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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[641.] EXPERIMENTUM CCXXVI.
Page: 672 (655)
[642.] EXPERIMENTUM CCXXVII.
Page: 672 (655)
[643.] EXPERIMENTUM CCXXVIII.
Page: 673 (656)
[644.] EXPERIMENTUM CCXXIX.
Page: 673 (656)
[645.] EXPERIMENTUM CCXXX.
Page: 673 (656)
[646.] EXPERIMENTUM CCXXXI.
Page: 673 (656)
[647.] EXPERIMENTUM CCXXXII.
Page: 673 (656)
[648.] EXPERIMENTUM CCXXXIII.
Page: 673 (656)
[649.] EXPERIMENTUM CCXXXIV.
Page: 673 (656)
[650.] EXPERIMENTUM CCXXXV.
Page: 674 (657)
[651.] EXPERIMENTUM CCXXXVI.
Page: 674 (657)
[652.] EXPERIMENTUM CCXXXVII.
Page: 674 (657)
[653.] EXPERIMENTUM CCXXXVIII.
Page: 674 (657)
[654.] EXPERIMENTUM CCXXXIX.
Page: 674 (657)
[655.] EXPERIMENTUM CCXL.
Page: 674 (657)
[656.] EXPERIMENTUM CCXLI.
Page: 674 (657)
[657.] EXPERIMENTUM CCXLII.
Page: 674 (657)
[658.] EXPERIMENTUM CCXLIII.
Page: 675 (658)
[659.] PROPOSITIO CXVIII.
Page: 675 (658)
[660.] PROPOSITIO CXIX.
Page: 677 (660)
[661.] Regula prima.
Page: 682 (665)
[662.] Regula Secunda.
Page: 683 (666)
[663.] Regula Tertia.
Page: 683 (666)
[664.] TABULA
Page: 684 (667)
[665.] CAPUT DECIMUM. Tentamen de corporum Duritie.
Page: 685 (668)
[666.] EPHEMERIDES METEOROLOGICÆ ULTRAJECTINÆ ANNI MDCCXXVIII.
Page: 690 (673)
[667.] FINIS.
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            maximum: </s>
            <s xml:id="echoid-s15872" xml:space="preserve">& </s>
            <s xml:id="echoid-s15873" xml:space="preserve">quia A C
              <emph style="super">q</emph>
            eſt majus rectangulo A E B, poterit ex E
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            ſuſpendi pondus multo majus: </s>
            <s xml:id="echoid-s15874" xml:space="preserve">imo quia A E B poteſt fieri infinite
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            parvum rectangulum, ſi A E fiat infinite parva, poterit ex E ſu-
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            ſpendi pondus inſinite magnum reſpectu ponderis ex C ſuſpen-
              <lb/>
            dendi.</s>
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          <p>
            <s xml:id="echoid-s15876" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s15877" xml:space="preserve">Quia pondus P ex medio C ipſius A B ſuſpenſum poteſt
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            eſſe quadruplo majus pondere ab extremo ſuſpenſo, ſi ſolidum A B
              <lb/>
            ab altero extremo parieti fuerit infixum, erit pondus P ex medio ſolidi
              <lb/>
            A B duobus fulcris impoſiti, ad pondus ex extremo ſolidi A B pa-
              <lb/>
            rieti infixi, uti
              <emph style="ol">AB</emph>
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            ad
              <emph style="ol">AC</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s15878" xml:space="preserve">vel uti 4
              <emph style="ol">AC</emph>
              <emph style="super">q</emph>
            ad
              <emph style="ol">AC</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s15879" xml:space="preserve">adeoque erit
              <lb/>
            pondus ex E ſuſpenſum, poſito ſolido ſuper duobus fulcris, ad pon-
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            dus ab extremo ſolidi parieti infixi annexum & </s>
            <s xml:id="echoid-s15880" xml:space="preserve">maximum, uti 4 A C
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            X C B ad A E X E B.</s>
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          <head xml:id="echoid-head726" xml:space="preserve">PROPOSITIO CIV.</head>
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            <s xml:id="echoid-s15882" xml:space="preserve">Tab. </s>
            <s xml:id="echoid-s15883" xml:space="preserve">XXIII. </s>
            <s xml:id="echoid-s15884" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15885" xml:space="preserve">40. </s>
            <s xml:id="echoid-s15886" xml:space="preserve">Dato pondere maximo P, quod ex medio
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            parallelopipedi, priſmatis vel Cylindri ferri poteft, datoque alio
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            majori, invenire locum in ſolido ex quo ſuſpendi poterit, & </s>
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            <s xml:id="echoid-s15890" xml:space="preserve">pondus majus ſit = d p. </s>
            <s xml:id="echoid-s15891" xml:space="preserve">ubi d notat
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            numerum vel integrum, vel integrum cum fractione quacunque.
              <lb/>
            </s>
            <s xml:id="echoid-s15892" xml:space="preserve">vocetur C A, a. </s>
            <s xml:id="echoid-s15893" xml:space="preserve">C E, x. </s>
            <s xml:id="echoid-s15894" xml:space="preserve">erit A E = a-x. </s>
            <s xml:id="echoid-s15895" xml:space="preserve">& </s>
            <s xml:id="echoid-s15896" xml:space="preserve">E B = a + x. </s>
            <s xml:id="echoid-s15897" xml:space="preserve">& </s>
            <s xml:id="echoid-s15898" xml:space="preserve">re-
              <lb/>
            ctangulum A E B = aa-xx.</s>
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          <p>
            <s xml:id="echoid-s15900" xml:space="preserve">Quia demonſtratum eſt pondus P ſuſpenſum ex medio C eſſe ad
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            pondus d p ſuſpendendum ex E, uti rectangulum A E B ad qua-
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            dratum A C erit a a-xx, a a:</s>
            <s xml:id="echoid-s15901" xml:space="preserve">: p. </s>
            <s xml:id="echoid-s15902" xml:space="preserve">d p. </s>
            <s xml:id="echoid-s15903" xml:space="preserve">adeoque x x = {a a -a a p.</s>
            <s xml:id="echoid-s15904" xml:space="preserve">/d p}
              <lb/>
            & </s>
            <s xml:id="echoid-s15905" xml:space="preserve">extracta radice erit x =aa-{aa/d} Ut ergo conſtructio fiat, ſupra
              <lb/>
            A C dimidiam ſolidi longitudinem deſcribatur ſemicirculus: </s>
            <s xml:id="echoid-s15906" xml:space="preserve">fiat
              <lb/>
            hæc proportio d. </s>
            <s xml:id="echoid-s15907" xml:space="preserve">a:</s>
            <s xml:id="echoid-s15908" xml:space="preserve">: a, {aa/d}. </s>
            <s xml:id="echoid-s15909" xml:space="preserve">quæ ſit = A F: </s>
            <s xml:id="echoid-s15910" xml:space="preserve">hæc accommodetur ſe-
              <lb/>
            micirculo, ut una extremitate jaceat in A, tum ducatur F C, ca-
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            piatur C E = C F, eritque punctum E quæſitum, ex quo pondus d p
              <lb/>
            ſuſpendi poterit & </s>
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