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

Table of contents

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[161.] DEMONSTRATIO.
Page: 46 (46)
[162.] 2 Exemplum.
Page: 46 (46)
[163.] DEMONSTRATIO.
Page: 46 (46)
[164.] 3 Exemplum.
Page: 47 (47)
[165.] DEMONSTRATIO.
Page: 47 (47)
[166.] 4 Exemplum.
Page: 47 (47)
[167.] DEMONSTRATIO.
Page: 47 (47)
[168.] 17 THEOREMA. 26 PROPOSITIO.
Page: 47 (47)
[169.] DEMONSTRATIO.
Page: 48 (48)
[170.] 18 PROBLEMA. 27 PROPOSITIO.
Page: 48 (48)
[171.] DEMONSTRATIO.
Page: 49 (49)
[172.] C*ONSECTARIUM*.
Page: 49 (49)
[173.] NOTATO.
Page: 49 (49)
[174.] 19 THEOREMA. 28 PROPOSITIO.
Page: 49 (49)
[175.] DEMONSTRATIO.
Page: 50 (50)
[176.] C*ONSECTARIUM*.
Page: 51 (51)
[177.] FINIS LIBRI PRIMI.
Page: 51 (51)
[178.] STATICES LIBER SECVNDVS QVI EST DE INVENIENDO GRAVITATIS CENTRO.
Page: 53
[179.] DE INVENIENDO GRAVITATIS CENTRO IN PLANIS, PARS PRIOR.
Page: 56 (56)
[180.] 1 THEOREMA. 1 PROPOSITIO.
Page: 56 (56)
[181.] 1 Exemplum.
Page: 56 (56)
[182.] DEMONSTRATIO.
Page: 56 (56)
[183.] 2 Exemplum.
Page: 56 (56)
[184.] DEMONSTRATIO.
Page: 57 (57)
[185.] 3 Exemplum.
Page: 57 (57)
[186.] DEMONSTRATIO.
Page: 57 (57)
[187.] 2 THEOREMA. 2 PROPOSITIO.
Page: 57 (57)
[188.] DEMONSTRATIO.
Page: 57 (57)
[189.] 1 PROBLEMA. 3 PROPOSITIO.
Page: 58 (58)
[190.] PRAGMATIA.
Page: 58 (58)
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          <pb o="141" file="527.01.141" n="141" rhead="*DE* H*YDROSTATICES ELEMENTIS*."/>
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        <div xml:id="echoid-div601" type="section" level="1" n="434">
          <head xml:id="echoid-head451" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s4259" xml:space="preserve">Deſignato D B æquale ipſi C, cum igitur D B triens ſit totius A B 6 ℔,
              <lb/>
            ipſum D B erit 2 ℔: </s>
            <s xml:id="echoid-s4260" xml:space="preserve">ſed gravitas materiæ D B ad C, ut 1 ad 2; </s>
            <s xml:id="echoid-s4261" xml:space="preserve">quare C pen-
              <lb/>
            det 4 ℔.</s>
            <s xml:id="echoid-s4262" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div602" type="section" level="1" n="435">
          <head xml:id="echoid-head452" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s4263" xml:space="preserve">Etenim ſi C majoris eſſet ponderis quam 4 ℔, gravi-
              <lb/>
            tas ejus ad C quæ eſt 2 ℔ (nam C five D B æquantur
              <lb/>
              <figure xlink:label="fig-527.01.141-01" xlink:href="fig-527.01.141-01a" number="202">
                <image file="527.01.141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.141-01"/>
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            tertiæ parti A B) erit majore ratione quam dupla; </s>
            <s xml:id="echoid-s4264" xml:space="preserve">quod
              <lb/>
            tamen theſi repugnat. </s>
            <s xml:id="echoid-s4265" xml:space="preserve">quare C non eſt majus eſt 4 ℔.
