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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            <s xml:id="echoid-s14773" xml:space="preserve">
              <pb o="597" file="0613" n="614" rhead="CORPORUM FIRMORUM."/>
            tas parabolæ, dabit {2/15} a a c r. </s>
            <s xml:id="echoid-s14774" xml:space="preserve">eodem modo reperitur momentum
              <lb/>
            ſegmenti D B E = {2a a c b
              <emph style="super">10</emph>
            /15 r
              <emph style="super">9</emph>
            }. </s>
            <s xml:id="echoid-s14775" xml:space="preserve">Eſt autem Cohærentia baſeos Parabo-
              <lb/>
            læ A B C = 8r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14776" xml:space="preserve">& </s>
            <s xml:id="echoid-s14777" xml:space="preserve">Cohærentia baſeos D G E = 8b3. </s>
            <s xml:id="echoid-s14778" xml:space="preserve">quare momen-
              <lb/>
            tum Parabolæ A B C, ad ſuam Cohærentiam eſt, ut {2/15} a a c r ad 8r3.
              <lb/>
            </s>
            <s xml:id="echoid-s14779" xml:space="preserve">& </s>
            <s xml:id="echoid-s14780" xml:space="preserve">momentum ſegmenti D B E ad ſuam Cohærentiam, uti {2a a c b
              <emph style="super">10</emph>
            /15 r
              <emph style="super">9</emph>
            .</s>
            <s xml:id="echoid-s14781" xml:space="preserve">}
              <lb/>
            ad 8b
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14782" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14783" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14784" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14785" xml:space="preserve">Ergo ſolidi Parabolici A B C, Cohærentia ad ſuum momen-
              <lb/>
            tum ex gravitate eſt in minori ratione, quam Cohærentia ſegmenti
              <lb/>
            D B E ad ſuum momentum. </s>
            <s xml:id="echoid-s14786" xml:space="preserve">Nam Cohærentia A B C ad ſuum mo-
              <lb/>
            mentum eſt ut r
              <emph style="super">3</emph>
            ad {2/15} a a c r. </s>
            <s xml:id="echoid-s14787" xml:space="preserve">ſive ut r
              <emph style="super">9</emph>
            ad {2/15} a a c r
              <emph style="super">7</emph>
            . </s>
            <s xml:id="echoid-s14788" xml:space="preserve">eſt Cohæren-
              <lb/>
            tia ſegmenti D B E ad ſuum momentum uti b3 ad {2 a a c b
              <emph style="super">10</emph>
            /15 r
              <emph style="super">9</emph>
            .</s>
            <s xml:id="echoid-s14789" xml:space="preserve">} ſive uti
              <lb/>
            r9 ad {2/15} a a c b
              <emph style="super">7</emph>
            . </s>
            <s xml:id="echoid-s14790" xml:space="preserve">quia autem r eſt major quam b. </s>
            <s xml:id="echoid-s14791" xml:space="preserve">erit ratio r
              <emph style="super">9</emph>
            ad {2/15}
              <lb/>
            a a c r
              <emph style="super">7</emph>
            minor quam r
              <emph style="super">9</emph>
            , ad {2/15} a a c b7.</s>
            <s xml:id="echoid-s14792" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14793" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14794" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14795" xml:space="preserve">Ergo majus pondus poterit vertici B ſegmenti D B E
              <lb/>
            appendi, quam paraboloidis A B C.</s>
            <s xml:id="echoid-s14796" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div553" type="section" level="1" n="553">
          <head xml:id="echoid-head667" xml:space="preserve">PROPOSITIO LXXIV.</head>
          <p style="it">
            <s xml:id="echoid-s14797" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14798" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14799" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s14800" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14801" xml:space="preserve">Dato ſegmento præcedentis Paraboloidis
              <lb/>
            D B E gravi, atque pondere P maximo, quod geſtari poſſit, inve-
              <lb/>
            nire pondus ex vertice B Parabolæ A B C geſtandum.</s>
            <s xml:id="echoid-s14802" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14803" xml:space="preserve">Quantitatibus deſignatis ut ante, & </s>
            <s xml:id="echoid-s14804" xml:space="preserve">pondere P vocato = p. </s>
            <s xml:id="echoid-s14805" xml:space="preserve">quæ-
              <lb/>
            ſito = x. </s>
            <s xml:id="echoid-s14806" xml:space="preserve">ordinanda erit hæc proportio {2 a a c b
              <emph style="super">10</emph>
            /15 r
              <emph style="super">9</emph>
            } + {a b
              <emph style="super">4</emph>
            p. </s>
            <s xml:id="echoid-s14807" xml:space="preserve">8 b
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14808" xml:space="preserve">:/r
              <emph style="super">4</emph>
            }
              <lb/>
            {2/15} a a c r + a x. </s>
            <s xml:id="echoid-s14809" xml:space="preserve">8r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14810" xml:space="preserve">ex quibus eruitur x = {2 a c b 7/15 r
              <emph style="super">6</emph>
            } + {b p/r}-{2/15
              <unsure/>
            } a c r.</s>
            <s xml:id="echoid-s14811" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div554" type="section" level="1" n="554">
          <head xml:id="echoid-head668" xml:space="preserve">PROPOSITIO LXXV.</head>
          <p style="it">
            <s xml:id="echoid-s14812" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s14813" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s14814" xml:space="preserve">Fig. </s>
            <s xml:id="echoid-s14815" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14816" xml:space="preserve">Sit Parabola Apolloniana A D B, cujus
              <lb/>
            Tangens ſit T A, ducta ſit T B parallela ad A D, circa A T veluti
              <lb/>
            axin & </s>
            <s xml:id="echoid-s14817" xml:space="preserve">radio T B circumagatur Parabola, deſcribetur corpus pa-
              <lb/>
            raboliforme A C B A fig. </s>
            <s xml:id="echoid-s14818" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14819" xml:space="preserve">cujus baſis eſt C T B, dico hoc </s>
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