Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
41 15
42
43 16
44
45 17
46
47 18
48
49 19
50
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
< >
page |< < (19) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div79" type="section" level="1" n="32">
          <p style="it">
            <s xml:id="echoid-s1083" xml:space="preserve">
              <pb o="19" file="0049" n="49" rhead="DE IIS QVAE VEH. IN AQVA."/>
            eam proportionem babebit, quam a f ad a e. </s>
            <s xml:id="echoid-s1084" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1085" xml:space="preserve">eandem habet
              <lb/>
            a s ad a r. </s>
            <s xml:id="echoid-s1086" xml:space="preserve">quare a s ipſi a x eſt æqualis, pars toti, quod fieri non
              <lb/>
              <note position="right" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve">9. quinti</note>
            poteſt. </s>
            <s xml:id="echoid-s1087" xml:space="preserve">Idem abſurdum ſequetur, ſi ponamus punctum t cadere ul-
              <lb/>
            tra lineam a c. </s>
            <s xml:id="echoid-s1088" xml:space="preserve">neceſſarium igitur est, ut in ipſam a c cadat. </s>
            <s xml:id="echoid-s1089" xml:space="preserve">quod
              <lb/>
            demonſtrandum propoſuimus.</s>
            <s xml:id="echoid-s1090" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div82" type="section" level="1" n="33">
          <head xml:id="echoid-head38" xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:id="echoid-s1091" xml:space="preserve">Sit parabole, cuius diameter a b: </s>
            <s xml:id="echoid-s1092" xml:space="preserve">atque eam cŏtingen
              <lb/>
            tes rectæ lineæ a c, b d; </s>
            <s xml:id="echoid-s1093" xml:space="preserve">a c quidem in puncto c, b d ue
              <lb/>
            ro in b: </s>
            <s xml:id="echoid-s1094" xml:space="preserve">& </s>
            <s xml:id="echoid-s1095" xml:space="preserve">per c ductis duabus lineis; </s>
            <s xml:id="echoid-s1096" xml:space="preserve">quarum alter a c e
              <lb/>
            diametro æquidiſtet, alter a c f æquidiſtet ipſi b d: </s>
            <s xml:id="echoid-s1097" xml:space="preserve">ſuma
              <lb/>
            tur quod uis punctum g in diametro: </s>
            <s xml:id="echoid-s1098" xml:space="preserve">fiatque ut f b, ad
              <lb/>
            b g, ita b g ad b h: </s>
            <s xml:id="echoid-s1099" xml:space="preserve">& </s>
            <s xml:id="echoid-s1100" xml:space="preserve">per g h ducantur g k l, h e m,
              <lb/>
            æquidiſtantes b d: </s>
            <s xml:id="echoid-s1101" xml:space="preserve">per m uero ducatur m n o ipſi a c
              <lb/>
            æquidistans, quæ diametrum ſecet in o: </s>
            <s xml:id="echoid-s1102" xml:space="preserve">& </s>
            <s xml:id="echoid-s1103" xml:space="preserve">per n ducta
              <lb/>
            n p uſque ad diametrum, ipſi b d æquidistet. </s>
            <s xml:id="echoid-s1104" xml:space="preserve">Dico h o
              <lb/>
            ipſius g b duplam eſſe.</s>
            <s xml:id="echoid-s1105" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1106" xml:space="preserve">V_EL_ igitur linea m n o ſccat diametrum in g, uel in alijs pun-
              <lb/>
            ctis: </s>
            <s xml:id="echoid-s1107" xml:space="preserve">& </s>
            <s xml:id="echoid-s1108" xml:space="preserve">ſi quidem ſecat in g, unum at que idem punctum duabus li-
              <lb/>
            teris go notabitur. </s>
            <s xml:id="echoid-s1109" xml:space="preserve">Itaque quoniam f c, p n, h e m ſibiipſis æqui
              <lb/>
            distant: </s>
            <s xml:id="echoid-s1110" xml:space="preserve">& </s>
            <s xml:id="echoid-s1111" xml:space="preserve">ipſi a c æquidiſtat m n o: </s>
            <s xml:id="echoid-s1112" xml:space="preserve">fient triangula a f c, o p n,
              <lb/>
            o h m inter ſe ſimilia. </s>
            <s xml:id="echoid-s1113" xml:space="preserve">quare erit o h ad h m, ut a f ad fc: </s>
            <s xml:id="echoid-s1114" xml:space="preserve">& </s>
            <s xml:id="echoid-s1115" xml:space="preserve">per-
              <lb/>
              <note position="right" xlink:label="note-0049-02" xlink:href="note-0049-02a" xml:space="preserve">4. ſexti.</note>
            mut ando o h ad a f, ut h m ad fc. </s>
            <s xml:id="echoid-s1116" xml:space="preserve">est autem quadratum h m ad
              <lb/>
            quadratum g l, ut linea h b ad lineam b g, ex uigeſima primi libri
              <lb/>
            conicorum: </s>
            <s xml:id="echoid-s1117" xml:space="preserve">& </s>
            <s xml:id="echoid-s1118" xml:space="preserve">quadratum g l ad quadratum fc, ut linea g b ad
              <lb/>
            ipſam b f: </s>
            <s xml:id="echoid-s1119" xml:space="preserve">ſuntq; </s>
            <s xml:id="echoid-s1120" xml:space="preserve">h b, b g, b f lineæ deinceps proportionales. </s>
            <s xml:id="echoid-s1121" xml:space="preserve">er-
              <lb/>
              <note position="right" xlink:label="note-0049-03" xlink:href="note-0049-03a" xml:space="preserve">22. ſexti.
                <lb/>
              cor. 20. ſe
                <lb/>
              xti.</note>
            go & </s>
            <s xml:id="echoid-s1122" xml:space="preserve">quadrata h m, g l, f c, & </s>
            <s xml:id="echoid-s1123" xml:space="preserve">ipſorum latera proportionalia
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s1124" xml:space="preserve">atque idcirco ut quadratum h m ad quadratum g l, ita </s>
          </p>
        </div>
      </text>
    </echo>
Impressum