Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
31 10
32
33 11
34
35 12
36
37 13
38
39 14
40
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
< >
page |< < of 213 > >|
ARCHIMEDIS
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="57">
          <p>
            <s xml:space="preserve">
              <pb file="0100" n="100" rhead="ARCHIMEDIS"/>
            quædam recta linea g i, ſectionibus a g q l, a x d interiecta,
              <lb/>
            & </s>
            <s xml:space="preserve">ipſi b d æquidiſtans; </s>
            <s xml:space="preserve">quæ mediam coni ſectionem in pun
              <lb/>
            cto h, & </s>
            <s xml:space="preserve">rectam
              <lb/>
              <anchor type="figure" xlink:label="fig-0100-01a" xlink:href="fig-0100-01"/>
            lineam r y in y
              <lb/>
            ſecet. </s>
            <s xml:space="preserve">demonſtra
              <lb/>
            bitur g h dupla
              <lb/>
            h i, quemadmo-
              <lb/>
            dum demonſtra
              <lb/>
            ta eſt o g ipſius
              <lb/>
            g x dupla. </s>
            <s xml:space="preserve">duca-
              <lb/>
            tur poſtea g ω cõ
              <lb/>
            tingens a g q l ſe
              <lb/>
            ctioneming: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            g c ad b d perpé
              <lb/>
            dicularis: </s>
            <s xml:space="preserve">iun-
              <lb/>
            ctaq; </s>
            <s xml:space="preserve">ai produ-
              <lb/>
            catur ad q. </s>
            <s xml:space="preserve">erit
              <lb/>
            ergo a i æqualis
              <lb/>
            i q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a q ipſi g ω
              <lb/>
            æquidiſtans. </s>
            <s xml:space="preserve">Demonſtrandũ eſt portionẽ in humidũ demiſ
              <lb/>
            fam, inclinatamq; </s>
            <s xml:space="preserve">adeo, ut baſis ipſius non cõtingat humi-
              <lb/>
            dũ, conſiſtere inclinatã ita, ut axis cum ſuperficie humidi
              <lb/>
            angulum faciat minorem angulo φ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">baſis humidi ſuper-
              <lb/>
            ficiem nullo modo contingat. </s>
            <s xml:space="preserve">Demittatur enim in humi-
              <lb/>
            dum; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">conſiſtat ita, ut baſis ipſius in uno puncto contin-
              <lb/>
            gat ſuperficiem humidi. </s>
            <s xml:space="preserve">ſecta autem portione per axem,
              <lb/>
            plano ad humidi ſuperficiem recto, ſit portionis ſectio a n
              <lb/>
            z l rectanguli coni ſectio: </s>
            <s xml:space="preserve">ſuperficiei humidi a z: </s>
            <s xml:space="preserve">axis autẽ
              <lb/>
            portionis, & </s>
            <s xml:space="preserve">ſectionis diameter b d: </s>
            <s xml:space="preserve">ſeceturq; </s>
            <s xml:space="preserve">b d in pun-
              <lb/>
            ctis _K_ r, ut ſuperius dictum eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ducatur n f quidem ipſi
              <lb/>
            a z æquidiſtans, & </s>
            <s xml:space="preserve">contingens coni ſectionem in pũcto n;
              <lb/>
            </s>
            <s xml:space="preserve">n t uero æquidiſtans ipſi b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">n s ad eandem perpendi-
              <lb/>
            cularis. </s>
            <s xml:space="preserve">Quoniam igitur portio ad humidum in grauitate,
              <lb/>
            cam habet proportionem, quam quadratum, quod fit à χ</s>
          </p>
        </div>
      </text>
    </echo>