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

Table of contents

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[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)
[141.] 9 C*ONSECTARIUM*.
Page: 39 (39)
[142.] 10 C*ONSECTARIUM*.
Page: 40 (40)
[143.] 11 C*ONSECTARIUM*.
Page: 40 (40)
[144.] 12 C*ONSECTARIUM*.
Page: 40 (40)
[145.] 12 THE OREMA. 20 PROPOSITIO.
Page: 41 (41)
[146.] NOTATO
Page: 42 (42)
[147.] 13 THEOREMA. 21 PROPOSITIO.
Page: 42 (42)
[148.] DEMONSTRATIO.
Page: 42 (42)
[149.] 9 PROBLEMA. 22 PROPOSITIO.
Page: 43 (43)
[150.] PRAGMATIA.
Page: 43 (43)
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          <pb o="155" file="527.01.155" n="155" rhead="S*TATICES*."/>
          <p>
            <s xml:id="echoid-s4641" xml:space="preserve">Notandum autem nonnullas demonſtrationes 1 lib. </s>
            <s xml:id="echoid-s4642" xml:space="preserve">Static. </s>
            <s xml:id="echoid-s4643" xml:space="preserve">itemq́ue Hydro-
              <lb/>
            ſtat. </s>
            <s xml:id="echoid-s4644" xml:space="preserve">ubi gravitas numero, notaq́ue librarum menſura exprimitur, ut mechanicis
              <lb/>
            demonſtrationibus accenſeri debere videantur, geminas à nobis exhibitas eſſe;
              <lb/>
            </s>
            <s xml:id="echoid-s4645" xml:space="preserve">alteras Arithmeticas ut 1 exemplo 1 propoſ. </s>
            <s xml:id="echoid-s4646" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s4647" xml:space="preserve">ubi propoſitionis ſententia
              <lb/>
            Arithmetico calculo oſtenditur, quam Mathematica demonſtratio ſecundo
              <lb/>
            exemplo ſtatim ſubſequitur. </s>
            <s xml:id="echoid-s4648" xml:space="preserve">Vt Mechanica demonſtratio Mathematicæ non-
              <lb/>
            nunquam tanquam miniſtra facem alluceat.</s>
            <s xml:id="echoid-s4649" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div635" type="section" level="1" n="456">
          <head xml:id="echoid-head480" xml:space="preserve">C*APVT V.*</head>
          <head xml:id="echoid-head481" style="it" xml:space="preserve">Vbi Propoſitio 8 Hydrostatices illustratur,
            <lb/>
          & clariùs exponitur.</head>
          <p>
            <s xml:id="echoid-s4650" xml:space="preserve">OCtava propoſitio Hydroſt. </s>
            <s xml:id="echoid-s4651" xml:space="preserve">docet: </s>
            <s xml:id="echoid-s4652" xml:space="preserve">Solidum in aqua levius eſſe quam in aëre
              <lb/>
            pondere aquæ magnitudine ſibi æqualis. </s>
            <s xml:id="echoid-s4653" xml:space="preserve">Vnde quis conſectaria huj
              <unsure/>
            uſmodi de-
              <lb/>
            duceret: </s>
            <s xml:id="echoid-s4654" xml:space="preserve">Solidum quodlibet in hydrargyro levius eſt quàm in aqua magnitudine hy-
              <lb/>
            drargyriſibi æqualis. </s>
            <s xml:id="echoid-s4655" xml:space="preserve">Velaliud hoc modo: </s>
            <s xml:id="echoid-s4656" xml:space="preserve">Solidum quodlibet in aqua levius eſt quam
              <lb/>
            in oleo magnitudine aquæ ſibi æqualis; </s>
            <s xml:id="echoid-s4657" xml:space="preserve">ſimiliq́ue analogia in cæteris. </s>
            <s xml:id="echoid-s4658" xml:space="preserve">Quæ vera de-
              <lb/>
            ductio, re ſimpliciter conſiderata experiĕtiæ contraria videtur; </s>
            <s xml:id="echoid-s4659" xml:space="preserve">nam libra plum-
              <lb/>
            binõ erit in aqua levior quam in oleo, põdere aquę ſibi æqualis, ſed tantò dun-
              <lb/>
            taxat levior quanta erit differentia aquæ & </s>
            <s xml:id="echoid-s4660" xml:space="preserve">olei dictæ plumbeæ libræ magnitu-
              <lb/>
            dine æqualium. </s>
            <s xml:id="echoid-s4661" xml:space="preserve">Sed tamen re penſiculatius expenſa theorema noſtrum omni-
              <lb/>
            bus numeris perfectum animadvertet, ſiquidem 1 poſtul. </s>
            <s xml:id="echoid-s4662" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s4663" xml:space="preserve">Hydroſt. </s>
            <s xml:id="echoid-s4664" xml:space="preserve">petie-
              <lb/>
            rim concedi, Ponderitatem corporum in aëre appellari propriè, item 5 poſt. </s>
            <s xml:id="echoid-s4665" xml:space="preserve">Vas ſu-
              <lb/>
            perficiarium effuſa aqua vacuum eſſe, hoc eſt per 11 defin. </s>
            <s xml:id="echoid-s4666" xml:space="preserve">aëris duntaxat plenum.
              <lb/>
            </s>
            <s xml:id="echoid-s4667" xml:space="preserve">ſi igitur media, in quibus gravitas æſtimatur, hydrargyrum & </s>
            <s xml:id="echoid-s4668" xml:space="preserve">aqua ponantur,
              <lb/>
            ac tum poſtuletur, Corporum gravitatem in aqua dici propriè. </s>
            <s xml:id="echoid-s4669" xml:space="preserve">Item, Vas ſuperſicia-
              <lb/>
            rium effuſo hydrargyro aquæplenam eſſe, certè his ita conſtitutis dicta propoſitio
              <lb/>
            (Solidum quodlibet in hydrargyro levius eſſe quam in aqua, pondere aquæ magnitudine
              <lb/>
            ſibi æqualis) omninò vera fuerit. </s>
            <s xml:id="echoid-s4670" xml:space="preserve">Vtres hæc magis fiat perſpicua, cogitatione
              <lb/>
            fingito hominem ſub aqua conſtitutum ſecum habere hydrargyrum & </s>
            <s xml:id="echoid-s4671" xml:space="preserve">aurum,
              <lb/>
            ſitq́ue aqua vice aëris, Ajo aurum iſtictantò fore levius, quam in hydrargyro
              <lb/>
            quantum erit pondus hydrargyri aurum magnitudine æquantis: </s>
            <s xml:id="echoid-s4672" xml:space="preserve">quod ſanè
              <lb/>
            manifeſtum eſt. </s>
            <s xml:id="echoid-s4673" xml:space="preserve">At verò ſi Corporum pondus in inani verè dici ſumatur, ut revera
              <lb/>
            ſe res habet, ſecundum hac inquam affectionem ita enuntiari poſſet. </s>
            <s xml:id="echoid-s4674" xml:space="preserve">Omne ſoli-
              <lb/>
            dum in aqua gravius eſt, quàm in inani pondere aquæ ſibi æqualis. </s>
            <s xml:id="echoid-s4675" xml:space="preserve">Verùm cum uſus
              <lb/>
            & </s>
            <s xml:id="echoid-s4676" xml:space="preserve">effectio (quò theoriam perpetuò dirigere decet) non in vacuo ſed in aëre
              <lb/>
            fiant, ſatiùs eſt ſecun dum modum nobis ſupra uſitatum, pondus rei proprium
              <lb/>
            in aëre ſupponi, cujus ratione & </s>
            <s xml:id="echoid-s4677" xml:space="preserve">reſpectu 8 noſtra propoſitio cæteræq́ue inde
              <lb/>
            derivatæ omnibus numeris perfectæ ſunt. </s>
            <s xml:id="echoid-s4678" xml:space="preserve">Quod annotaſſe fuit operæ pre-
              <lb/>
            tium.</s>
            <s xml:id="echoid-s4679" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div636" type="section" level="1" n="457">
          <head xml:id="echoid-head482" xml:space="preserve">A*PPENDICIS* F*INIS*.</head>
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