Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

Page concordance

< >
Scan Original
11 11
12 12
13 13
14 14
15 15
16 16
17 17
18 18
19 19
20 20
21 21
22 22
23 23
24 24
25 25
26 26
27 27
28 28
29 29
30 30
31 31
32 32
33 33
34 34
35 35
36 36
37 37
38 38
39 39
40 40
< >
page |< < (17) of 197 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div78" type="section" level="1" n="66">
          <pb o="17" file="527.01.017" n="17" rhead="*DE STATICÆ* ELEMENTIS."/>
        </div>
        <div xml:id="echoid-div79" type="section" level="1" n="67">
          <head xml:id="echoid-head76" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s422" xml:space="preserve">Gravioris põderis A, in primo paradigma-
              <lb/>
              <figure xlink:label="fig-527.01.017-01" xlink:href="fig-527.01.017-01a" number="22">
                <image file="527.01.017-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.017-01"/>
              </figure>
            te, ea eſt ratio ad levius B, quę longioris radii
              <lb/>
            E D ad breviorem E C. </s>
            <s xml:id="echoid-s423" xml:space="preserve">E F itaque per 9
              <lb/>
            definitionem anſa erit. </s>
            <s xml:id="echoid-s424" xml:space="preserve">Reliquorum exem-
              <lb/>
            plorum eadem demonſtratio fuerit, quibus
              <lb/>
            brevitatis cauſa ſuperſedemus.</s>
            <s xml:id="echoid-s425" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s426" xml:space="preserve">*CONCLVSIO.</s>
            <s xml:id="echoid-s427" xml:space="preserve">* Cognitis igitur ponde-
              <lb/>
            ribus datis anſam illorum invenerimus.</s>
            <s xml:id="echoid-s428" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div81" type="section" level="1" n="68">
          <head xml:id="echoid-head77" xml:space="preserve">NOTATO.</head>
          <p style="it">
            <s xml:id="echoid-s429" xml:space="preserve">Si ad γ, 2 paradigmatis pondus, 1 ℔ adderetur, & </s>
            <s xml:id="echoid-s430" xml:space="preserve">ex V 1 ℔ ſuſpenderetur, at
              <lb/>
            hîc infra ponitur, ex antecedentibus manifeſtum
              <lb/>
              <figure xlink:label="fig-527.01.017-02" xlink:href="fig-527.01.017-02a" number="23">
                <image file="527.01.017-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.017-02"/>
              </figure>
            eſt X N anſam nibilo minus manere, & </s>
            <s xml:id="echoid-s431" xml:space="preserve">quæcung
              <lb/>
            ex ea dependĕt ſitu æquilibria eſſe. </s>
            <s xml:id="echoid-s432" xml:space="preserve">Idem N X ma-
              <lb/>
            nebit ſi Z 1 ℔ pendeat ex T, & </s>
            <s xml:id="echoid-s433" xml:space="preserve">γ 14 ℔ valeat;
              <lb/>
            </s>
            <s xml:id="echoid-s434" xml:space="preserve">aut Z 1 ℔ ex S, & </s>
            <s xml:id="echoid-s435" xml:space="preserve">γ ſit ℔ 15: </s>
            <s xml:id="echoid-s436" xml:space="preserve">itidem Z 1 ℔ ex
              <lb/>
            R, & </s>
            <s xml:id="echoid-s437" xml:space="preserve">γ ſit 16 ℔, aut ex P, & </s>
            <s xml:id="echoid-s438" xml:space="preserve">γ ſit 17 ℔. </s>
            <s xml:id="echoid-s439" xml:space="preserve">& </s>
            <s xml:id="echoid-s440" xml:space="preserve">
              <lb/>
            ita deinceps ſi jugum longius fuerit, perpetuo 1 ℔
              <lb/>
            ad γ addendo, pro longitudine cujus{q́ue} partis
              <lb/>
            æquantis X V, quò Z promovetur. </s>
            <s xml:id="echoid-s441" xml:space="preserve">Vnde quali-
              <lb/>
            tates & </s>
            <s xml:id="echoid-s442" xml:space="preserve">affectiones Stater æ cognoſcuntur, ut ple-
              <lb/>
            nius in Statices praxi tr actabitur.</s>
            <s xml:id="echoid-s443" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div83" type="section" level="1" n="69">
          <head xml:id="echoid-head78" xml:space="preserve">2 PROBLEMA. 3 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s444" xml:space="preserve">Datis ponderibus ſitu æquipondiis, altero cognito, al-
              <lb/>
            tero incognito, unà cum ansâ: </s>
            <s xml:id="echoid-s445" xml:space="preserve">incognitum cognitum
              <lb/>
            reddere.</s>
            <s xml:id="echoid-s446" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div84" type="section" level="1" n="70">
          <head xml:id="echoid-head79" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s447" xml:space="preserve">*DATVM.</s>
            <s xml:id="echoid-s448" xml:space="preserve">* A & </s>
            <s xml:id="echoid-s449" xml:space="preserve">B duo pondera ſitu æquipondia ſunto
              <lb/>
              <figure xlink:label="fig-527.01.017-03" xlink:href="fig-527.01.017-03a" number="24">
                <image file="527.01.017-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.017-03"/>
              </figure>
            quorum A ex C ſuſpenſum 3 ℔ pendeat, B verò ſuſpenſum
              <lb/>
            ex D ignorator, E F anſa. </s>
            <s xml:id="echoid-s450" xml:space="preserve">*QVAESITVM.</s>
            <s xml:id="echoid-s451" xml:space="preserve">* Pondus B
              <lb/>
            innoteſcat.</s>
            <s xml:id="echoid-s452" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div86" type="section" level="1" n="71">
          <head xml:id="echoid-head80" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s453" xml:space="preserve">In rationem radii E D ad radium E C inquirendum eſt,
              <lb/>
            ſit autem ex hypotheſi, ut 3 ad 1, dico igitur quemadmodum
              <lb/>
            E D 3, ad E C 1: </s>
            <s xml:id="echoid-s454" xml:space="preserve">ita & </s>
            <s xml:id="echoid-s455" xml:space="preserve">3 ℔ ad quem? </s>
            <s xml:id="echoid-s456" xml:space="preserve">proportione conclu-
              <lb/>
            ditur 1 ℔.</s>
            <s xml:id="echoid-s457" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div87" type="section" level="1" n="72">
          <head xml:id="echoid-head81" style="it" xml:space="preserve">2 Exemplum.</head>
          <p>
            <s xml:id="echoid-s458" xml:space="preserve">*DATVM.</s>
            <s xml:id="echoid-s459" xml:space="preserve">* Quemadmodum 2 propoſitionis 2 exemplo, columna A B C D
              <lb/>
            pro altero pondere 6 ℔ pendeat, reliquum pondus incognitũ, & </s>
            <s xml:id="echoid-s460" xml:space="preserve">inde ſuſpen-
              <lb/>
            ſum Y ſit, anſa autĕ X N. </s>
            <s xml:id="echoid-s461" xml:space="preserve">*QVAESITVM.</s>
            <s xml:id="echoid-s462" xml:space="preserve">* In põdus X inquirendũ nobis eſt.</s>
            <s xml:id="echoid-s463" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum