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

Table of contents

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[31.] DECLARATIO.
[32.] 13 DEFINITIO.
[33.] 14 DEFINITIO.
[34.] DECLARATIO.
[35.] NOTATO.
[36.] *POSTVLATA.*
[37.] 1 POSTVLATVM.
[38.] 2 POSTVLATVM.
[39.] 3 POSTVLATVM.
[40.] DECLARATIO.
[41.] 4 POSTVLATVM.
[42.] 5 POSTVLATVM.
[43.] DECLARATIO.
[44.] PARS ALTERA DE PROPOSITIONIBVS. 1 THE OREMA. I PROPOSITIO.
[45.] 1 Exemplum.
[46.] DEMONSTRATIO.
[47.] 2 Exemplum.
[48.] DEMONSTRATIO. 1 MEMBRVM.
[49.] 2 MEMBRVM.
[50.] 3 MEMBRVM.
[51.] 3 Exemplum.
[52.] C*ONSECTARIUM*.
[53.] 1 PROBLEMA. 2 PROPOSITIO.
[54.] 1 Exemplum.
[55.] PRAGMATIA.
[56.] 2 Exemplum.
[57.] *PRAGMATIA*.
[58.] 3 Exemplum.
[59.] *PRAGMATIA.*
[60.] *PRAGMATIA ALIVSMODI.*
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        <div xml:id="echoid-div42" type="section" level="1" n="40">
          <pb o="11" file="527.01.011" n="11" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
        </div>
        <div xml:id="echoid-div43" type="section" level="1" n="41">
          <head xml:id="echoid-head48" xml:space="preserve">4 POSTVLATVM.</head>
          <p>
            <s xml:id="echoid-s202" xml:space="preserve">Perplanum columnæ, quodillam per axis longitudi-
              <lb/>
            nem dividit, datam columnam intelligi.</s>
            <s xml:id="echoid-s203" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s204" xml:space="preserve">Vt AB columna eſto, & </s>
            <s xml:id="echoid-s205" xml:space="preserve">ejus axis CD plano
              <lb/>
              <figure xlink:label="fig-527.01.011-01" xlink:href="fig-527.01.011-01a" number="8">
                <image file="527.01.011-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.011-01"/>
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            aliquo, ut EFGH, per axem ſecta. </s>
            <s xml:id="echoid-s206" xml:space="preserve">plano EFGH
              <lb/>
            nominato, omiſſis cæteris omnibus, totam colum-
              <lb/>
            nam intelligi poſtulamus.</s>
            <s xml:id="echoid-s207" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div45" type="section" level="1" n="42">
          <head xml:id="echoid-head49" xml:space="preserve">5 POSTVLATVM.</head>
          <p>
            <s xml:id="echoid-s208" xml:space="preserve">Omnes perpendiculares parallelas haberi.</s>
            <s xml:id="echoid-s209" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div46" type="section" level="1" n="43">
          <head xml:id="echoid-head50" xml:space="preserve">DECLARATIO.</head>
          <p>
            <s xml:id="echoid-s210" xml:space="preserve">Cauſa ejuſmodi eſt. </s>
            <s xml:id="echoid-s211" xml:space="preserve">ABCD terræglobus eſto, cujus centrum E, horizon
              <lb/>
            AC, & </s>
            <s xml:id="echoid-s212" xml:space="preserve">FG jugum ad horizontem parallelum, ejusq́; </s>
            <s xml:id="echoid-s213" xml:space="preserve">æquales radii HF, HG,
              <lb/>
            exiisq́; </s>
            <s xml:id="echoid-s214" xml:space="preserve">æqualia põdera I, K ſuſpenſa; </s>
            <s xml:id="echoid-s215" xml:space="preserve">unde perpĕdiculares FI & </s>
            <s xml:id="echoid-s216" xml:space="preserve">GK parallelas
              <lb/>
            noneſſe manifeſtũ eſt quod inſeriora illarũ magis
              <lb/>
              <figure xlink:label="fig-527.01.011-02" xlink:href="fig-527.01.011-02a" number="9">
                <image file="527.01.011-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.011-02"/>
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            annuant, quam ſuperiora, neq; </s>
            <s xml:id="echoid-s217" xml:space="preserve">diſtent ubiq́ æqualiter.
