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 contents

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[551.] PROPOSITIO LXXII.
Page: 612 (595)
[552.] PROPOSITIO LXXIII.
Page: 613 (596)
[553.] PROPOSITIO LXXIV.
Page: 614 (597)
[554.] PROPOSITIO LXXV.
Page: 614 (597)
[555.] PROPOSITIO LXXVI.
Page: 616 (599)
[556.] PROPOSITIO LXXVII.
Page: 616 (599)
[557.] PROPOSITIO LXXVIII.
Page: 617 (600)
[558.] PROPOSITIO LXXIX.
Page: 618 (601)
[559.] PROPOSITIO LXXX.
Page: 619 (602)
[560.] PROPOSITIO LXXXI.
Page: 619 (602)
[561.] PROPOSITIO LXXXII.
Page: 619 (602)
[562.] PROPOSITIO LXXXIII.
Page: 620 (603)
[563.] PROPOSITIO LXXXIV.
Page: 621 (604)
[564.] De Corporibus Hyperbolicis. PROPOSITIO LXXXV.
Page: 622 (605)
[565.] PROPOSITIO LXXXVI.
Page: 622 (605)
[566.] PROPOSITIO LXXXVII.
Page: 623 (606)
[567.] PROPOSITIO LXXXVIII.
Page: 623 (606)
[568.] PROPOSITIO LXXXIX.
Page: 624 (607)
[569.] De Hemisphæriis. PROPOSITIO XC.
Page: 624 (607)
[570.] PROPOSITIO XCI.
Page: 625 (608)
[571.] PROPOSITIO XCII.
Page: 625 (608)
[572.] PROPOSITIO XCIII.
Page: 626 (609)
[573.] CAPUT SEXTUM. De Cohærentia Corporum quibus fulcrum ſupponitur. PROPOSITIO XCIV.
Page: 627 (610)
[574.] EXPERIMENTUM CLXXXVI.
Page: 629 (612)
[575.] PROPOSITIO XCV.
Page: 629 (612)
[576.] PROPOSITIO CXVI.
Page: 630 (613)
[577.] CAPUT SEPTIMUM. De Cohærentia reſpectiva ſolidorum duobus fulcris impoſitorum.
Page: 631 (614)
[578.] EXPERIMENTUM CLXXXVII.
Page: 632 (615)
[579.] EXPERIMENTUM CLXXXVIII.
Page: 633 (616)
[580.] EXPERIMENTUM CLXXXIX.
Page: 633 (616)
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        <div xml:id="echoid-div564" type="section" level="1" n="564">
          <head xml:id="echoid-head678" style="it" xml:space="preserve">De Corporibus Hyperbolicis.</head>
          <head xml:id="echoid-head679" xml:space="preserve">PROPOSITIO LXXXV.</head>
          <p>
            <s xml:id="echoid-s15091" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15092" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15093" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15094" xml:space="preserve">10. </s>
            <s xml:id="echoid-s15095" xml:space="preserve">Corporis Hyperbolici generati ex circum-
              <lb/>
            gyrata Hyperbola A B D circa axin A D, cujus baſis E D B eſt pa-
              <lb/>
            rieti perpendiculari ad horizontem affixa, determinare momentum
              <lb/>
            ex gravitate, & </s>
            <s xml:id="echoid-s15096" xml:space="preserve">Cohærentiam baſeos B D E reſpectivam.</s>
            <s xml:id="echoid-s15097" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15098" xml:space="preserve">Vocetur A D, a. </s>
            <s xml:id="echoid-s15099" xml:space="preserve">& </s>
            <s xml:id="echoid-s15100" xml:space="preserve">axis Hyperbolæ primus A L, 2 b. </s>
            <s xml:id="echoid-s15101" xml:space="preserve">B D radius
              <lb/>
            baſeos, r. </s>
            <s xml:id="echoid-s15102" xml:space="preserve">circumferentia circuli a puncto B deſ
              <unsure/>
            cripti, c. </s>
            <s xml:id="echoid-s15103" xml:space="preserve">tum erue-
              <lb/>
            tur ſoliditas corporis Hyperbolici = {a a c r + 3 a b c r.</s>
            <s xml:id="echoid-s15104" xml:space="preserve">/6 a + 12 b} Centri
              <lb/>
            gravitatis in axe A D diſtantia â puncto D eſt = {a a + 4 a b.</s>
            <s xml:id="echoid-s15105" xml:space="preserve">/4 a + 12 b}
              <lb/>
            Soliditate igitur per hanc diſtantiam â D multiplicata, habebitur
              <lb/>
            momentum corporis Hyperbolici
              <lb/>
            {a
              <emph style="super">4</emph>
            c r + 7 a
              <emph style="super">3</emph>
            b c r + 12 a a b b c r.</s>
            <s xml:id="echoid-s15106" xml:space="preserve">/24 a a + 120 a b + 144 b b}
              <lb/>
            Cohærentia autem baſeos eſt = 8 r
              <emph style="super">3</emph>
            .</s>
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          <head xml:id="echoid-head680" xml:space="preserve">PROPOSITIO LXXXVI.</head>
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            <s xml:id="echoid-s15109" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s15110" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15111" xml:space="preserve">10. </s>
            <s xml:id="echoid-s15112" xml:space="preserve">Corporis Hyperbolici A B E Cohærentia, eſt
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            ad Cohærentiam ſegmenti F A G, in ratione compoſita ex D A X
              <lb/>
            D L X B E. </s>
            <s xml:id="echoid-s15113" xml:space="preserve">ad H A X H L X G F.</s>
            <s xml:id="echoid-s15114" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15115" xml:space="preserve">A L ſupponitur axis Hyperbolæ primus, ponatur pondus I pen-
              <lb/>
            dens ex vertice Hyperbolæ A B E eſſe ſummum, quod appendi poſ-
              <lb/>
            ſit, adeoque æquale Cohærentiæ baſeos B D E. </s>
            <s xml:id="echoid-s15116" xml:space="preserve">& </s>
            <s xml:id="echoid-s15117" xml:space="preserve">pondus K pen-
              <lb/>
            dens ex vertice ſegmenti F A G etiam ſummum, ſeu æquale Co-
              <lb/>
            hærentiæ baſeos F G, tum pondus I eſt ad pondus K in ratione
              <lb/>
            Cubi B E ad Cubum F G, ſive
              <emph style="ol">B E
                <emph style="super">q</emph>
              </emph>
            X B E ad
              <emph style="ol">F G</emph>
            X F G. </s>
            <s xml:id="echoid-s15118" xml:space="preserve">ſed eſt
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            B E ad
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                <emph style="super">q</emph>
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            ex natura Hyperbolæ, uti D A X D L ad H A
              <lb/>
            X H L. </s>
            <s xml:id="echoid-s15119" xml:space="preserve">adeoque his loco quadratorum poſitis, erit pondus I ad pon-
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            dus K, uti D A X D L X B E, ad H A X H L X F G.</s>
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