              <lb/>
            </s>
            <s xml:id="echoid-s4266" xml:space="preserve">Sed neque minus eſſe eadem ratione concludes. </s>
            <s xml:id="echoid-s4267" xml:space="preserve">Itaque
              <lb/>
            ipſis 4 ℔ æquale. </s>
            <s xml:id="echoid-s4268" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s4269" xml:space="preserve">Datis itaque duo-
              <lb/>
            rum corporum magnitudinis & </s>
            <s xml:id="echoid-s4270" xml:space="preserve">ſoliditatis rationibus, cum pondere alterius; </s>
            <s xml:id="echoid-s4271" xml:space="preserve">
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            reliqui corporis pondus, ut petcbatur, invenimus.</s>
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          </p>
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        <div xml:id="echoid-div604" type="section" level="1" n="436">
          <head xml:id="echoid-head453" xml:space="preserve">C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s4273" xml:space="preserve">Ex his liquet,</s>
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          <p style="it">
            <s xml:id="echoid-s4274" xml:space="preserve">Magnitudinis ratione ſublatâ à ratione ponderis, relinqui materiæ gravitatis ra-
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            tionem.</s>
            <s xml:id="echoid-s4275" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s4276" xml:space="preserve">Et, Materiæ gravitatis ratione ſublatâ à ratione ponderis, relinqui magnitudinis
              <lb/>
            rationem.</s>
            <s xml:id="echoid-s4277" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4278" xml:space="preserve">Et, Materiæ gravitatis ratione addita ad rationem magnitudinis binc ponderis ra-
              <lb/>
            tionem existere.</s>
            <s xml:id="echoid-s4279" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4280" xml:space="preserve">EX quibus perſpicitur, datis quinque harum rationum terminis ſextum con-
              <lb/>
            ſtanti ratione inveniri. </s>
            <s xml:id="echoid-s4281" xml:space="preserve">In exemplo A 6 ℔ eſto,
              <lb/>
              <figure xlink:label="fig-527.01.141-02" xlink:href="fig-527.01.141-02a" number="203">
                <image file="527.01.141-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.141-02"/>
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            magnitudine 5 pedũ; </s>
            <s xml:id="echoid-s4282" xml:space="preserve">ponduſq́ue alterius corporis B
              <lb/>
            ignoretur, aſt magnitudine eſto 2 pedũ, ponderitatis
              <lb/>
            autem materiæ A ad B ratio, ut 4 ad 7. </s>
            <s xml:id="echoid-s4283" xml:space="preserve">Iam ad in-
              <lb/>
            ventionem ignorati ponderis B, addes rationem materiæ ponderitatis, nempe
              <lb/>
            {4/7} ad rationem magnitudinis {5/2} unde oritur ratio ponderis {10/7}, pondus igitur A
              <lb/>
            ad B eſt ut 10 ad 7. </s>
            <s xml:id="echoid-s4284" xml:space="preserve">Itaque quia A pendet 6 ℔, concludes ut 10 ad 7 ſic 6 ℔ ad
              <lb/>
            pondus B 4 {1/5} ℔.</s>
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          <p>
            <s xml:id="echoid-s4286" xml:space="preserve">SEcundò ignoretur magnitudo B, cujus inventio è cæteris quinque terminis
              <lb/>
            inveſtiganda. </s>
            <s xml:id="echoid-s4287" xml:space="preserve">Deducito materiæ ponderitatis rationem {4/7}, de ponderis ra-
              <lb/>
            tione {10/7}, relinquetur magnitudinis ratio {5/2}. </s>
            <s xml:id="echoid-s4288" xml:space="preserve">Itaque magnitudo A eſt ad B ut 5
              <lb/>
            ad 2, atqui A eſt 5 pedum, unde concludes etiam B 2 eſſe pedum.</s>
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          </p>
          <p>
            <s xml:id="echoid-s4290" xml:space="preserve">DEnique ignoretur materiæ gravitatis ratio, quę è cognitis reliquis duabus
              <lb/>
            rationibus ſit eruenda. </s>
            <s xml:id="echoid-s4291" xml:space="preserve">Subducito magnitudinis rationem {5/2} de ratione
              <lb/>
            ponderis {11
              <unsure/>
            /7}, reliqua erit materiæ gravitatis ratio 4 ad 7.</s>
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          </p>
          <p>
            <s xml:id="echoid-s4293" xml:space="preserve">Quamvis propoſitio iſta & </s>
            <s xml:id="echoid-s4294" xml:space="preserve">antecedens omni materiæ homogeneæ genera-
              <lb/>
            lis ſint, maximus tamen uſus circa aquea Zetemata verſari videtur. </s>
            <s xml:id="echoid-s4295" xml:space="preserve">Atque ita
              <lb/>
            quarti libri</s>
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          <head xml:id="echoid-head454" xml:space="preserve">FINIS ESTO.</head>
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