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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[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)
[561.] PROPOSITIO LXXXII.
Page: 619 (602)
[562.] PROPOSITIO LXXXIII.
Page: 620 (603)
[563.] PROPOSITIO LXXXIV.
Page: 621 (604)
[564.] De Corporibus Hyperbolicis. PROPOSITIO LXXXV.
Page: 622 (605)
[565.] PROPOSITIO LXXXVI.
Page: 622 (605)
[566.] PROPOSITIO LXXXVII.
Page: 623 (606)
[567.] PROPOSITIO LXXXVIII.
Page: 623 (606)
[568.] PROPOSITIO LXXXIX.
Page: 624 (607)
[569.] De Hemisphæriis. PROPOSITIO XC.
Page: 624 (607)
[570.] PROPOSITIO XCI.
Page: 625 (608)
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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"/>
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          <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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