              <lb/>
            </s>
            <s xml:id="echoid-s218" xml:space="preserve">Super ſtabili puncto H, jugũ FG moveatur,
              <lb/>
            ut G in locum L, F in M tranſeant, pondusq́ K
              <lb/>
            adſcĕdat in N, I vero deſcendat in O: </s>
            <s xml:id="echoid-s219" xml:space="preserve">& </s>
            <s xml:id="echoid-s220" xml:space="preserve">angulus
              <lb/>
            LME recto propior ſit, quam MLE; </s>
            <s xml:id="echoid-s221" xml:space="preserve">ex iſto ſitu
              <lb/>
            (ut è 24 propoſit. </s>
            <s xml:id="echoid-s222" xml:space="preserve">patebit) O quam N gravius
              <lb/>
            fuerit. </s>
            <s xml:id="echoid-s223" xml:space="preserve">Ex his conſequens eſft nullum corpus five
              <lb/>
            ſolidum in rerum Naturâ eſſe, ut Mathematicè
              <lb/>
            loquar, præter Globum, quod ex ſuæ gravitatis
              <lb/>
            centro cogitatione ſuſpenſum, quemlibet datum
              <lb/>
            ſitum retinet: </s>
            <s xml:id="echoid-s224" xml:space="preserve">five, per quod planum quodlibet
              <lb/>
            ipſum corpus in partes fitu æquipondias dividit, verum propter varios, & </s>
            <s xml:id="echoid-s225" xml:space="preserve">in-
              <lb/>
            finitos ſitus, varia etiam & </s>
            <s xml:id="echoid-s226" xml:space="preserve">infinita gravitatis centra erunt. </s>
            <s xml:id="echoid-s227" xml:space="preserve">Neque gravius pon-
              <lb/>
            dus (quod 1 propoſitioni repugnat) eam rationem haberet ad levius, quæ
              <lb/>
            longioris radii eſt ad breviorem, ſed unum altero ponderoſius eſſe ex ſitu ar-
              <lb/>
            gueretur, quod angulus ejus major & </s>
            <s xml:id="echoid-s228" xml:space="preserve">recto propior eſſet; </s>
            <s xml:id="echoid-s229" xml:space="preserve">qu i
              <unsure/>
            m alterius an-
              <lb/>
            gulus. </s>
            <s xml:id="echoid-s230" xml:space="preserve">Verumenimverò ut exemplo clarius fiat, AB bre-
              <lb/>
              <figure xlink:label="fig-527.01.011-03" xlink:href="fig-527.01.011-03a" number="10">
                <image file="527.01.011-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.011-03"/>
              </figure>
            vior radius eſto, ejusq́ue pondus C: </s>
            <s xml:id="echoid-s231" xml:space="preserve">AD vero longior, ex
              <lb/>
            eoque pondus E ſuſpenſum illam rationem habeto ad C;
              <lb/>
            </s>
            <s xml:id="echoid-s232" xml:space="preserve">quam AB ad AD, F autem univerſitatis centrum: </s>
            <s xml:id="echoid-s233" xml:space="preserve">ubi an-
              <lb/>
            gulus FBA hebetior, rectoq́ue propior eſſe apparet, quam
              <lb/>
            angulus ADE. </s>
            <s xml:id="echoid-s234" xml:space="preserve">Hinc (ex 24 propoſitionis ſententiâ) C pon-
              <lb/>
            deroſius eſſe, quam E, conſequens eſt.</s>
            <s xml:id="echoid-s235" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s236" xml:space="preserve">Hæc inconvenientia inde ſuntnata, quòd in primâ figurâ
              <lb/>
            FE & </s>
            <s xml:id="echoid-s237" xml:space="preserve">GE, in ſecundâ verò BF & </s>
            <s xml:id="echoid-s238" xml:space="preserve">DF parallelæ non ſint.
              <lb/>
            </s>
            <s xml:id="echoid-s239" xml:space="preserve">Verum, quandoquidem diſcrimen illud, in iis quæ ab homi-
              <lb/>
            nibus ponderantur, nullum, ſaltem inobſervabile eſt, jugum enim aliquot mi-
              <lb/>
            lia longum eſſe deberet, antequam deprehendi poſſet, perpendiculares paral-
              <lb/>
            lelas habendas eſſe concedi nobis poſtulamus. </s>
            <s xml:id="echoid-s240" xml:space="preserve">Verum equidem eſt, ex naturâ
              <lb/>
            fuâ illas æſtimantes, perfectè operari poſſeſecundum illarum ſpeciem, ſed quia
              <lb/>
            moleſtius illud eſſet, nec tamen ad remipſam, hoc eſt, *STATICES* praxin
              <lb/>
            utili
              <unsure/>
            us, ſuperſedere conſultius eſt.</s>
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