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 Notes

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              <pb o="556" file="0572" n="573" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            paretur nunc Cohærentia hujus parallelopipedi, cum ea datæ Tra-
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            bis, quæ erit in ratione compoſita ex duplicata altitudinis & </s>
            <s xml:id="echoid-s13216" xml:space="preserve">ſim-
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            plici latitudinis, adeoque uti a a b ad A A B. </s>
            <s xml:id="echoid-s13217" xml:space="preserve">per Prop. </s>
            <s xml:id="echoid-s13218" xml:space="preserve">X X I & </s>
            <s xml:id="echoid-s13219" xml:space="preserve">
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            XXII. </s>
            <s xml:id="echoid-s13220" xml:space="preserve">pondera igitur parallelopipedo & </s>
            <s xml:id="echoid-s13221" xml:space="preserve">Trabi appendenda erunt
              <lb/>
            ut hæ Cohærentiæ, adeoque a a b. </s>
            <s xml:id="echoid-s13222" xml:space="preserve">A A B:</s>
            <s xml:id="echoid-s13223" xml:space="preserve">: {l p/L} x. </s>
            <s xml:id="echoid-s13224" xml:space="preserve">quare erit
              <lb/>
            x = {A A B l p.</s>
            <s xml:id="echoid-s13225" xml:space="preserve">/a a b L} Hoc pondus extremitati Trabis appendi poſſet, ſi
              <lb/>
            ipſa nullam gravitatem haberet; </s>
            <s xml:id="echoid-s13226" xml:space="preserve">nam non conſideravimus gravita-
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            tem parallelopipedi ejusdem cum Trabe longitudinis: </s>
            <s xml:id="echoid-s13227" xml:space="preserve">ſed trabs
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            habet gravitatem = G, ejusque centrum gravitatis eſt in dimidiâ
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            longitudine, ſive ad {1/2} L. </s>
            <s xml:id="echoid-s13228" xml:space="preserve">adeoque momentum illius erit {1/2} L G.
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            </s>
            <s xml:id="echoid-s13229" xml:space="preserve">quod idem manebit poſito dimidio ponderis ad duplo majorem di-
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            ſtantiam, ergo hac quantitate pondus appenſum imminendum eſt,
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            quod manebit = {A A B l p-{1/2}/a a b L} G.</s>
            <s xml:id="echoid-s13230" xml:space="preserve"/>
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            <s xml:id="echoid-s13231" xml:space="preserve">Quia hoc Problema eſt maximæ utilitatis, Exemplo ulterius il-
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            luſtrabo: </s>
            <s xml:id="echoid-s13232" xml:space="preserve">Sit Trabs Quercica, unum pedem alta & </s>
            <s xml:id="echoid-s13233" xml:space="preserve">lata, 10 pedes
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            longa, altero extremo parieti horizontaliter infixa, quæritur quan-
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            tum ponderis ab altero extremo ferre poſſit?</s>
            <s xml:id="echoid-s13234" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s13235" xml:space="preserve">Experimentum CVIII. </s>
            <s xml:id="echoid-s13236" xml:space="preserve">hujus Capitis exhibet parallelopipedum
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            Quercicum latitudinis & </s>
            <s xml:id="echoid-s13237" xml:space="preserve">altitudinis o, 25 poll. </s>
            <s xml:id="echoid-s13238" xml:space="preserve">quod ad diſtantiam
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            8 {1/2} pollicum ſuſtinuit fere uncias 48, ab his enim ruprum fuit:
              <lb/>
            </s>
            <s xml:id="echoid-s13239" xml:space="preserve">adeoque hoc idem longitudinis 10 pedum ferre tantum ab extremo
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            potuiſſet uncias 3 {2/5}, non conſiderando ejus gravitatem: </s>
            <s xml:id="echoid-s13240" xml:space="preserve">ſunt Co-
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            hærentiæ hujus ligni & </s>
            <s xml:id="echoid-s13241" xml:space="preserve">propoſitæ Trabis, uti quadrata altitudinum
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            ductain latitudines ad ſe mutuo ſunt, quæ inter ſe uti 5 ad 47616. </s>
            <s xml:id="echoid-s13242" xml:space="preserve">
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            adeoque uncias feret Trabs 34385 {17/29}, ſive libras 2149. </s>
            <s xml:id="echoid-s13243" xml:space="preserve">abextremo,
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            ſi careret gravitate: </s>
            <s xml:id="echoid-s13244" xml:space="preserve">quam cum habet, ejus ratio tenenda eſt: </s>
            <s xml:id="echoid-s13245" xml:space="preserve">pes
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            Cubicus Ligni Quercici modo cæſi eſt plerumque librarum 59 {1/2}, pon-
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            dus diſcrepat paululum pro variâ ſiccitate: </s>
            <s xml:id="echoid-s13246" xml:space="preserve">unde gravitas Trabis eſt
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            librar. </s>
            <s xml:id="echoid-s13247" xml:space="preserve">595. </s>
            <s xml:id="echoid-s13248" xml:space="preserve">quæ ſuſpenſa concipiatur ex dimidia longitudine tra-
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            bis, agit enim hæc gravitas ex centro in dimidia longitudine hæ-
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            rente; </s>
            <s xml:id="echoid-s13249" xml:space="preserve">verum habet pondus dimidium ex duplo majori intervallo
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            momentum idem, quare ad extremitatem Trabis appenſæ </s>
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