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 |< < (12) of 213 > >|
DE CENTRO GRA VIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="73">
          <p>
            <s xml:space="preserve">
              <pb o="12" file="0135" n="135" rhead="DE CENTRO GRA VIT. SOLID."/>
            Itaque ſolidi parallelepipedi y γ centrum grauitatis eſt in
              <lb/>
            linea δ: </s>
            <s xml:space="preserve">ſolidi u β centrum eſt in linea ε η: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſolidi s z in li
              <lb/>
            nea η m, quæ quidem lineæ axes ſunt, cum planorum oppo
              <lb/>
            ſitorum centra coniungant. </s>
            <s xml:space="preserve">ergo magnitudinis ex his ſoli
              <lb/>
            dis compoſitæ centrum grauitatis eſt in linea δ m, quod ſit
              <lb/>
            θ; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta θ o producatur: </s>
            <s xml:space="preserve">à puncto autem h ducatur h μ
              <lb/>
            ipſi m κ æquidiſtans, quæ cum θ o in μ conueniat. </s>
            <s xml:space="preserve">triangu
              <lb/>
            lum igitur g h κ ad omnia triangula g z r, r β t, t γ x, x δ k,
              <lb/>
            κ δ y, y u, u s, s α h eandem habet proportionem, quam h m
              <lb/>
            ad m q; </s>
            <s xml:space="preserve">hoc eſt, quam μ θ ad θ λ: </s>
            <s xml:space="preserve">nam ſi h m, μ θ produci in
              <lb/>
            telligantur, quouſque coeant; </s>
            <s xml:space="preserve">erit ob linearum q y, m k æ-
              <lb/>
            quidiſtantiam, ut h q ad q m, ita μ λ ad ad λ θ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">componen
              <lb/>
            do, ut h m ad m q, ita μ θ ad θ λ. </s>
            <s xml:space="preserve">linea uero θ o maior eſt,
              <lb/>
            quàm θ λ: </s>
            <s xml:space="preserve">habebit igitur μ θ ad θ λ maiorem proportio-
              <lb/>
              <anchor type="note" xlink:label="note-0135-01a" xlink:href="note-0135-01"/>
            nem, quàm ad θ o. </s>
            <s xml:space="preserve">quare triangulum etiam g h k ad omnia
              <lb/>
            iam dicta triangula maiorem proportionẽ habebit, quàm
              <lb/>
            μ θ ad θ o. </s>
            <s xml:space="preserve">ſed ut triangulũ g h k ad omnia triangula, ita to-
              <lb/>
            tũ priſma a f ad omnia priſmata g z r, r β t, t γ x, x δ k, k δ y,
              <lb/>
            y u, u s, s α h: </s>
            <s xml:space="preserve">quoniam enim ſolida parallelepipeda æque al
              <lb/>
            ta, eandem inter ſe proportionem habent, quam baſes; </s>
            <s xml:space="preserve">ut
              <lb/>
            ex trigeſimaſecunda undecimi elementorum conſtat. </s>
            <s xml:space="preserve">ſunt
              <lb/>
              <anchor type="note" xlink:label="note-0135-02a" xlink:href="note-0135-02"/>
            autem ſolida parallelepipeda priſmatum triangulares ba-
              <lb/>
            ſes habentium dupla: </s>
            <s xml:space="preserve">ſequitur, ut etiam huiuſmodi priſ-
              <lb/>
              <anchor type="note" xlink:label="note-0135-03a" xlink:href="note-0135-03"/>
            matainter ſe ſint, ſicut eorum baſes. </s>
            <s xml:space="preserve">ergo totum priſma ad
              <lb/>
            omnia priſmata maiorem proportionem habet, quam μ θ
              <lb/>
            ad θ o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuidendo ſolida parallelepipeda y γ, u β, s z ad o-
              <lb/>
              <anchor type="note" xlink:label="note-0135-04a" xlink:href="note-0135-04"/>
            mnia prifmata proportionem habent maiorem, quàm μ o
              <lb/>
            ad o θ. </s>
            <s xml:space="preserve">fiat @ o ad o θ, ut folida parallelepipeda y γ, u β, s z ad
              <lb/>
            omnia priſmata. </s>
            <s xml:space="preserve">Itaque cum à priſmate a f, cuius cẽtrum
              <lb/>
            grauitatis eſt o, auferatur magnitudo ex ſolidis parallelepi
              <lb/>
            pedis y γ, u β, s z conſtans: </s>
            <s xml:space="preserve">atque ipfius grauitatis centrum
              <lb/>
            ſit θ: </s>
            <s xml:space="preserve">reliquæ magnitudinis, quæ ex omnibus priſmatibus
              <lb/>
            conſtat, grauitatis centrum erit in linea θ o producta: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            in puncto ν, ex o ctaua propoſitione eiuſdem libri Archi-</s>
          </p>
        </div>
      </text>
    </echo>