Musschenbroek, Petrus van, Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae

Table of handwritten notes

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        <div xml:id="echoid-div599" type="section" level="1" n="599">
          <pb o="625" file="0641" n="642" rhead="CORPORUM FIRMORUM."/>
          <p>
            <s xml:id="echoid-s15700" xml:space="preserve">Ut manifeſto appareret, quomodo diminuendo quantitatem Ligni,
              <lb/>
            & </s>
            <s xml:id="echoid-s15701" xml:space="preserve">Trabibus variam dando altitudinem, augeretur earum robur, Pa-
              <lb/>
            rentius ſequentem tabulam dedit in L’Hiſt. </s>
            <s xml:id="echoid-s15702" xml:space="preserve">de L’Acad. </s>
            <s xml:id="echoid-s15703" xml:space="preserve">Roy. </s>
            <s xml:id="echoid-s15704" xml:space="preserve">1708.</s>
            <s xml:id="echoid-s15705" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          Latitudo. # Altitudo. # Firmltas. # Soliditas.
            <lb/>
          12 # 12 # 1728 # 144.
            <lb/>
          11 # 13 # 1859 # 143.
            <lb/>
          10 # 14 # 1960 # 140.
            <lb/>
          9 # 15 # 2025 # 135.
            <lb/>
          8 # 16 # 2048 # 128.
            <lb/>
          7 # 17 # 2023 # 119.
            <lb/>
          6 # 18 # 1944 # 108.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s15706" xml:space="preserve">Non tamen licet latitudinem imminuere ad lubitum, quippe tum
              <lb/>
            a vi minima laterali facillime rumperetur, quamobrem certa requiri-
              <lb/>
            tur latitudo reſpectu altitudinis, quam in ſequenti Propoſitione
              <lb/>
            determinabimus.</s>
            <s xml:id="echoid-s15707" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div600" type="section" level="1" n="600">
          <head xml:id="echoid-head719" xml:space="preserve">PROPOSITIO XCVIII.</head>
          <p style="it">
            <s xml:id="echoid-s15708" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15709" xml:space="preserve">XXIV. </s>
            <s xml:id="echoid-s15710" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15711" xml:space="preserve">8. </s>
            <s xml:id="echoid-s15712" xml:space="preserve">Dato Cylindro R A S V B T, ex eo fabre-
              <lb/>
            facere parallelopipedum R S V T maximæ Cohærentiæ.</s>
            <s xml:id="echoid-s15713" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15714" xml:space="preserve">Sit baſis Cylindri circulus R A S V B T, cui ſit inſcripta baſis pa-
              <lb/>
            rallelopipedi rectangula R S V T maximæ reſiftentiæ, & </s>
            <s xml:id="echoid-s15715" xml:space="preserve">maxi-
              <lb/>
            mum, quod huic circulo inſcribi poſſit: </s>
            <s xml:id="echoid-s15716" xml:space="preserve">Sit R S ipſius latitudo,
              <lb/>
            quæ ſecet A B in Q, ſit S V ipſius altitudo: </s>
            <s xml:id="echoid-s15717" xml:space="preserve">poterit C Q conſide-
              <lb/>
            rari ut abſciſſa, quam voco x. </s>
            <s xml:id="echoid-s15718" xml:space="preserve">radius C S vocetur = r. </s>
            <s xml:id="echoid-s15719" xml:space="preserve">erit ob
              <lb/>
            Triangulum rectangulum C Q S: </s>
            <s xml:id="echoid-s15720" xml:space="preserve">recta Q S = rr - xx.</s>
            <s xml:id="echoid-s15721" xml:space="preserve"> unde
              <lb/>
            R S dupla ipſius Q S, erit = 2 rr - xx.</s>
            <s xml:id="echoid-s15722" xml:space="preserve"> quare multiplicando qua-
              <lb/>
            dratum S V per R S, ut habeatur omnis firmitas, dabitur 4 xx X 2
              <lb/>
            rr - xx ſive 8 xx rr - xx.</s>
            <s xml:id="echoid-s15723" xml:space="preserve"> hujus valoris ſumendo maximum,
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            habebitur {8dx X 2rrx - 3x
              <emph style="super">3</emph>
            /rr - xx} = 0. </s>
            <s xml:id="echoid-s15724" xml:space="preserve">unde deducitur 2rr = 3xx.
              <lb/>
            </s>
            <s xml:id="echoid-s15725" xml:space="preserve">atque dividendo utrumque membrum per 3, erit {2/3} rr = xx. </s>
            <s xml:id="echoid-s15726" xml:space="preserve">hinc
              <lb/>
            quadratum Q S eſt = {1/3} rr. </s>
            <s xml:id="echoid-s15727" xml:space="preserve">quamobrem erit
              <emph style="ol">C Q</emph>
              <emph style="super">q</emph>
            .</s>
            <s xml:id="echoid-s15728" xml:space="preserve">
              <emph style="ol">QS</emph>
              <emph style="super">q</emph>
            :</s>
            <s xml:id="echoid-s15729" xml:space="preserve">: {2/3}, {1/3}:</s>
            <s xml:id="echoid-s15730" xml:space="preserve">: 2, 1. </s>
            <s xml:id="echoid-s15731" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s15732" xml:space="preserve">C Q, QS:</s>
            <s xml:id="echoid-s15733" xml:space="preserve">: SV. </s>
            <s xml:id="echoid-s15734" xml:space="preserve">RS:</s>
            <s xml:id="echoid-s15735" xml:space="preserve">: 2, 1:</s>
            <s xml:id="echoid-s15736" xml:space="preserve">: 7. </s>
            <s xml:id="echoid-s15737" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15738" xml:space="preserve">proxime. </s>
            <s xml:id="echoid-s15739" xml:space="preserve">Ut in </s>
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