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 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div216" type="section" level="1" n="73">
          <p>
            <s xml:id="echoid-s3402" xml:space="preserve">
              <pb file="0134" n="134" rhead="FED. COMMANDINI"/>
            t u, x y ipſi g h æquidiſtare. </s>
            <s xml:id="echoid-s3403" xml:space="preserve">Et quoniam triangula, quæ
              <lb/>
            fiunt à lineis K y, y u, u s, s h æqualia ſuntinter ſe, & </s>
            <s xml:id="echoid-s3404" xml:space="preserve">ſimilia
              <lb/>
            triangulo K m h: </s>
            <s xml:id="echoid-s3405" xml:space="preserve">habebit triangulum K m h ad triangulũ
              <lb/>
              <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">19. ſexti</note>
            K δ y duplam proportionem eius, quæ eſt lineæ k h ad K y.
              <lb/>
            </s>
            <s xml:id="echoid-s3406" xml:space="preserve">ſed _K_ h poſita eſt quadrupla ipſius k y. </s>
            <s xml:id="echoid-s3407" xml:space="preserve">ergo triangulum
              <lb/>
            κ m h ad triangulum _K_ δ y eãdem proportionem habebit,
              <lb/>
            quam ſexdecim ad unũ & </s>
            <s xml:id="echoid-s3408" xml:space="preserve">ad quatuor triangula k δ y, y u,
              <lb/>
            u s, s α h habebit eandem, quam fexdecim ad quatuor, hoc
              <lb/>
            eſt quam h K ad κ y: </s>
            <s xml:id="echoid-s3409" xml:space="preserve">& </s>
            <s xml:id="echoid-s3410" xml:space="preserve">ſimiliter eandem habere demonſtra
              <lb/>
            bitur trian-
              <lb/>
              <figure xlink:label="fig-0134-01" xlink:href="fig-0134-01a" number="90">
                <image file="0134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0134-01"/>
              </figure>
            gulum κ m g
              <lb/>
            ad quatuor
              <lb/>
            triãgula K δ
              <lb/>
            x, x γ t, t β r,
              <lb/>
            r z g. </s>
            <s xml:id="echoid-s3411" xml:space="preserve">quare
              <lb/>
              <note position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">2. uel 121
                <lb/>
              quinti.</note>
            totum trian
              <lb/>
            gulum K g h
              <lb/>
            ad omnia tri
              <lb/>
            angula g z r,
              <lb/>
            r β t, t γ x, x δ
              <lb/>
            _K_, K δ y, y u,
              <lb/>
            u s, s α h ita
              <lb/>
            erit, ut h κ a d
              <lb/>
            k y, hoc eſt
              <lb/>
            ut h m ad m
              <lb/>
            q. </s>
            <s xml:id="echoid-s3412" xml:space="preserve">Si igitur in
              <lb/>
            triangulis a b c, d e f deſcribantur figuræ ſimiles ei, quæ de-
              <lb/>
            ſcripta eſt in g h K triangulo: </s>
            <s xml:id="echoid-s3413" xml:space="preserve">& </s>
            <s xml:id="echoid-s3414" xml:space="preserve">per lineas ſibi reſp onden-
              <lb/>
            tes plana ducantur: </s>
            <s xml:id="echoid-s3415" xml:space="preserve">totum priſma a f diuiſum eritin tria
              <lb/>
            ſolida parallelepipeda y γ, u β, s z, quorum baſes ſunt æ qua
              <lb/>
            les & </s>
            <s xml:id="echoid-s3416" xml:space="preserve">ſimiles ipſis parallelogrammis y γ, u β, s z: </s>
            <s xml:id="echoid-s3417" xml:space="preserve">& </s>
            <s xml:id="echoid-s3418" xml:space="preserve">in octo
              <lb/>
            priſmata g z r, r β t, t γ x, x δ K, κ δ y, y u, u s, s α h: </s>
            <s xml:id="echoid-s3419" xml:space="preserve">quorum
              <lb/>
            item baſes æquales, & </s>
            <s xml:id="echoid-s3420" xml:space="preserve">ſimiles ſunt dictis triangulis; </s>
            <s xml:id="echoid-s3421" xml:space="preserve">altitu-
              <lb/>
            do autem in omnibus, totius priſmatis altitudini æ qualis.</s>
            <s xml:id="echoid-s3422" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum