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

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              <pb o="27" file="527.01.027" n="27" rhead="*DE* S*TATIGÆ ELEMENTIS*."/>
            unà cum ponderibus G & </s>
            <s xml:id="echoid-s783" xml:space="preserve">I, quorum
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            omnium totus eſt 9 ℔, quæ eſt 1 ad
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            2. </s>
            <s xml:id="echoid-s784" xml:space="preserve">S 4 {1/2} quæſitum pondus eſſe dico.</s>
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        <div xml:id="echoid-div138" type="section" level="1" n="108">
          <head xml:id="echoid-head117" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s786" xml:space="preserve">Gravius pódus 9 ℔ radii R Q eam
              <lb/>
            habet rationem ad levius 4 {1/2} ℔ radii
              <lb/>
            R P, quæ longioris radii eſt R P ad
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            breviorem R Q, ſitu igitur æquipon-
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            dia ſunt ex ansâ E F per 1 propoſitio-
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            nem, &</s>
            <s xml:id="echoid-s787" xml:space="preserve">, quod inde conſequitur, axis
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            L M in dato ſitu manet, quod demon-
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            ſtrandum fuit.</s>
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          <p>
            <s xml:id="echoid-s789" xml:space="preserve">C*ONCLU
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            SIO*. </s>
            <s xml:id="echoid-s790" xml:space="preserve">Datâ igitur & </s>
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            cognitâ columnâ unà cum pun-
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            cto, &</s>
            <s xml:id="echoid-s792" xml:space="preserve">c.</s>
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          <head xml:id="echoid-head118" xml:space="preserve">6 THEOREMA. 13 PROPOSITIO.</head>
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            <s xml:id="echoid-s794" xml:space="preserve">Æqualia pondera, unumelevans, alterum demittens
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            æqualibus & </s>
            <s xml:id="echoid-s795" xml:space="preserve">angulis, & </s>
            <s xml:id="echoid-s796" xml:space="preserve">radiis, æquales potentias habent.</s>
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          <head xml:id="echoid-head119" xml:space="preserve">I Exemplum rectorum ponderum.</head>
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            <s xml:id="echoid-s798" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s799" xml:space="preserve">A punctum eſto, in jugo ſive trabe B C firmum, A B & </s>
            <s xml:id="echoid-s800" xml:space="preserve">A C
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            æquales radii, pendeatq́ue de B rectum pondus demittens ſive deſcendens,
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            de C vero adſcendens ſive attollens, hujusq́ue jugum F G, firmumq́ue ejus
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            punctum H, æquales autem radii H F, H G, angulusq́ue A B I æquetur an-
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            gulo A C F. </s>
            <s xml:id="echoid-s801" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s802" xml:space="preserve">Rectum pondus deſcendens D, rectumq́ue
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            adſcendens E, ex æqualibus radiis A B, A C æquales potentias habere de-
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            monſtrandum nobis eſt. </s>
            <s xml:id="echoid-s803" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s804" xml:space="preserve">DeC pondus K, æquale pon-
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            deri D, pendeto.</s>
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        <div xml:id="echoid-div141" type="section" level="1" n="111">
          <head xml:id="echoid-head120" xml:space="preserve">DEMONSTRATIO.</head>
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            <s xml:id="echoid-s806" xml:space="preserve">Amoto E, potentiam D eſſe radios A B,
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            A C in dato ſitu retinere, manifeſtum
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            eſt, pondera enim D & </s>
            <s xml:id="echoid-s807" xml:space="preserve">K, item radii A B
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            & </s>
            <s xml:id="echoid-s808" xml:space="preserve">A C æqualia ſunt. </s>
            <s xml:id="echoid-s809" xml:space="preserve">Amoto viciſſim D,
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            appenditor E, & </s>
            <s xml:id="echoid-s810" xml:space="preserve">hujus potentia eſt, radios
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            A B & </s>
            <s xml:id="echoid-s811" xml:space="preserve">A C in dato ſitu retinere, pondera
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            enim K & </s>
            <s xml:id="echoid-s812" xml:space="preserve">E, radiiq́ue H F & </s>
            <s xml:id="echoid-s813" xml:space="preserve">H G æquan-
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            tur, Eigitur & </s>
            <s xml:id="echoid-s814" xml:space="preserve">D pari potentiâ & </s>
            <s xml:id="echoid-s815" xml:space="preserve">vi in ra-
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            dios A B & </s>
            <s xml:id="echoid-s816" xml:space="preserve">A C agunt.</s>
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