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

Page concordance

< >
Scan Original
1
2 2
3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
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
< >
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