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 |< < (27) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div111" type="section" level="1" n="38">
          <p>
            <s xml:id="echoid-s1562" xml:space="preserve">
              <pb o="27" file="0065" n="65" rhead="DE IIS QVAE VEH. IN AQVA."/>
            æqualis r ψ: </s>
            <s xml:id="echoid-s1563" xml:space="preserve">& </s>
            <s xml:id="echoid-s1564" xml:space="preserve">ducatur ψ r perpendicularis ad b d, quæ
              <lb/>
            posſit dimidium eius, quod ipſis k r, ψ b, continetur. </s>
            <s xml:id="echoid-s1565" xml:space="preserve">Dico
              <lb/>
            portionem in humidum demiſſam adeo, ut baſis ipſius to-
              <lb/>
            ta ſit in humido, ita conſiſtere, ut axis cum ſuperficie humi
              <lb/>
            di faciat angulum angulo b æqualem. </s>
            <s xml:id="echoid-s1566" xml:space="preserve">Demittatur enim
              <lb/>
            portio in humidum, ſicuti dictum eſt; </s>
            <s xml:id="echoid-s1567" xml:space="preserve">& </s>
            <s xml:id="echoid-s1568" xml:space="preserve">axis cum humidi
              <lb/>
            ſuperficie non faciat angulum æqualẽ ipſi b, ſed primo ma
              <lb/>
            iorem: </s>
            <s xml:id="echoid-s1569" xml:space="preserve">ſecta autem ipſa plano per axem, recto ad ſuperfi-
              <lb/>
            ciem humidi, ſectio portionis ſit a p o l rectanguli coni ſe-
              <lb/>
            ctio; </s>
            <s xml:id="echoid-s1570" xml:space="preserve">ſuperficiei humidi ſectio c i; </s>
            <s xml:id="echoid-s1571" xml:space="preserve">ſitq, axis portionis, & </s>
            <s xml:id="echoid-s1572" xml:space="preserve">ſe
              <lb/>
            ctionis diameter n o, quæ fecetur in punctis ω t, ut prius. </s>
            <s xml:id="echoid-s1573" xml:space="preserve">& </s>
            <s xml:id="echoid-s1574" xml:space="preserve">
              <lb/>
            ducantur y p quidem ipſi ci æquidiſtans, contingensq; </s>
            <s xml:id="echoid-s1575" xml:space="preserve">ſe
              <lb/>
            ctionem in p; </s>
            <s xml:id="echoid-s1576" xml:space="preserve">m p uero æquidiſtans n o: </s>
            <s xml:id="echoid-s1577" xml:space="preserve">& </s>
            <s xml:id="echoid-s1578" xml:space="preserve">p s ad axem
              <lb/>
            perpendicularis. </s>
            <s xml:id="echoid-s1579" xml:space="preserve">Quoniam igitur axis portionis cum ſu-
              <lb/>
            perficie humidi facit angulum maiorem angulo b; </s>
            <s xml:id="echoid-s1580" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s1581" xml:space="preserve">
              <lb/>
            angulus s y p angulo b maior. </s>
            <s xml:id="echoid-s1582" xml:space="preserve">quare quadratum p s ad
              <lb/>
            quadratum s y maiorem habet proportionem, quàm qua
              <lb/>
            dratum ψ e ad quadratum ψ b: </s>
            <s xml:id="echoid-s1583" xml:space="preserve">& </s>
            <s xml:id="echoid-s1584" xml:space="preserve">propterea _K_ r ad s y ma
              <lb/>
              <note position="right" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">B</note>
            iorem habet, quàm dimidium ipſius κ r ad ψ b. </s>
            <s xml:id="echoid-s1585" xml:space="preserve">ergo s y
              <lb/>
            minor eſt, quam dupla ψ b; </s>
            <s xml:id="echoid-s1586" xml:space="preserve">& </s>
            <s xml:id="echoid-s1587" xml:space="preserve">s o minor, quam ψ b. </s>
            <s xml:id="echoid-s1588" xml:space="preserve">quare
              <lb/>
              <note position="right" xlink:label="note-0065-02" xlink:href="note-0065-02a" xml:space="preserve">C</note>
            s ω maior, quàm r ψ; </s>
            <s xml:id="echoid-s1589" xml:space="preserve">& </s>
            <s xml:id="echoid-s1590" xml:space="preserve">p h maior, quàm f. </s>
            <s xml:id="echoid-s1591" xml:space="preserve">Itaque quoniã
              <lb/>
            portio ad humidum in grauitate eam habet proportionẽ,
              <lb/>
              <note position="right" xlink:label="note-0065-03" xlink:href="note-0065-03a" xml:space="preserve">D</note>
            quam exceſſus, quo quadratum b d excedit quadratum f q
              <lb/>
            ad quadratum b d: </s>
            <s xml:id="echoid-s1592" xml:space="preserve">quam uero proportionem habet por-
              <lb/>
            tio ad humidum in grauitate, eandem pars ipſius demerſa
              <lb/>
            habet ad totam portionẽ: </s>
            <s xml:id="echoid-s1593" xml:space="preserve">ſequitur partẽ demerſam ad to
              <lb/>
            tam portionem, eam proportionem habere, quã exceſſus,
              <lb/>
            quo quadratum b d excedit quadratũ f q, ad quadratū b d.
              <lb/>
            </s>
            <s xml:id="echoid-s1594" xml:space="preserve">habebit ergo tota portio ad eam, quæ eſt extra humidum
              <lb/>
              <note position="right" xlink:label="note-0065-04" xlink:href="note-0065-04a" xml:space="preserve">E</note>
            proportionem eandem, quam quadratum b d ad quadra-
              <lb/>
            tum f q. </s>
            <s xml:id="echoid-s1595" xml:space="preserve">Sed quam proportionem habet tota portio ad eã,
              <lb/>
            quæ eſt extra humidum, eandem habet quadratum n o ad
              <lb/>
            quadratum p m. </s>
            <s xml:id="echoid-s1596" xml:space="preserve">ergo p m ipſi f q æ qualis etit. </s>
            <s xml:id="echoid-s1597" xml:space="preserve">demonſtra
              <lb/>
            ta eſt autem p h maior, quàm f: </s>
            <s xml:id="echoid-s1598" xml:space="preserve">quare m h minor </s>
          </p>
        </div>
      </text>
    </echo>