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

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            <s xml:id="echoid-s10371" xml:space="preserve">
              <pb o="455" file="0469" n="469" rhead="CORPORUM FIRMORUM."/>
            erecta ſit perpendicularis P A, ſitque P quædam particula attracta ab
              <lb/>
            omnibus circuli partibus; </s>
            <s xml:id="echoid-s10372" xml:space="preserve">â P ad quodcunque punctum radii A D,
              <lb/>
            ducatur recta P E, in recta P A ducatur P F = P E, ex F ducatur
              <lb/>
            F K parallela ad A D, quæ repræſentet vires, quibus punctum E at-
              <lb/>
            trahit particulam P, ſitque I K L curva linea, quam punctum K
              <lb/>
            perpetuo tangit: </s>
            <s xml:id="echoid-s10373" xml:space="preserve">Occurrat eadem circuli plano in L. </s>
            <s xml:id="echoid-s10374" xml:space="preserve">in P A capia-
              <lb/>
            tur P H æqualis P D, & </s>
            <s xml:id="echoid-s10375" xml:space="preserve">erigatur perpendiculum H I cur væ oc-
              <lb/>
            currens in I. </s>
            <s xml:id="echoid-s10376" xml:space="preserve">demonſtravit Newtonus Lib. </s>
            <s xml:id="echoid-s10377" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10378" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s10379" xml:space="preserve">90. </s>
            <s xml:id="echoid-s10380" xml:space="preserve">Princ. </s>
            <s xml:id="echoid-s10381" xml:space="preserve">Philoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s10382" xml:space="preserve">corpuſculi P attractionem eſſe, ut area A H I L. </s>
            <s xml:id="echoid-s10383" xml:space="preserve">eſt ducta in alti-
              <lb/>
            tudinem A P.</s>
            <s xml:id="echoid-s10384" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10385" xml:space="preserve">Vocetur P F x. </s>
            <s xml:id="echoid-s10386" xml:space="preserve">F K y, & </s>
            <s xml:id="echoid-s10387" xml:space="preserve">ſit F K, vel vis quâ punctum E
              <lb/>
            attrahit corpus P, reciproce ut aliqua potentia ipſius P F, ſit
              <lb/>
            hæc n. </s>
            <s xml:id="echoid-s10388" xml:space="preserve">tum æquatio curvæ erit y = {1/X
              <emph style="super">n</emph>
            } & </s>
            <s xml:id="echoid-s10389" xml:space="preserve">area A H I K L uti
              <lb/>
            {1/PA
              <emph style="super">n - 1</emph>
            } - {1/PH
              <emph style="super">n - 1</emph>
            } unde attractio corpuſculi P in circulum erit
              <lb/>
            ut {1/PA
              <emph style="super">n - 2</emph>
            } - {PA/PH
              <emph style="super">n - 1</emph>
            }.</s>
            <s xml:id="echoid-s10390" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10391" xml:space="preserve">Hæc Cl. </s>
            <s xml:id="echoid-s10392" xml:space="preserve">Chynæus in Philoſophical Principles of Natural reli-
              <lb/>
            gion eleganter explicuit §. </s>
            <s xml:id="echoid-s10393" xml:space="preserve">44. </s>
            <s xml:id="echoid-s10394" xml:space="preserve">Si n = i, & </s>
            <s xml:id="echoid-s10395" xml:space="preserve">P A = 0. </s>
            <s xml:id="echoid-s10396" xml:space="preserve">tum radius cir-
              <lb/>
            culi attrahentis productus coincidet cum Aſy mptoto P O, in quo
              <lb/>
            caſu area A H I L erit infinita, cum curva ſit Hyperbola vulgaris;
              <lb/>
            </s>
            <s xml:id="echoid-s10397" xml:space="preserve">& </s>
            <s xml:id="echoid-s10398" xml:space="preserve">P A = 0, ſive evaneſcente intervallo inter particulam & </s>
            <s xml:id="echoid-s10399" xml:space="preserve">circu-
              <lb/>
            lum attrahentem, erit attractio = P A X A H I L = 0 X ? </s>
            <s xml:id="echoid-s10400" xml:space="preserve">= i.</s>
            <s xml:id="echoid-s10401" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10402" xml:space="preserve">Si n = 1, & </s>
            <s xml:id="echoid-s10403" xml:space="preserve">P A = ?</s>
            <s xml:id="echoid-s10404" xml:space="preserve">, hoc eſt quando planum attrahens A D
              <lb/>
            poſitum eſt ad concurſum Hyperbolæ, cum ſuâ Aſymptoto P H,
              <lb/>
            tum arcus D H, cujus centrum eſt P, & </s>
            <s xml:id="echoid-s10405" xml:space="preserve">cujus radius eſt P D = P A
              <lb/>
            = ?</s>
            <s xml:id="echoid-s10406" xml:space="preserve">, coincidet cum A D, & </s>
            <s xml:id="echoid-s10407" xml:space="preserve">ideo A L coincidet cum H I, unde
              <lb/>
            P A X A H I L = ? </s>
            <s xml:id="echoid-s10408" xml:space="preserve">X 0 = i.</s>
            <s xml:id="echoid-s10409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10410" xml:space="preserve">Si n = i. </s>
            <s xml:id="echoid-s10411" xml:space="preserve">& </s>
            <s xml:id="echoid-s10412" xml:space="preserve">P A = a tum A H vocetur y, & </s>
            <s xml:id="echoid-s10413" xml:space="preserve">P H = x = a + y,
              <lb/>
            unde corpuſculum P a circulo attrahetur vi = P A X A H I L =
              <lb/>
            {y-yy/2a} + {y
              <emph style="super">3</emph>
            /3aa} - {y
              <emph style="super">4</emph>
            /4a
              <emph style="super">3</emph>
            } &</s>
            <s xml:id="echoid-s10414" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10415" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10416" xml:space="preserve">Si n = 2 & </s>
            <s xml:id="echoid-s10417" xml:space="preserve">P A = 0. </s>
            <s xml:id="echoid-s10418" xml:space="preserve">tum area A H I L erit plus quam infinita,
              <lb/>
            unde attractio erit A P X A H I L = 0 multiplicato per pluſquam
              <lb/>
            infinitum, unde liquet attractionem in hoc caſu, poſito P A = 0.</s>
            <s xml:id="echoid-s10419" xml:space="preserve"/>
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