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

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            <s xml:id="echoid-s14819" xml:space="preserve">
              <pb o="598" file="0614" n="615" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            baſi C B parieti infixum, ita ut axis A T ſit horizontalis, ſua gra-
              <lb/>
            vitate eſſe in omni ſectione æqualis Cohærentiæ.</s>
            <s xml:id="echoid-s14820" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14821" xml:space="preserve">Propoſuit hoc Cl. </s>
            <s xml:id="echoid-s14822" xml:space="preserve">Leibnitſius in Actis Lipſ. </s>
            <s xml:id="echoid-s14823" xml:space="preserve">A°. </s>
            <s xml:id="echoid-s14824" xml:space="preserve">1684 inſtar ad-
              <lb/>
            ditamenti, quod abſque demonſtratione reliquit, quam hic adde-
              <lb/>
            mus: </s>
            <s xml:id="echoid-s14825" xml:space="preserve">Vocetur A T, a. </s>
            <s xml:id="echoid-s14826" xml:space="preserve">T B, r. </s>
            <s xml:id="echoid-s14827" xml:space="preserve">circumferentia circuli, cujus T B
              <lb/>
            eſt radius, ſit = c. </s>
            <s xml:id="echoid-s14828" xml:space="preserve">Erit ſoliditas corporis A C B = {1/10} a c r. </s>
            <s xml:id="echoid-s14829" xml:space="preserve">Cen-
              <lb/>
            trum vero gravitatis eſt in axe A T, diſſitum a puncto T = {1/6} a, un-
              <lb/>
            de momentum gravitatis in hoc corpore A C B eſt = {1/60} a a c r. </s>
            <s xml:id="echoid-s14830" xml:space="preserve">Co-
              <lb/>
            hærentia autem eſt ut Cubus baſeos C B = 8 r
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s14831" xml:space="preserve">fiat ſectio in O, pla-
              <lb/>
            no F O E parallelo baſi C T B. </s>
            <s xml:id="echoid-s14832" xml:space="preserve">voceturque A O = d. </s>
            <s xml:id="echoid-s14833" xml:space="preserve">erit O E = {d d r/a a}.
              <lb/>
            </s>
            <s xml:id="echoid-s14834" xml:space="preserve">quia T B. </s>
            <s xml:id="echoid-s14835" xml:space="preserve">O E:</s>
            <s xml:id="echoid-s14836" xml:space="preserve">: peripheria circuli â B deſcripti, ad peripheriam ab E. </s>
            <s xml:id="echoid-s14837" xml:space="preserve">
              <lb/>
            erit hæc peripheria = {c d d/a a}. </s>
            <s xml:id="echoid-s14838" xml:space="preserve">quare ſoliditas corporis A F O E
              <lb/>
            = {c d
              <emph style="super">5</emph>
            r.</s>
            <s xml:id="echoid-s14839" xml:space="preserve">/10a
              <emph style="super">4</emph>
            } Centrum gravitatis in A F E diſtat ab O = {1/6} d. </s>
            <s xml:id="echoid-s14840" xml:space="preserve">adeoque
              <lb/>
            erit momentum hujus corporis ex gravitate = {c d
              <emph style="super">6</emph>
            r.</s>
            <s xml:id="echoid-s14841" xml:space="preserve">/60 a
              <emph style="super">4</emph>
            } Cohærentia
              <lb/>
            baſeos E O F eſt uti Cubus ex E F = {8d
              <emph style="super">6</emph>
            r
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14842" xml:space="preserve">/a
              <emph style="super">6</emph>
            } Si igitur momenta
              <lb/>
            gravitatis in corpore A C B & </s>
            <s xml:id="echoid-s14843" xml:space="preserve">A F E ſint ad Cohærentias ſuarum
              <lb/>
            baſium in eadem ratione, erunt quantitates proportionales, ordi-
              <lb/>
            nentur igitur in proportionem
              <lb/>
            {1/60} a a c r. </s>
            <s xml:id="echoid-s14844" xml:space="preserve">8r
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s14845" xml:space="preserve">: {1 c d
              <emph style="super">6</emph>
            r/60 a
              <emph style="super">4</emph>
            }, {8d
              <emph style="super">6</emph>
            r
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14846" xml:space="preserve">/a
              <emph style="super">6</emph>
            }</s>
          </p>
          <p>
            <s xml:id="echoid-s14847" xml:space="preserve">Multiplicatis extremis mediisque terminis, habetur
              <lb/>
            {1/60} a a c r X {8 d
              <emph style="super">6</emph>
            r
              <emph style="super">3</emph>
            .</s>
            <s xml:id="echoid-s14848" xml:space="preserve">/a
              <emph style="super">6</emph>
            } & </s>
            <s xml:id="echoid-s14849" xml:space="preserve">{1 c d
              <emph style="super">6</emph>
            r/60 a
              <emph style="super">4</emph>
            } X 8 r
              <emph style="super">3</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s14850" xml:space="preserve">quæ quantitates ſunt inter ſe æquales, adeoque priores erant pro-
              <lb/>
            portionales, unde momenta cujuslibet ſectionis in hoc corpore
              <lb/>
            paraboliformi ſunt ſemper ad ſuas Cohærentias in eadem propor-
              <lb/>
            tione, hoc eſt, erit corpus grave ubivis æquabilis reſiſtentiæ. </s>
            <s xml:id="echoid-s14851" xml:space="preserve">
              <lb/>
            Q. </s>
            <s xml:id="echoid-s14852" xml:space="preserve">E. </s>
            <s xml:id="echoid-s14853" xml:space="preserve">D.</s>
            <s xml:id="echoid-s14854" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14855" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s14856" xml:space="preserve">Si corpus paraboliforme A B C ſecetur bifariam plano ho-
              <lb/>
            rizontali tranſeunte per axem A T, erit corpus A T B E A in qua-
              <lb/>
            libet Sectione O E æquabilis Cohærentiæ.</s>
            <s xml:id="echoid-s14857" xml:space="preserve"/>
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