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

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          <pb o="140" file="527.01.140" n="140" rhead="4 L*IBER* S*TATICÆ*"/>
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        <div xml:id="echoid-div593" type="section" level="1" n="428">
          <head xml:id="echoid-head445" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s4209" xml:space="preserve">Primùm corpus aqueum preſſu fundo
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                <image file="527.01.140-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.140-01"/>
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            D E inſidenti æquepondium per 13 propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s4210" xml:space="preserve">inveniatur, idque eſto D E F G, cujus gra-
              <lb/>
            vitatis centrum per 21 propoſ. </s>
            <s xml:id="echoid-s4211" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s4212" xml:space="preserve">Static. </s>
            <s xml:id="echoid-s4213" xml:space="preserve">
              <lb/>
            inventum ſit H, unde H I parallela agatur
              <lb/>
            contra G E, ejus in fundo D E terminus I
              <lb/>
            optatũ erit preſſus gravitatis centrum; </s>
            <s xml:id="echoid-s4214" xml:space="preserve">cujus
              <lb/>
            demonſtratio antecedentium 18 & </s>
            <s xml:id="echoid-s4215" xml:space="preserve">19 propoſ. </s>
            <s xml:id="echoid-s4216" xml:space="preserve">ſimilis erit.</s>
            <s xml:id="echoid-s4217" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4218" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s4219" xml:space="preserve">Itaque dati fundi plani rectilinei, & </s>
            <s xml:id="echoid-s4220" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4221" xml:space="preserve"/>
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        <div xml:id="echoid-div595" type="section" level="1" n="429">
          <head xml:id="echoid-head446" xml:space="preserve">8 PROBLEMA. 21 PROPOSITIO.</head>
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            <s xml:id="echoid-s4222" xml:space="preserve">Data aqua magnitudinis ignotæ, gravitatis verò notæ;
              <lb/>
            </s>
            <s xml:id="echoid-s4223" xml:space="preserve">magnitudinem ex ſua propriaq́ue ponderitate invenire.</s>
            <s xml:id="echoid-s4224" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div596" type="section" level="1" n="430">
          <head xml:id="echoid-head447" xml:space="preserve">NOTA.</head>
          <p>
            <s xml:id="echoid-s4225" xml:space="preserve">Quamvis magnitudinis inventio Geometrica ratione inveniri & </s>
            <s xml:id="echoid-s4226" xml:space="preserve">explicari
              <lb/>
            poſſit, quia tamen Statica factio expeditior certiorq́ue ſit, & </s>
            <s xml:id="echoid-s4227" xml:space="preserve">in corporibus, præ-
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            ſertim inordinatis propius verum collimet, eam hic exponere ſtatui.</s>
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            <s xml:id="echoid-s4229" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s4230" xml:space="preserve">Aquæ A magnitudo ignoretur, gravitas autem nota eſto,
              <lb/>
            hoc eſt per 1 defin. </s>
            <s xml:id="echoid-s4231" xml:space="preserve">hujus cujus nota magnitudo cognita ponderitate expri-
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            mitur. </s>
            <s xml:id="echoid-s4232" xml:space="preserve">Itaque pedem cubicum 65 ℔ pondere taxabo.</s>
            <s xml:id="echoid-s4233" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4234" xml:space="preserve">Q*VAESITVM.</s>
            <s xml:id="echoid-s4235" xml:space="preserve">* Magnitudinem A ex ſua ponderitate concludere.</s>
            <s xml:id="echoid-s4236" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div597" type="section" level="1" n="431">
          <head xml:id="echoid-head448" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s4237" xml:space="preserve">Ponderato aquam A, ſitq́ue 5 ℔, quæ per 65 ℔ diviſæ efficiunt 1 {1/3} pedis
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            cubici pro quæſita magnitudine corporis A.</s>
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          </p>
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        <div xml:id="echoid-div598" type="section" level="1" n="432">
          <head xml:id="echoid-head449" xml:space="preserve">DEMONSTRATIO.</head>
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            <s xml:id="echoid-s4239" xml:space="preserve">Cum enim A ſit 5 ℔, pes autem aquæ ejuſdem 65 ℔ pendeat,
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            ipſaq́ue per 2 poſtul. </s>
            <s xml:id="echoid-s4240" xml:space="preserve">ponderitatis ſit homogeneæ, ratio ponderi-
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            tatis ſuæ ad 65 ℔ eadem erit, quæ magnitudinis ad pedem cubi-
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            cum; </s>
            <s xml:id="echoid-s4241" xml:space="preserve">atqui 5 ℔ & </s>
            <s xml:id="echoid-s4242" xml:space="preserve">65 ℔ eſt ſubtredecupla, itaque etiam magnitu-
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            dine æquatur 1 {1/3} pedis. </s>
            <s xml:id="echoid-s4243" xml:space="preserve">quod demonſtraſſe oportebat.</s>
            <s xml:id="echoid-s4244" xml:space="preserve"/>
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            <s xml:id="echoid-s4245" xml:space="preserve">C*ONCLVSIO.</s>
            <s xml:id="echoid-s4246" xml:space="preserve">* Quare ex aquæ gravitate nota, licet ignota
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            magnitudine; </s>
            <s xml:id="echoid-s4247" xml:space="preserve">ipſam magnitudinem eruimus.</s>
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          <head xml:id="echoid-head450" xml:space="preserve">9 PROBLEMA. 22 PROPOSITIO.</head>
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            <s xml:id="echoid-s4249" xml:space="preserve">Datis duorum corporum magnitudinis & </s>
            <s xml:id="echoid-s4250" xml:space="preserve">materiæ gra-
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            vitatis rationibus inter ſe, cum pondere alterius, reliqui
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            quoque pondus invenire.</s>
            <s xml:id="echoid-s4251" xml:space="preserve"/>
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            <s xml:id="echoid-s4252" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s4253" xml:space="preserve">Exponantur corpora A B & </s>
            <s xml:id="echoid-s4254" xml:space="preserve">C, ſitq́ue A B ad C ut 3 ad 1,
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            materiæ autem gravitas ut 1 ad 2, atque A B librarum 6.</s>
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            <s xml:id="echoid-s4256" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s4257" xml:space="preserve">Corporis C pondus invenire.</s>
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