομένας; </s>
            <s xml:id="echoid-s1781" xml:space="preserve">hoc est. </s>
            <s xml:id="echoid-s1782" xml:space="preserve">in quibus ſi du-
              <lb/>
            cantnr lineæ æquidistantes baſi numero æquales: </s>
            <s xml:id="echoid-s1783" xml:space="preserve">æquidiſtantes atq;
              <lb/>
            </s>
            <s xml:id="echoid-s1784" xml:space="preserve">baſes ad partes diametrorum, quæ ab ipſis ad uerticem abſcindũtur,
              <lb/>
            eandem proportionem babent: </s>
            <s xml:id="echoid-s1785" xml:space="preserve">it émq; </s>
            <s xml:id="echoid-s1786" xml:space="preserve">partes abſciſſæ ad abſciſſas. </s>
            <s xml:id="echoid-s1787" xml:space="preserve">
              <lb/>
            ducuntur autem lineæ baſi æquidistantes: </s>
            <s xml:id="echoid-s1788" xml:space="preserve">ut opinor, deſcripta in ſin
              <lb/>
            gulis plane rectilinea figura, quæ lateribus numero æqualibus conti
              <lb/>
              <note position="left" xlink:label="note-0072-06" xlink:href="note-0072-06a" xml:space="preserve">γνωρίμως</note>
            neatur. </s>
            <s xml:id="echoid-s1789" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s1790" xml:space="preserve">portiones ſimiles à ſimilibus coni ſectionibus abſcindũ
              <lb/>
            tur: </s>
            <s xml:id="echoid-s1791" xml:space="preserve">& </s>
            <s xml:id="echoid-s1792" xml:space="preserve">earum diametri ſiue ad baſes rectæ, ſiue cum baſibus æ qua-
              <lb/>
            les angulos facientes, ad ipſas baſes eandem habent proportionem.</s>
            <s xml:id="echoid-s1793" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1794" xml:space="preserve">_Tranſibit igitur a e i coni ſectio per k.</s>
            <s xml:id="echoid-s1795" xml:space="preserve">]_ Sienim fieri po
              <lb/>
              <note position="left" xlink:label="note-0072-07" xlink:href="note-0072-07a" xml:space="preserve">L</note>
            teſt non tranſeat per k, ſed per aliud punctum lineæ d b, ut per u.
              <lb/>
            </s>
            <s xml:id="echoid-s1796" xml:space="preserve">Quoniam igitur in rectáguli coni ſectione a e i, cuius diameter e z,
              <lb/>
            ducta eſt a e, & </s>
            <s xml:id="echoid-s1797" xml:space="preserve">producta: </s>
            <s xml:id="echoid-s1798" xml:space="preserve">& </s>
            <s xml:id="echoid-s1799" xml:space="preserve">d b diametro æquidistans utraſque
              <lb/>
            a e, a i ſecat; </s>
            <s xml:id="echoid-s1800" xml:space="preserve">a e quidem in b, ai uero in d: </s>
            <s xml:id="echoid-s1801" xml:space="preserve">habebit d b ad b u
              <lb/>
            proportionem eandem, quam a z, ad z d, ex quarta propoſitione li
              <lb/>
            bri. </s>
            <s xml:id="echoid-s1802" xml:space="preserve">Archimedis de quadratura parabol
              <unsure/>
            æ. </s>
            <s xml:id="echoid-s1803" xml:space="preserve">Sed a z ſeſquialtera eſt
              <lb/>
            ipſius z d: </s>
            <s xml:id="echoid-s1804" xml:space="preserve">eſt enim ut tria ad duo, quod mox demonſtrabimus. </s>
            <s xml:id="echoid-s1805" xml:space="preserve">ergo
              <lb/>
            d b ſeſquialtera eſt ipſius b u. </s>
            <s xml:id="echoid-s1806" xml:space="preserve">eſt auté d b & </s>
            <s xml:id="echoid-s1807" xml:space="preserve">ipſius b k ſeſquialte
              <lb/>
            ra. </s>
            <s xml:id="echoid-s1808" xml:space="preserve">quare lineæ b u, b k inter ſe æ quales ſunt; </s>
            <s xml:id="echoid-s1809" xml:space="preserve">quod fieri non po-
              <lb/>
              <note position="left" xlink:label="note-0072-08" xlink:href="note-0072-08a" xml:space="preserve">2. quinti.</note>
            teſt. </s>
            <s xml:id="echoid-s1810" xml:space="preserve">restanguli igitur com ſectio a e i per punctum k tranſibit.
              <lb/>
            </s>
            <s xml:id="echoid-s1811" xml:space="preserve">quod demonstrare uolebamus.</s>
            <s xml:id="echoid-s1812" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum