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

Table of contents

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[111.] DEMONSTRATIO.
Page: 27 (27)
[112.] 2 Exemplum obliquorum ponderum.
Page: 28 (28)
[113.] DEMONSTRATIO.
Page: 28 (28)
[114.] 3 Exemplum.
Page: 28 (28)
[115.] DEMONSTRATIO.
Page: 28 (28)
[116.] 8 PROBLEMA. 14 PROPOSITIO.
Page: 29 (29)
[117.] PRAGMATIA.
Page: 29 (29)
[118.] DEMONSTRATIO.
Page: 29 (29)
[119.] NOTATO
Page: 29 (29)
[120.] 1 C*ONSECTARIUM*.
Page: 29 (29)
[121.] 2 C*ONSECTARIUM*.
Page: 30 (30)
[122.] 7 THEOREMA. 15 PROPOSITIO.
Page: 31 (31)
[123.] DECLARATIO.
Page: 31 (31)
[124.] 8 THEOREMA. 16 PROPOSITIO.
Page: 31 (31)
[125.] DEMONSTRATIO.
Page: 31 (31)
[126.] 9 THEOREMA. 17 PROPOSITIO.
Page: 32 (32)
[127.] DEMONSTRATIO.
Page: 32 (32)
[128.] C*ONSECTARIUM*.
Page: 33 (33)
[129.] 10 THEOREMA. 18 PROPOSITIO.
Page: 33 (33)
[130.] C*ONSECTARIUM*.
Page: 34 (34)
[131.] HACTENVS RECTORVM PONDERVM GENERA DICTA SVNT; OBLI-QVORVM PROPRIETATES DEINCEPS deſcribendæ ſunt, quarum omnium genera-lem veritatem tanquam fundamentum istud theoremata complectitur. 11 THEOREMA. 19 PROPOSITIO.
Page: 34 (34)
[132.] DEMONSTRATIO.
Page: 35 (35)
[133.] 1 C*ONSECTARIUM*.
Page: 35 (35)
[134.] 2 C*ONSECTARIUM*.
Page: 35 (35)
[135.] 3 C*ONSECTARIUM*.
Page: 35 (35)
[136.] 4 C*ONSECTARIUM*.
Page: 36 (36)
[137.] 5 C*ONSECTARIUM*.
Page: 36 (36)
[138.] 6 C*ONSECTARIUM*.
Page: 36 (36)
[139.] 7 C*ONSECTARIUM*.
Page: 38 (38)
[140.] 8 C*ONSECTARIUM*.
Page: 38 (38)
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          <head xml:id="echoid-head374" xml:space="preserve">2 C*ONSECTARIUM.*</head>
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            <s xml:id="echoid-s3476" xml:space="preserve">Secundò in aquam ABCD immittitor corpus ſolidum, ſolidavé quot-
              <lb/>
            cunque materiâ aquæ æquipondiâ, inter quæ, reliqua omnia aqua expulſa,
              <lb/>
            tantùm comprehendatur IKFELM; </s>
            <s xml:id="echoid-s3477" xml:space="preserve">quæ cum ita ſint, hæc corpora fundum
              <lb/>
            EF nec aggravant neque relevant
              <lb/>
            ab eo pódere quo aqua prius ipſum
              <lb/>
              <figure xlink:label="fig-527.01.120-01" xlink:href="fig-527.01.120-01a" number="166">
                <image file="527.01.120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.120-01"/>
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            afficiebat. </s>
            <s xml:id="echoid-s3478" xml:space="preserve">quare etiamnum ex ſen-
              <lb/>
            tentia propoſitionis dicimus, fun-
              <lb/>
            do EF inſidere pondus æquale
              <lb/>
            aqueo ponderi, magnitudine co-
              <lb/>
            lumnam æquante, cujus baſis EF,
              <lb/>
            altitudo perpendicularis GE abaquæ ſummo AB ſeu MI ad imum EF de-
              <lb/>
            miſſa.</s>
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          <head xml:id="echoid-head375" xml:space="preserve">3 C*ONSECTARIUM.*</head>
          <p>
            <s xml:id="echoid-s3480" xml:space="preserve">Sittertiùm ABCD mera aqua, & </s>
            <s xml:id="echoid-s3481" xml:space="preserve">in ipſa EF fundum horizonti parallelum.
              <lb/>
            </s>
            <s xml:id="echoid-s3482" xml:space="preserve">Quibus poſitis, aqua ſub fundo EF tam potenter ipſum ſurſum premit, quam
              <lb/>
            aqua ſupra inſidens deorſum; </s>
            <s xml:id="echoid-s3483" xml:space="preserve">ſecus enim per 1 propoſ. </s>
            <s xml:id="echoid-s3484" xml:space="preserve">infirmius validiori con-
              <lb/>
            cederet, quod hîc non fit quia utrumque loco ſuo permanet. </s>
            <s xml:id="echoid-s3485" xml:space="preserve">lam corpus ſoli-
              <lb/>
            dum iſti aquæ pondere homogeneum ita collocator ut
              <lb/>
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                <image file="527.01.120-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.120-02"/>
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            aqua IKEFLM ab inferiori parte preſſet fundum EF,
              <lb/>
            ut hîc. </s>
            <s xml:id="echoid-s3486" xml:space="preserve">Quibus poſitis, aqua ſubter EF nunc tam validè
              <lb/>
            premit fundum EF, ſive ipſum ſolidum, quàm prius
              <lb/>
            ipſam aquam oppoſitam: </s>
            <s xml:id="echoid-s3487" xml:space="preserve">ſed impreſſio tanta tunc erat
              <lb/>
            quanta ſuperioris aquæ ad EF depreſſio, ut ſupra pa-
              <lb/>
            tuit, ſuperioris autem aquæ depreſſio æqualis erat ponderi columnæ aqueæ
              <lb/>
            cujus baſis EF, altitudo perpendicularis GE, à ſuperficie AB ſeu MI ad
              <lb/>
            fundum EF demiſſa. </s>
            <s xml:id="echoid-s3488" xml:space="preserve">Itaque aquæ ſubter EF conſtitutæ impreſſio erit quoque
              <lb/>
            tanta.</s>
            <s xml:id="echoid-s3489" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div500" type="section" level="1" n="359">
          <head xml:id="echoid-head376" xml:space="preserve">4 C*ONSECTARIUM.*</head>
          <p>
            <s xml:id="echoid-s3490" xml:space="preserve">Corpora ſolida ſecundi tertiiq́ue conſectatii iſtic ita firmentur, effuſaq́ue
              <lb/>
            aqua ſpatium IKFELM vacuum nullo amplius pondere afficiet fundũ EF;
              <lb/>
            </s>
            <s xml:id="echoid-s3491" xml:space="preserve">unde apparetaqua in vacuum locum rurſum infusâ fundũ EF tam validè pre-
              <lb/>
            mi, ac ſi integrũ vas ABCD, ſublato iſto corpore ſolido, aquâ repletum foret.</s>
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          <head xml:id="echoid-head377" xml:space="preserve">5 C*ONSECTARIUM.*</head>
          <p>
            <s xml:id="echoid-s3493" xml:space="preserve">Atverò quia immiſſa ſolida 2 & </s>
            <s xml:id="echoid-s3494" xml:space="preserve">3 conſectarii ſunt ſuo loco defixa, ipſorum
              <lb/>
            materia extrema nec gravitate nec levitate ulla afficiet fundum EF, quam-
              <lb/>
            obrem ſublata omni aquam ambiente materia, relinquentur internæ iſtæ aqueæ
              <lb/>
            figuræ MIKFEL, quales hic vides.</s>
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          <figure number="168">
            <image file="527.01.120-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.120-03"/>
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          <p>
            <s xml:id="echoid-s3496" xml:space="preserve">Atque hic etiam ex ſententia propoſitionis dicimus baſe EF ſubnixum </s>
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