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 |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div84" type="section" level="1" n="34">
          <p style="it">
            <s xml:id="echoid-s1179" xml:space="preserve">
              <pb file="0052" n="52" rhead="ARCHIMEDIS"/>
            q o; </s>
            <s xml:id="echoid-s1180" xml:space="preserve">uidelicet ut h g ad f p: </s>
            <s xml:id="echoid-s1181" xml:space="preserve">quod proxime demonſtr atum eſt. </s>
            <s xml:id="echoid-s1182" xml:space="preserve">At
              <lb/>
              <note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">2. lem:</note>
            ueroipſi g q æquales ſunt duæ lineæ ſimul ſumptæ qb, hoc eſt h b,
              <lb/>
              <note position="left" xlink:label="note-0052-02" xlink:href="note-0052-02a" xml:space="preserve">4. lem.</note>
            & </s>
            <s xml:id="echoid-s1183" xml:space="preserve">b g: </s>
            <s xml:id="echoid-s1184" xml:space="preserve">atque ipſi q a æqualis eſt h f. </s>
            <s xml:id="echoid-s1185" xml:space="preserve">Sienim ab æqualibus h b,
              <lb/>
            bq, æqualia fb,
              <lb/>
              <figure xlink:label="fig-0052-01" xlink:href="fig-0052-01a" number="32">
                <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0052-01"/>
              </figure>
            ba demantur, re
              <lb/>
            manentia æqua-
              <lb/>
            lia erunt. </s>
            <s xml:id="echoid-s1186" xml:space="preserve">ergo
              <lb/>
            dempta h g ex
              <lb/>
            duabus lineis h
              <lb/>
            b, h g, relinqui-
              <lb/>
            tur dupla ipſius
              <lb/>
            b g; </s>
            <s xml:id="echoid-s1187" xml:space="preserve">hoc eſt o h:
              <lb/>
            </s>
            <s xml:id="echoid-s1188" xml:space="preserve">& </s>
            <s xml:id="echoid-s1189" xml:space="preserve">dempta p f ex
              <lb/>
            f h, reliqua est
              <lb/>
            b p. </s>
            <s xml:id="echoid-s1190" xml:space="preserve">quare o h
              <lb/>
              <note position="left" xlink:label="note-0052-03" xlink:href="note-0052-03a" xml:space="preserve">19. quinti</note>
            ad h p, eſt ut g q
              <lb/>
            ad q a. </s>
            <s xml:id="echoid-s1191" xml:space="preserve">Sed ut
              <lb/>
            g q ad q a, ita
              <lb/>
            h q ad q o; </s>
            <s xml:id="echoid-s1192" xml:space="preserve">hoc
              <lb/>
            eſt h g ad n c:
              <lb/>
            </s>
            <s xml:id="echoid-s1193" xml:space="preserve">& </s>
            <s xml:id="echoid-s1194" xml:space="preserve">ut o h ad h p,
              <lb/>
              <note position="left" xlink:label="note-0052-04" xlink:href="note-0052-04a" xml:space="preserve">15. quin-
                <lb/>
              ti.</note>
            ita g b ad c k. </s>
            <s xml:id="echoid-s1195" xml:space="preserve">eſt
              <lb/>
            cnim o h dupla
              <lb/>
            g b, & </s>
            <s xml:id="echoid-s1196" xml:space="preserve">h p item
              <lb/>
            dupla gf; </s>
            <s xml:id="echoid-s1197" xml:space="preserve">hoc eſt
              <lb/>
            c k. </s>
            <s xml:id="echoid-s1198" xml:space="preserve">eandem igitur proportionem habet h g ad n c, qnam g b ad
              <lb/>
            c k: </s>
            <s xml:id="echoid-s1199" xml:space="preserve">& </s>
            <s xml:id="echoid-s1200" xml:space="preserve">permutando n c ad c k eandem habet, quam b g ad g b.</s>
            <s xml:id="echoid-s1201" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1202" xml:space="preserve">Sumatur deinde aliud quod uis punctum in ſectum in ſectione,
              <lb/>
            quod ſit s: </s>
            <s xml:id="echoid-s1203" xml:space="preserve">& </s>
            <s xml:id="echoid-s1204" xml:space="preserve">per s duæ lineæ ducantur: </s>
            <s xml:id="echoid-s1205" xml:space="preserve">st quidem
              <lb/>
            æquidistans ipſi db, diametrumque in puncto t ſecans;
              <lb/>
            </s>
            <s xml:id="echoid-s1206" xml:space="preserve">s u uero æquidistans ac, & </s>
            <s xml:id="echoid-s1207" xml:space="preserve">ſecans c e in u. </s>
            <s xml:id="echoid-s1208" xml:space="preserve">Dico u c
              <lb/>
            ad ck maiorem proportionem habere, quamtg ad gb.</s>
            <s xml:id="echoid-s1209" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>