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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[601.] PROPOSITIO XCIX.
Page: 643 (626)
[602.] PROPOSITIO C.
Page: 644 (627)
[603.] PROPOSITIO CI.
Page: 644 (627)
[604.] PROPOSITIO CII.
Page: 645 (628)
[605.] EXPERIMENTUM CCVIII.
Page: 645 (628)
[606.] PROPOSITIO CIII.
Page: 646 (629)
[607.] PROPOSITIO CIV.
Page: 647 (630)
[608.] PROPOSITIO CV.
Page: 648 (631)
[609.] PROPOSITIO CVI.
Page: 648 (631)
[610.] PROPOSITIO CVII.
Page: 649 (632)
[611.] PROPOSITIO CVIII.
Page: 650 (633)
[612.] PROPOSITIO CIX.
Page: 650 (633)
[613.] PROPOSITIO CX.
Page: 651 (634)
[614.] PROPOSITIO CXI.
Page: 652 (635)
[615.] PROPOSITIO CXII.
Page: 653 (636)
[616.] PROPOSITIO CXIII.
Page: 653 (636)
[617.] PROPOSITIO CXIV.
Page: 654 (637)
[618.] PROPOSITIO CXV.
Page: 654 (637)
[619.] PROPOSITIO CXVI.
Page: 655 (638)
[620.] PROPOSITIO CXVII.
Page: 655 (638)
[621.] CAPUT OCTAVUM. De Cohærentia ſolidorum utrimque a foramine arcto exceptorum.
Page: 656 (639)
[622.] EXPERIMENTUM CCIX.
Page: 657 (640)
[623.] EXPERIMENTUM CCX.
Page: 657 (640)
[624.] EXPERIMENTUM CCXI.
Page: 658 (641)
[625.] EXPERIMENTUM CCXII.
Page: 658 (641)
[626.] EXPERIMENTUM CCXIII.
Page: 659 (642)
[627.] EXPERIMENTUM CCXIV.
Page: 659 (642)
[628.] EXPERIMENTUM CCXV.
Page: 659 (642)
[629.] EXPERIMENTUM CCXVI.
Page: 660 (643)
[630.] EXPERIMENTUM CCXVII.
Page: 660 (643)
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              <pb o="560" file="0576" n="577" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            rallelopipedum A E F D, quod vix vix reſiſtat ſuo ponderi.</s>
            <s xml:id="echoid-s13348" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13349" xml:space="preserve">Sit a e = e o, & </s>
            <s xml:id="echoid-s13350" xml:space="preserve">vocetur a. </s>
            <s xml:id="echoid-s13351" xml:space="preserve">a k = b. </s>
            <s xml:id="echoid-s13352" xml:space="preserve">A D = d. </s>
            <s xml:id="echoid-s13353" xml:space="preserve">A E quaeſita ſit = x.</s>
            <s xml:id="echoid-s13354" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13355" xml:space="preserve">Erit parallelopipedum a e o k = a a b. </s>
            <s xml:id="echoid-s13356" xml:space="preserve">ejuſque momentum ex gra-
              <lb/>
            vitate = {1/2} a a b b. </s>
            <s xml:id="echoid-s13357" xml:space="preserve">Cohærentia baſeos = a
              <emph style="super">3</emph>
            parallelopipedum quæſitum
              <lb/>
            F D eſt = d x x. </s>
            <s xml:id="echoid-s13358" xml:space="preserve">ejuſque momentum ex gravitate = {1/2} d d x x. </s>
            <s xml:id="echoid-s13359" xml:space="preserve">Cohæ-
              <lb/>
            rentia baſeos = x
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13360" xml:space="preserve">debet eſſe momentum ex gravitate utriuſque pa-
              <lb/>
            rallelopipedi ad Cohærentiam ſuam in eâdem proportione, adeo-
              <lb/>
            que {1/2} a a b b, a
              <emph style="super">3</emph>
            :</s>
            <s xml:id="echoid-s13361" xml:space="preserve">: {1/2} d d x x. </s>
            <s xml:id="echoid-s13362" xml:space="preserve">x
              <emph style="super">3</emph>
            . </s>
            <s xml:id="echoid-s13363" xml:space="preserve">multiplicatis extremis & </s>
            <s xml:id="echoid-s13364" xml:space="preserve">mediis
              <lb/>
            per ſe, ſit {1/2} a a b b x
              <emph style="super">3</emph>
            = {1/2} a
              <emph style="super">3</emph>
            d d x x. </s>
            <s xml:id="echoid-s13365" xml:space="preserve">diviſo utroque termino per {1/2}
              <lb/>
            a a x x, fit b b x = a d d. </s>
            <s xml:id="echoid-s13366" xml:space="preserve">ergo x = {a d d:</s>
            <s xml:id="echoid-s13367" xml:space="preserve">/b b} ſive b b. </s>
            <s xml:id="echoid-s13368" xml:space="preserve">d d:</s>
            <s xml:id="echoid-s13369" xml:space="preserve">: a. </s>
            <s xml:id="echoid-s13370" xml:space="preserve">x.</s>
            <s xml:id="echoid-s13371" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13372" xml:space="preserve">Scholion. </s>
            <s xml:id="echoid-s13373" xml:space="preserve">Hoc modo breviſſime Problema ſolvitur, quod Ga-
              <lb/>
            lilæus ſubtile & </s>
            <s xml:id="echoid-s13374" xml:space="preserve">operoſum vocat, cujus inventioni haud exiguum
              <lb/>
            tempus ſe impendiſſe fatetur; </s>
            <s xml:id="echoid-s13375" xml:space="preserve">pulcerrimas inde interea elegit ſeque-
              <lb/>
            las: </s>
            <s xml:id="echoid-s13376" xml:space="preserve">nempe fieri non poſſe per artem, nec per Naturam, ut ma-
              <lb/>
            chinæ augeantur ad immenſam vaſtitatem, vel ut navigia, pala-
              <lb/>
            tia, templa exſtruantur vaſtiſſima, quorum remi, antennæ, tra-
              <lb/>
            beationes, catenæ ferreæ, reliquæve conſiſtant partes: </s>
            <s xml:id="echoid-s13377" xml:space="preserve">imo nec
              <lb/>
            Naturam arbores immenſæ magnitudinis producere poſſe, cum ipſa-
              <lb/>
            rum rami proprio pondere tandem inflecterentur & </s>
            <s xml:id="echoid-s13378" xml:space="preserve">frange-
              <lb/>
            rentur: </s>
            <s xml:id="echoid-s13379" xml:space="preserve">ſicut ipſi etiam foret impoſſibile hominibus, equis, aut a-
              <lb/>
            liis animalibus oſſa concedere ita conſtructa, ut ſubſiſtere, & </s>
            <s xml:id="echoid-s13380" xml:space="preserve">ha-
              <lb/>
            bita proportione, munia ſua obire queant, cum talia animalia in
              <lb/>
            immenſam augenda forent altitudinem, niſi materia adhibeatur,
              <lb/>
            quæ ultra vulgarem & </s>
            <s xml:id="echoid-s13381" xml:space="preserve">dura ſit & </s>
            <s xml:id="echoid-s13382" xml:space="preserve">reſiſtens, aut talia oſſa ad eam
              <lb/>
            deducanter craſſitiem, quæ omnis proportionis expers monſtro-
              <lb/>
            ſum reddat animal: </s>
            <s xml:id="echoid-s13383" xml:space="preserve">Ut hoc aliquo confirmetur exemplo, os femo-
              <lb/>
            ris humanum ſumatur, cujus craſſities quidem inæqualis eſt, ſed po-
              <lb/>
            natur diameter unius pollicis, & </s>
            <s xml:id="echoid-s13384" xml:space="preserve">longitudo ſesquipedis, quæro quan-
              <lb/>
            ta deſideretur alterius triplo longioris oſſis diameter, ut Cohæren-
              <lb/>
            tia hujus ſit æqualis priori? </s>
            <s xml:id="echoid-s13385" xml:space="preserve">Ex hac Propoſitione diameter poſtula-
              <lb/>
            tur 9 pollicum, ergo ut Gigas formaretur 18 altus pedes, quam
              <lb/>
            informe monſtrum fieri deberet, cujus os femoris diametrum 9
              <lb/>
            pollicum habeat: </s>
            <s xml:id="echoid-s13386" xml:space="preserve">cogita qualis craſſities reliquorum oſſium manum
              <lb/>
            pedemque conſtituentium erit? </s>
            <s xml:id="echoid-s13387" xml:space="preserve">ut hoc clarius intelligeretur, Ga-
              <lb/>
            lilæus ejuſmodi duo oſſa, quorum unum eſt femur vulgaris </s>
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