Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
< >
page |< < of 213 > >|
ARCHIMEDIS
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="41">
          <p style="it">
            <s xml:space="preserve">
              <pb file="0072" n="72" rhead="ARCHIMEDIS"/>
            quindecim ad quatuor; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ad eam, quæ uſque ad axem maiorem pro
              <lb/>
            portionem habeat: </s>
            <s xml:space="preserve">erit quæ uſ que ad axem minor ipſa k c.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="6">
            <note position="right" xlink:label="note-0071-07" xlink:href="note-0071-07a" xml:space="preserve">F</note>
          </div>
          <note position="left" xml:space="preserve">10. quinti</note>
          <p>
            <s xml:space="preserve">Sit ei, quæ uſque ad axem æ qualis k r.</s>
            <s xml:space="preserve">] _Hac nos addidimus,_
              <lb/>
              <anchor type="note" xlink:label="note-0072-02a" xlink:href="note-0072-02"/>
            _quæ in translatione non erant._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="7">
            <note position="left" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">G</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Eſt autem & </s>
            <s xml:space="preserve">s b ſeſquialtera ipſius b r.</s>
            <s xml:space="preserve">]_ Ponitur enim
              <lb/>
              <anchor type="note" xlink:label="note-0072-03a" xlink:href="note-0072-03"/>
            d b ſeſquialtera ipſius b k; </s>
            <s xml:space="preserve">itémq; </s>
            <s xml:space="preserve">d ſ ſeſquialtera k r. </s>
            <s 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:space="preserve">ergo & </s>
            <s xml:space="preserve">reliqua
              <lb/>
              <anchor type="note" xlink:label="note-0072-04a" xlink:href="note-0072-04"/>
            s b ad reliquim b r, ut d b ad b k.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="8">
            <note position="left" xlink:label="note-0072-03" xlink:href="note-0072-03a" xml:space="preserve">H</note>
            <note position="left" xlink:label="note-0072-04" xlink:href="note-0072-04a" xml:space="preserve">19. quinti</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Quæ ſimiles ſint portioni a b l.</s>
            <s xml:space="preserve">]_ Similes portiones coni ſe-
              <lb/>
              <anchor type="note" xlink:label="note-0072-05a" xlink:href="note-0072-05"/>
            ctionum Apollonius it. </s>
            <s 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:space="preserve">hoc est. </s>
            <s xml:space="preserve">in quibus ſi du-
              <lb/>
            cantnr lineæ æquidistantes baſi numero æquales: </s>
            <s xml:space="preserve">æquidiſtantes atq;
              <lb/>
            </s>
            <s xml:space="preserve">baſes ad partes diametrorum, quæ ab ipſis ad uerticem abſcindũtur,
              <lb/>
            eandem proportionem babent: </s>
            <s xml:space="preserve">it émq; </s>
            <s xml:space="preserve">partes abſciſſæ ad abſciſſas. </s>
            <s xml:space="preserve">
              <lb/>
            ducuntur autem lineæ baſi æquidistantes: </s>
            <s xml:space="preserve">ut opinor, deſcripta in ſin
              <lb/>
            gulis plane rectilinea figura, quæ lateribus numero æqualibus conti
              <lb/>
              <anchor type="note" xlink:label="note-0072-06a" xlink:href="note-0072-06"/>
            neatur. </s>
            <s xml:space="preserve">Itaq; </s>
            <s xml:space="preserve">portiones ſimiles à ſimilibus coni ſectionibus abſcindũ
              <lb/>
            tur: </s>
            <s xml:space="preserve">& </s>
            <s 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:space="preserve"/>
          </p>
          <div type="float" level="2" n="9">
            <note position="left" xlink:label="note-0072-05" xlink:href="note-0072-05a" xml:space="preserve">K</note>
            <note position="left" xlink:label="note-0072-06" xlink:href="note-0072-06a" xml:space="preserve">γνωρίμως</note>
          </div>
          <p style="it">
            <s xml:space="preserve">_Tranſibit igitur a e i coni ſectio per k.</s>
            <s xml:space="preserve">]_ Sienim fieri po
              <lb/>
              <anchor type="note" xlink:label="note-0072-07a" xlink:href="note-0072-07"/>
            teſt non tranſeat per k, ſed per aliud punctum lineæ d b, ut per u.
              <lb/>
            </s>
            <s xml:space="preserve">Quoniam igitur in rectáguli coni ſectione a e i, cuius diameter e z,
              <lb/>
            ducta eſt a e, & </s>
            <s xml:space="preserve">producta: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">d b diametro æquidistans utraſque
              <lb/>
            a e, a i ſecat; </s>
            <s xml:space="preserve">a e quidem in b, ai uero in d: </s>
            <s 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:space="preserve">Archimedis de quadratura parabol
              <unsure/>
            æ. </s>
            <s xml:space="preserve">Sed a z ſeſquialtera eſt
              <lb/>
            ipſius z d: </s>
            <s xml:space="preserve">eſt enim ut tria ad duo, quod mox demonſtrabimus. </s>
            <s xml:space="preserve">ergo
              <lb/>
            d b ſeſquialtera eſt ipſius b u. </s>
            <s xml:space="preserve">eſt auté d b & </s>
            <s xml:space="preserve">ipſius b k ſeſquialte
              <lb/>
            ra. </s>
            <s xml:space="preserve">quare lineæ b u, b k inter ſe æ quales ſunt; </s>
            <s xml:space="preserve">quod fieri non po-
              <lb/>
              <anchor type="note" xlink:label="note-0072-08a" xlink:href="note-0072-08"/>
            teſt. </s>
            <s xml:space="preserve">restanguli igitur com ſectio a e i per punctum k tranſibit.
              <lb/>
            </s>
            <s xml:space="preserve">quod demonstrare uolebamus.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="10">
            <note position="left" xlink:label="note-0072-07" xlink:href="note-0072-07a" xml:space="preserve">L</note>
            <note position="left" xlink:label="note-0072-08" xlink:href="note-0072-08a" xml:space="preserve">2. quinti.</note>
          </div>
        </div>
      </text>
    </echo>