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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[531.] EXPERIMENTUM CLXXXV.
Page: 593 (576)
[532.] PROPOSITIO LIII.
Page: 596 (579)
[533.] PROPOSITIO LIV.
Page: 598 (581)
[534.] PROPOSITIO LV.
Page: 599 (582)
[535.] PROPOSITIO LVI.
Page: 600 (583)
[536.] PROPOSITIO LVII.
Page: 601 (584)
[537.] De Conis & Pyramidibus. PROPOSITIO LVIII.
Page: 602 (585)
[538.] PROPOSITIO LIX.
Page: 602 (585)
[539.] PROPOSITIO LX.
Page: 603 (586)
[540.] PROPOSITIO LXI.
Page: 604 (587)
[541.] PROPOSITIO LXII.
Page: 605 (588)
[542.] PROPOSITIO LXIII.
Page: 605 (588)
[543.] De Conidibus Parabolicis. PROPOSITIO LXIV.
Page: 606 (589)
[544.] PROPOSITIO LXV.
Page: 607 (590)
[545.] PROPOSITIO LXVI.
Page: 608 (591)
[546.] PROPOSITIO LXVII.
Page: 609 (592)
[547.] PROPOSITIO LXVIII.
Page: 610 (593)
[548.] PROPOSITIO LXIX.
Page: 611 (594)
[549.] PROPOSITIO LXX.
Page: 611 (594)
[550.] PROPOSITIO LXXI.
Page: 612 (595)
[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)
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        <div xml:id="echoid-div555" type="section" level="1" n="555">
          <head xml:id="echoid-head669" xml:space="preserve">PROPOSITIO LXXVI.</head>
          <p style="it">
            <s xml:id="echoid-s14858" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14859" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14860" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14861" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14862" xml:space="preserve">Dato ſegmento gravi E A F corporis ejusdem
              <lb/>
            par aboliformis A B C & </s>
            <s xml:id="echoid-s14863" xml:space="preserve">pondere P maximo appenſo vertici A; </s>
            <s xml:id="echoid-s14864" xml:space="preserve">in-
              <lb/>
            venire pondus maximum, quod ex vertice eodem A ſolidi gravis
              <lb/>
            B A C ſuſpendi poterit.</s>
            <s xml:id="echoid-s14865" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14866" xml:space="preserve">Quantitibus vocatis ut ante, erit momentum ſegmenti E A F
              <lb/>
            ex gravitate = {1 d
              <emph style="super">6</emph>
            c r/60a
              <emph style="super">4</emph>
            }. </s>
            <s xml:id="echoid-s14867" xml:space="preserve">pondus P vocetur = p. </s>
            <s xml:id="echoid-s14868" xml:space="preserve">erit hujus momen-
              <lb/>
            tum = p d. </s>
            <s xml:id="echoid-s14869" xml:space="preserve">pondus quæſitum vocetur = x, erit momentum = a x. </s>
            <s xml:id="echoid-s14870" xml:space="preserve">qua-
              <lb/>
            re ſegmenti momentum E A F una cum ſuo pondere P debet ha-
              <lb/>
            bere eandem rationem ad ſuam Cohærentiam, uti momentum A B C
              <lb/>
            cum ſuo pondere x ad ſuam, unde ordinanda erit hæc proportio
              <lb/>
            {1 d
              <emph style="super">6</emph>
            c r/60 a
              <emph style="super">4</emph>
            } + d p. </s>
            <s xml:id="echoid-s14871" xml:space="preserve">{8 d
              <emph style="super">6</emph>
            r
              <emph style="super">3</emph>
            /a
              <emph style="super">6</emph>
            }:</s>
            <s xml:id="echoid-s14872" xml:space="preserve">: {1/66
              <unsure/>
            } a a c r. </s>
            <s xml:id="echoid-s14873" xml:space="preserve">+ a x. </s>
            <s xml:id="echoid-s14874" xml:space="preserve">8 r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14875" xml:space="preserve">unde erit
              <lb/>
            x = {a
              <emph style="super">5</emph>
            p/d
              <emph style="super">5</emph>
            }.</s>
            <s xml:id="echoid-s14876" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div556" type="section" level="1" n="556">
          <head xml:id="echoid-head670" xml:space="preserve">PROPOSITIO LXXVII.</head>
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            <s xml:id="echoid-s14877" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14878" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14879" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14880" xml:space="preserve">5. </s>
            <s xml:id="echoid-s14881" xml:space="preserve">Sit Parabola D A B, in qua D B or dinata
              <lb/>
            habeatur pro axe, circa quem parabola circum volvatur, genera-
              <lb/>
            bitur corpus paraboliforme, cujus momentum ex gravitate & </s>
            <s xml:id="echoid-s14882" xml:space="preserve">Cohæ-
              <lb/>
            rentia reſpectiva poſtulentur determinanda, ut & </s>
            <s xml:id="echoid-s14883" xml:space="preserve">ſegmenti F K B F.</s>
            <s xml:id="echoid-s14884" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14885" xml:space="preserve">Vocetur A D, r. </s>
            <s xml:id="echoid-s14886" xml:space="preserve">D B, a. </s>
            <s xml:id="echoid-s14887" xml:space="preserve">peripheria circuli a puncto A deſcri-
              <lb/>
            bendi ſit = c. </s>
            <s xml:id="echoid-s14888" xml:space="preserve">erit ſoliditas corporis paraboliformis = {4/45} a c r: </s>
            <s xml:id="echoid-s14889" xml:space="preserve">diſtat
              <lb/>
            autem centrum gravitatis in axe D B a puncto D, quantitate {5/16} a.
              <lb/>
            </s>
            <s xml:id="echoid-s14890" xml:space="preserve">adeoque erit momentum ex gravitate hujus ſolidi = {1/12} a a c r. </s>
            <s xml:id="echoid-s14891" xml:space="preserve">Co-
              <lb/>
            hærentia vero reſpectiva erit = 8r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14892" xml:space="preserve">ut autem momentum ſeg-
              <lb/>
            menti F K B C determinemus, vocetur A E, x. </s>
            <s xml:id="echoid-s14893" xml:space="preserve">erit E D = r - x. </s>
            <s xml:id="echoid-s14894" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s14895" xml:space="preserve">C B = a-a{x.</s>
            <s xml:id="echoid-s14896" xml:space="preserve">/r} peripheria a puncto F circuli deſcribenda erit
              <lb/>
            = {c r- c x.</s>
            <s xml:id="echoid-s14897" xml:space="preserve">/r} quare ſoliditas hujus ſegmenti </s>
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