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

Page concordance

< >
Scan Original
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
41 41
42 42
43 43
44 44
45 45
46 46
47 47
48 48
49 49
50 50
< >
page |< < (46) of 197 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div216" type="section" level="1" n="157">
          <pb o="46" file="527.01.046" n="46" rhead="1 L*IBER* S*TATICÆ*"/>
        </div>
        <div xml:id="echoid-div218" type="section" level="1" n="158">
          <head xml:id="echoid-head170" xml:space="preserve">C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s1432" xml:space="preserve">Hinc facile iſtud deducitur. </s>
            <s xml:id="echoid-s1433" xml:space="preserve">Quò anguli ductariarum linearum unde pon-
              <lb/>
            dera ſuſpenſa ſunt, recto angulo proximiores ſunt: </s>
            <s xml:id="echoid-s1434" xml:space="preserve">eò ponderum por
              <unsure/>
            étias eſſe
              <lb/>
            majores. </s>
            <s xml:id="echoid-s1435" xml:space="preserve">Et contra, quo longius indidem, id eſt ab angulo recto diffident, po-
              <lb/>
            tentias eorundem eò quoque minores eſſe.</s>
            <s xml:id="echoid-s1436" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div219" type="section" level="1" n="159">
          <head xml:id="echoid-head171" xml:space="preserve">16 THEOREMA. 25 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1437" xml:space="preserve">Duæ annuentes lineæ, unde columna dependet,
              <note symbol="*" position="left" xlink:label="note-527.01.046-01" xlink:href="note-527.01.046-01a" xml:space="preserve">Inaæquali-
                <lb/>
              ter diftantes,
                <lb/>
              n
                <unsure/>
              on paral
                <unsure/>
              -
                <lb/>
              le@e
                <unsure/>
              .</note>
            nitùm continuatæ, in columnæ pendula gravitatis dia-
              <lb/>
            metro ſeſe interſecant.</s>
            <s xml:id="echoid-s1438" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div221" type="section" level="1" n="160">
          <head xml:id="echoid-head172" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1439" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1440" xml:space="preserve">AB columna, ex duabus lineis annuentibus C D, E F, depen-
              <lb/>
            deto, quæ in G & </s>
            <s xml:id="echoid-s1441" xml:space="preserve">H continuatæ, ſeſe inutuò in I ſecant.</s>
            <s xml:id="echoid-s1442" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1443" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1444" xml:space="preserve">Punctum I in columnæ A B pendulâ gravitatis diame-
              <lb/>
            tro eſſe, demonſtrandum eſt.</s>
            <s xml:id="echoid-s1445" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div222" type="section" level="1" n="161">
          <head xml:id="echoid-head173" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1446" xml:space="preserve">Anguli FEC, IEC, HEC unus idemq́;
              <lb/>
            </s>
            <s xml:id="echoid-s1447" xml:space="preserve">
              <figure xlink:label="fig-527.01.046-01" xlink:href="fig-527.01.046-01a" number="78">
                <image file="527.01.046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.046-01"/>
              </figure>
            eſt angulus; </s>
            <s xml:id="echoid-s1448" xml:space="preserve">idem de DCE, ICE, GCE
              <lb/>
            judicum eſto, ut quicunq; </s>
            <s xml:id="echoid-s1449" xml:space="preserve">punctus in rectis
              <lb/>
            HE, GF pro extremo ſumptus fuerit, co-
              <lb/>
            lumna, ex eo datum ſitum ſervet. </s>
            <s xml:id="echoid-s1450" xml:space="preserve">Eſto autern
              <unsure/>
              <lb/>
            I extremus punctus, utriuſque lineæ com-
              <lb/>
            munis, ex illo igitur columna ſitum ſuum
              <lb/>
            retinebit. </s>
            <s xml:id="echoid-s1451" xml:space="preserve">Atqui columnâ ex I dependente,
              <lb/>
            perpendicularis per I columnæ pendula
              <lb/>
            gravitatis diametris fuerit, in qua eſt I.</s>
            <s xml:id="echoid-s1452" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div224" type="section" level="1" n="162">
          <head xml:id="echoid-head174" xml:space="preserve">2 Exemplum.</head>
          <p>
            <s xml:id="echoid-s1453" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1454" xml:space="preserve">AB columna ex duabus lineis annuentibus CD, EF depen-
              <lb/>
            deto, continuatis in G, H uſque, mutuò ſe in I ſecantibus.</s>
            <s xml:id="echoid-s1455" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1456" xml:space="preserve">Q*VAESITVM* Punctum I in columnæ AB pendulâ gravitatis diame-
              <lb/>
            tro eſſe, demonſtrandum eſt.</s>
            <s xml:id="echoid-s1457" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div225" type="section" level="1" n="163">
          <head xml:id="echoid-head175" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1458" xml:space="preserve">DG, & </s>
            <s xml:id="echoid-s1459" xml:space="preserve">FH tibicines & </s>
            <s xml:id="echoid-s1460" xml:space="preserve">fulcra ſunto, vel
              <lb/>
              <figure xlink:label="fig-527.01.046-02" xlink:href="fig-527.01.046-02a" number="79">
                <image file="527.01.046-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.046-02"/>
              </figure>
            rigidæ & </s>
            <s xml:id="echoid-s1461" xml:space="preserve">inflexibiles lineæ, per 2 poſtulat.
              <lb/>
            </s>
            <s xml:id="echoid-s1462" xml:space="preserve">quibus columna ſuffulcitur; </s>
            <s xml:id="echoid-s1463" xml:space="preserve">quarũ potentiæ
              <lb/>
            æquales ſunt potétiis CD. </s>
            <s xml:id="echoid-s1464" xml:space="preserve">DF, ut enim iftę,
              <lb/>
            ita etiam illæ columnam in ſuo ſitu ſuſtinent. </s>
            <s xml:id="echoid-s1465" xml:space="preserve">
              <lb/>
            Et quodcun que punctum in illis extremum
              <lb/>
            nobis fuerit, illud columnam in ſuo ſitu ſer-
              <lb/>
            vaverit. </s>
            <s xml:id="echoid-s1466" xml:space="preserve">Eſto autem I extremus & </s>
            <s xml:id="echoid-s1467" xml:space="preserve">utriuſque
              <lb/>
            lineæ communis punctus; </s>
            <s xml:id="echoid-s1468" xml:space="preserve">ex iſto igitur co-
              <lb/>
            lumna (Mathematicè intelligas) datum ſi-
              <lb/>
            rum retinet, & </s>
            <s xml:id="echoid-s1469" xml:space="preserve">pendula gravitatis diametrus
              <lb/>
            per I fuerit, & </s>
            <s xml:id="echoid-s1470" xml:space="preserve">in eâ punctum I.</s>
            <s xml:id="echoid-s1471" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum