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 |< < (22) of 197 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div112" type="section" level="1" n="90">
          <p style="it">
            <s xml:id="echoid-s621" xml:space="preserve">
              <pb o="22" file="527.01.022" n="22" rhead="*I* L*IBER* S*TATICÆ*"/>
            fuerit, experientia testabitur, cujus rei cauſa è 6, 7, 8 propoſitionibus mani-
              <lb/>
            festa eſt.</s>
            <s xml:id="echoid-s622" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div114" type="section" level="1" n="91">
          <head xml:id="echoid-head100" xml:space="preserve">5 THEOREMA. 9 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s623" xml:space="preserve">Anſa infinitum cõtinuata binorum ponderum jugum
              <lb/>
            quodvis in ſuos radios ſecat.</s>
            <s xml:id="echoid-s624" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s625" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s626" xml:space="preserve">* A, B duo pondera ſunto, C D & </s>
            <s xml:id="echoid-s627" xml:space="preserve">E F eorum diametri. </s>
            <s xml:id="echoid-s628" xml:space="preserve">& </s>
            <s xml:id="echoid-s629" xml:space="preserve">ju-
              <lb/>
            gum CE, anſa denique G H, ita ut C G ſit ad G E, ut pondus B ad A.
              <lb/>
            </s>
            <s xml:id="echoid-s630" xml:space="preserve">Eſto & </s>
            <s xml:id="echoid-s631" xml:space="preserve">I K jugum inæqualiter à C E diſtans, & </s>
            <s xml:id="echoid-s632" xml:space="preserve">G H infinitum continuator
              <lb/>
            L verſus ſecans jugum I K in M. </s>
            <s xml:id="echoid-s633" xml:space="preserve">Q*VAESITVM.</s>
            <s xml:id="echoid-s634" xml:space="preserve">* Demonſtrandum nobis
              <lb/>
            eſt I M & </s>
            <s xml:id="echoid-s635" xml:space="preserve">M K etiam radios eſſe ponderum A, B. </s>
            <s xml:id="echoid-s636" xml:space="preserve">id eſt, ut B ad A: </s>
            <s xml:id="echoid-s637" xml:space="preserve">ſic etiam
              <lb/>
            M I eſſe ad M K.</s>
            <s xml:id="echoid-s638" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s639" xml:space="preserve">P*RAEPARATIO.</s>
            <s xml:id="echoid-s640" xml:space="preserve">* C N ducaturad I K parallela, ſe-
              <lb/>
            cans H L in O.</s>
            <s xml:id="echoid-s641" xml:space="preserve"/>
          </p>
          <figure number="33">
            <image file="527.01.022-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.022-01"/>
          </figure>
        </div>
        <div xml:id="echoid-div115" type="section" level="1" n="92">
          <head xml:id="echoid-head101" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s642" xml:space="preserve">Quemadmodum C G ad G E: </s>
            <s xml:id="echoid-s643" xml:space="preserve">ita C O ad O N. </s>
            <s xml:id="echoid-s644" xml:space="preserve">Atqui
              <lb/>
            C O æquatur I M, & </s>
            <s xml:id="echoid-s645" xml:space="preserve">N O ipſi M K, quapropter ut C G
              <lb/>
            ad G E: </s>
            <s xml:id="echoid-s646" xml:space="preserve">ita I M ad M K. </s>
            <s xml:id="echoid-s647" xml:space="preserve">Atqui ut B ad A: </s>
            <s xml:id="echoid-s648" xml:space="preserve">ita ex con-
              <lb/>
            ceſſo C G ad G E, ideoq́ue ut B ad A: </s>
            <s xml:id="echoid-s649" xml:space="preserve">ita M I ad M K:
              <lb/>
            </s>
            <s xml:id="echoid-s650" xml:space="preserve">eadem cujuſvis jugi demonſtratio eſt lineis C D & </s>
            <s xml:id="echoid-s651" xml:space="preserve">E F ter-
              <lb/>
            minati, ut P Q ſecti in R, & </s>
            <s xml:id="echoid-s652" xml:space="preserve">quæcunque alia lineari poſſuntinter dictos ter-
              <lb/>
            minos. </s>
            <s xml:id="echoid-s653" xml:space="preserve">C*ONCLUSIO.</s>
            <s xml:id="echoid-s654" xml:space="preserve">* Anſa in infinitum cõtinuata ſecat quodvis jugum
              <lb/>
            in ſuos radios, quod nobis demonſtrandum fuit.</s>
            <s xml:id="echoid-s655" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div116" type="section" level="1" n="93">
          <head xml:id="echoid-head102" xml:space="preserve">1 C*ONSECTARIUM.*</head>
          <p>
            <s xml:id="echoid-s656" xml:space="preserve">Hinc conſequens eſt, ut duorum ponderum pendula gravitatis diametros
              <lb/>
            inveniatur, non neceſſe eſſe ut jugum horizonti ſit parallelum. </s>
            <s xml:id="echoid-s657" xml:space="preserve">Verum quoli-
              <lb/>
            bet modo ſitum iſti uſui ſufficere.</s>
            <s xml:id="echoid-s658" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div117" type="section" level="1" n="94">
          <head xml:id="echoid-head103" xml:space="preserve">2 C*ONSECTARIUM.*</head>
          <p>
            <s xml:id="echoid-s659" xml:space="preserve">Quandoquidé centrum gravitatis in pendulâ gravitatis diametro eſt, quam-
              <lb/>
            libet rectam inter duo gravitatis centra terminatam, etiam ponderum jugum
              <lb/>
            eſſe cõſequens eſt, & </s>
            <s xml:id="echoid-s660" xml:space="preserve">radiorum jugi diſcriminationem gravitatis centrum eſſe
              <lb/>
            amborum ponderum.</s>
            <s xml:id="echoid-s661" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div118" type="section" level="1" n="95">
          <head xml:id="echoid-head104" xml:space="preserve">5 PROBLEMA. 10 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s662" xml:space="preserve">Datis, firmitudinis puncto notæ columnæ, notisque
              <lb/>
            ponderibus ſitu æquipondiis inde dependentibus: </s>
            <s xml:id="echoid-s663" xml:space="preserve">inveni-
              <lb/>
            rian axis parallelus futurus eſt horizonti; </s>
            <s xml:id="echoid-s664" xml:space="preserve">an quem dede-
              <lb/>
            ris ſitum fervaturus: </s>
            <s xml:id="echoid-s665" xml:space="preserve">an verò ſe inverſurus, donec gravita-
              <lb/>
            tis centrum in pendul à gravitatis diametro ſit.</s>
            <s xml:id="echoid-s666" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s667" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s668" xml:space="preserve">* A B C D columna eſto 4 ℔, fecta per gravitatis centrum E. </s>
            <s xml:id="echoid-s669" xml:space="preserve">pla-
              <lb/>
            no F G ad baſin A D parallelo, H firmitudinis punctum inſra centrum </s>
          </p>
        </div>
      </text>
    </echo>
Impressum