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

Table of Notes

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          <pb o="97" file="527.01.097" n="97" rhead="DE S*TATICÆ* PRAXI."/>
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        <div xml:id="echoid-div409" type="section" level="1" n="294">
          <head xml:id="echoid-head309" xml:space="preserve">9 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2905" xml:space="preserve">Axium in peritrochio & </s>
            <s xml:id="echoid-s2906" xml:space="preserve">tractorum ponderum rationes
              <lb/>
            inquirere.</s>
            <s xml:id="echoid-s2907" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2908" xml:space="preserve">Pondus movens & </s>
            <s xml:id="echoid-s2909" xml:space="preserve">motum ſemidiametris tympani & </s>
            <s xml:id="echoid-s2910" xml:space="preserve">axis proportionales
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            ſunt, unde majoris evidentiæ gratia, theorema tale inſtituimus.</s>
            <s xml:id="echoid-s2911" xml:space="preserve"/>
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        <div xml:id="echoid-div410" type="section" level="1" n="295">
          <head xml:id="echoid-head310" xml:space="preserve">THEOREMA.</head>
          <p style="it">
            <s xml:id="echoid-s2912" xml:space="preserve">Si & </s>
            <s xml:id="echoid-s2913" xml:space="preserve">ab axe & </s>
            <s xml:id="echoid-s2914" xml:space="preserve">ab extremâ tympani ſemidiametro horizonti par allelâ.
              <lb/>
            </s>
            <s xml:id="echoid-s2915" xml:space="preserve">ponder a ſitu æquipondia dependeant, hæc erunt ſemidiametris reciproce pro-
              <lb/>
            portionalia.</s>
            <s xml:id="echoid-s2916" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2917" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s2918" xml:space="preserve">* Eſto tympanum A B C D E F G, quod verſetur circa axem
              <lb/>
            E F G cujus diameter E F, centrum H, pondus I ab axe dependeat, A B C D
              <lb/>
            ſit ipſa rota ſeu tympanum, cujus ſemidiameter horizonti parallela A C, & </s>
            <s xml:id="echoid-s2919" xml:space="preserve">à
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            termino A pondus K dependeat ſitu æquipondium ipſi I; </s>
            <s xml:id="echoid-s2920" xml:space="preserve">L autem axis & </s>
            <s xml:id="echoid-s2921" xml:space="preserve">
              <lb/>
            ſuſtentaculi ſui infimus contactus. </s>
            <s xml:id="echoid-s2922" xml:space="preserve">Q*VAESITVM.</s>
            <s xml:id="echoid-s2923" xml:space="preserve">* Demonſtrato, H A, H F,
              <lb/>
            & </s>
            <s xml:id="echoid-s2924" xml:space="preserve">I, K, in eadem analogia eſſe.</s>
            <s xml:id="echoid-s2925" xml:space="preserve"/>
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        <div xml:id="echoid-div411" type="section" level="1" n="296">
          <head xml:id="echoid-head311" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2926" xml:space="preserve">Enimverò tympanum A B C D librilis iſtar eſto, cujus anſa L B, ut ſublatis
              <unsure/>
              <lb/>
            ponderibus K, I, partes tympa-
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            ni B D A, B D C ſint æquili-
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            bres. </s>
            <s xml:id="echoid-s2927" xml:space="preserve">Siigitur pondus I ab F de-
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            pendere fingas, quia hic tantæ
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            eſt potentiæ quantæ ſuo loco, K
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            autem è loco ſuo A, per 1 prop.
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            </s>
            <s xml:id="echoid-s2928" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s2929" xml:space="preserve">eadem ratio erit radii lon-
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            gioris H A, ad breviorem H F,
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            quæ ponderis majoris I ad mi-
              <lb/>
            nus K. </s>
            <s xml:id="echoid-s2930" xml:space="preserve">Quamobrem ſi H A ſex-
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            tuplus ſit ipſius H F, etiam I
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            ſextuplum fuerit ipſius K, ut ſi
              <lb/>
            I ponatur 600 librarum, K erit
              <lb/>
            100, ideo q́ue potentia hominis
              <lb/>
            ad A æquivalens 100 libris, ſitu
              <lb/>
            æquipondia foret 600 libris ad
              <lb/>
            I, & </s>
            <s xml:id="echoid-s2931" xml:space="preserve">quo attolli poſſit (propter
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            impedimenta contactus axis & </s>
            <s xml:id="echoid-s2932" xml:space="preserve">ſuſtentaculi C) paulo potentius quam 100 ℔
              <lb/>
            agat neceſſe erit.</s>
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        <div xml:id="echoid-div413" type="section" level="1" n="297">
          <head xml:id="echoid-head312" xml:space="preserve">2 Exemplum.</head>
          <p>
            <s xml:id="echoid-s2934" xml:space="preserve">Hinc tympanorum qui Græcis γέζανθι ſimiliumq́ue rotarum ratio, quæ à
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            calcantibus hominibus verſantur, manifeſta eſt. </s>
            <s xml:id="echoid-s2935" xml:space="preserve">Exponatur enim tympanum
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            A B C D, diametro A C horizonti parallela, cujus axis craſſities ad tornum
              <lb/>
            rotundati ſit E F, centrum G, pondus ab axe H; </s>
            <s xml:id="echoid-s2936" xml:space="preserve">homo ad I ſitu æquilibris
              <lb/>
            ponderi H, & </s>
            <s xml:id="echoid-s2937" xml:space="preserve">I K gtavitatis ejus perpendicularis in A C. </s>
            <s xml:id="echoid-s2938" xml:space="preserve">Notumautem G K,
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            ad G F eſt
              <unsure/>
            e, ſicut pondus H ad gravitatem hominis qui ad I, ſi igitur G K </s>
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