Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
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
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="73">
          <p>
            <s xml:space="preserve">
              <pb file="0132" n="132" rhead="FED. COMMANDINI"/>
            centrum z: </s>
            <s xml:space="preserve">parallelogram mi a d, θ: </s>
            <s xml:space="preserve">parallelogrammi f g, φ:
              <lb/>
            </s>
            <s xml:space="preserve">parallelogrammi d h, χ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="figure" xlink:label="fig-0132-01a" xlink:href="fig-0132-01"/>
            parallelogrammi c g centrũ
              <lb/>
            ψ: </s>
            <s xml:space="preserve">atque erit ω punctum me
              <lb/>
            dium uniuſcuiuſque axis, ui
              <lb/>
            delicet eius lineæ, quæ oppo
              <lb/>
            ſitorum planorũ centra con
              <lb/>
            iungit. </s>
            <s xml:space="preserve">Dico ω centrum effe
              <lb/>
            grauitatis ipſius ſolidi. </s>
            <s xml:space="preserve">eſt
              <lb/>
            enim, ut demonſtrauimus,
              <lb/>
              <anchor type="note" xlink:label="note-0132-01a" xlink:href="note-0132-01"/>
            ſolidi a f centrum grauitatis
              <lb/>
            in plano K n; </s>
            <s xml:space="preserve">quod oppoſi-
              <lb/>
            tis planis a d, g f æ quidiſtans
              <lb/>
            reliquorum planorum late-
              <lb/>
            ra biſariam diuidit: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">fimili
              <lb/>
            rationeidem centrum eſt in plano o r, æ quidiſtante planis
              <lb/>
            a e, b f oppo ſitis. </s>
            <s xml:space="preserve">ergo in communi ipſorum fectione: </s>
            <s xml:space="preserve">ui-
              <lb/>
            delicet in linea y z. </s>
            <s xml:space="preserve">Sed eſt etiam in plano t u, quod quidẽ
              <lb/>
            y z ſecat in ω. </s>
            <s xml:space="preserve">Conſtat igitur centrum grauitatis ſolidi eſſe
              <lb/>
            punctum ω, medium ſcilicet axium, hoc eſt linearum, quæ
              <lb/>
            planorum oppoſitorum centra coniungunt.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0132-01" xlink:href="fig-0132-01a">
              <image file="0132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0132-01"/>
            </figure>
            <note position="left" xlink:label="note-0132-01" xlink:href="note-0132-01a" xml:space="preserve">6. huius</note>
          </div>
          <p>
            <s xml:space="preserve">Sit aliud prima a f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in eo plana, quæ opponuntur, tri-
              <lb/>
            angula a b c, d e f: </s>
            <s xml:space="preserve">diuiſisq; </s>
            <s xml:space="preserve">bifariam parallelogrammorum
              <lb/>
            lateribus a d, b e, c f in punctis g h κ, per diuiſiones planũ
              <lb/>
            ducatur, quod oppoſitis planis æ quidiſtans faciet ſe ctionẽ
              <lb/>
            triangulum g h k æ quale, & </s>
            <s xml:space="preserve">ſimile ipſis a b c, d e f. </s>
            <s xml:space="preserve">Rurſus
              <lb/>
            diuidatur a b bifariam in l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta c l per ipſam, & </s>
            <s xml:space="preserve">per
              <lb/>
            c _K_ f planum ducatur priſma ſecans, cuius, & </s>
            <s xml:space="preserve">parallelogrã
              <lb/>
            mi a e communis ſcctio ſit l m n. </s>
            <s xml:space="preserve">diuidet pun ctum m li-
              <lb/>
            neam g h bifariam; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita n diuidet lineam d e: </s>
            <s xml:space="preserve">quoniam
              <lb/>
            triangula a c l, g k m, d f n æ qualia ſunt, & </s>
            <s xml:space="preserve">ſimilia, ut ſu pra
              <lb/>
              <anchor type="note" xlink:label="note-0132-02a" xlink:href="note-0132-02"/>
            demonſtrauimus. </s>
            <s xml:space="preserve">Iam ex iis, quæ tradita ſunt, conſtat cen
              <lb/>
            trum greuitatis priſmatis in plano g h k contineri. </s>
            <s xml:space="preserve">Dico
              <lb/>
            ipſum eſſe in linea k m. </s>
            <s xml:space="preserve">Si enim fieri poteſt, ſit o centrum;</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>