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="529" file="0543" n="543" rhead="CORPORUM FIRMORUM."/>
            ctum H a pariete recedendo fibram ſuam tendit, elongatque ut ac-
              <lb/>
            quirat extenſionem 1H 2H, hoc modo omnes fibræ inter B & </s>
            <s xml:id="echoid-s12428" xml:space="preserve">A
              <lb/>
            tenduntur, extrahuntur, elongantur, maxime ſupremæ 1B 2B,
              <lb/>
            minus mediæ 1H 2H, omnium minime, quæ ſunt proximæ pun-
              <lb/>
            cto A. </s>
            <s xml:id="echoid-s12429" xml:space="preserve">proinde fibræ intermediæ 1H 2H minus reſiſtunt potentiæ
              <lb/>
            Q, quam 1B 2B propter duas rationes, 1°. </s>
            <s xml:id="echoid-s12430" xml:space="preserve">Quia B A C vectis eſt
              <lb/>
            incurvus, cujus unum crus eſt B A, adeoque vi eâdem applicatâ di-
              <lb/>
            verſis punctis 2B, 2H, erit momentum in 2B, ad id in 2H, uti
              <lb/>
            A B eſt ad A H; </s>
            <s xml:id="echoid-s12431" xml:space="preserve">hoc eſtuti diſtantia â puncto? </s>
            <s xml:id="echoid-s12432" xml:space="preserve">A: </s>
            <s xml:id="echoid-s12433" xml:space="preserve">quare momentum
              <lb/>
            Cohærentiæ in B, ad illud in H, erit uti diſtantia AB, ad AH,
              <lb/>
            quemadmodum ex natura vectis ſequitur. </s>
            <s xml:id="echoid-s12434" xml:space="preserve">2°. </s>
            <s xml:id="echoid-s12435" xml:space="preserve">Quoniam ambæ
              <lb/>
            fibræ 1B 2B, & </s>
            <s xml:id="echoid-s12436" xml:space="preserve">1H 2H ſimul tenduntur a potentia Q, minus ta-
              <lb/>
            men 1H 2H, quam 1B 2B: </s>
            <s xml:id="echoid-s12437" xml:space="preserve">ſupponamus vires retrotrahentes fi-
              <lb/>
            brarum tenſarum eſſe in ratione extenſionum, ita ut fibra tenſa & </s>
            <s xml:id="echoid-s12438" xml:space="preserve">
              <lb/>
            elongata aliquouſque a pondere uno, duplo plus elongetur a pon-
              <lb/>
            deribus duobus, triplo plus â tribus, & </s>
            <s xml:id="echoid-s12439" xml:space="preserve">ſic porro: </s>
            <s xml:id="echoid-s12440" xml:space="preserve">tum erunt vires
              <lb/>
            retrotrahentes, uti ſunt tenſiones, ſive elongationes, hoc eſt erit
              <lb/>
            vis in H, ad eam in B, uti 1H 2H, ad 1B 2B. </s>
            <s xml:id="echoid-s12441" xml:space="preserve">ſed ſunt A1 H
              <lb/>
            2H. </s>
            <s xml:id="echoid-s12442" xml:space="preserve">& </s>
            <s xml:id="echoid-s12443" xml:space="preserve">A 1B 2B duo Triangula ſimilia, & </s>
            <s xml:id="echoid-s12444" xml:space="preserve">1H 2H, ad 1B 2B
              <lb/>
            ;</s>
            <s xml:id="echoid-s12445" xml:space="preserve">: A 1H ad A 1B. </s>
            <s xml:id="echoid-s12446" xml:space="preserve">quare erunt vires fibrarum retrotrahentes in
              <lb/>
            1H & </s>
            <s xml:id="echoid-s12447" xml:space="preserve">1B, uti A 1H ad A 1B ſed ob rationem vectis modo da-
              <lb/>
            tam. </s>
            <s xml:id="echoid-s12448" xml:space="preserve">erant momenta virium in H&</s>
            <s xml:id="echoid-s12449" xml:space="preserve">B, uti A 1H ad A 1B. </s>
            <s xml:id="echoid-s12450" xml:space="preserve">qua-
              <lb/>
            re ob duas rationes ſimul, erunt vires in H ad eas in B, in ra-
              <lb/>
            tione compoſita ex AH ad AB, & </s>
            <s xml:id="echoid-s12451" xml:space="preserve">ex AH ad AB, hoc
              <lb/>
            eſt in ratione duplicata diſtantiæ AH ad AB, a centro mo-
              <lb/>
            tus A.</s>
            <s xml:id="echoid-s12452" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12453" xml:space="preserve">Quæcunque demonſtravimus de viribus duorum punctorum H & </s>
            <s xml:id="echoid-s12454" xml:space="preserve">
              <lb/>
            B conveniunt viribus omnium punctorum inter A & </s>
            <s xml:id="echoid-s12455" xml:space="preserve">B, ideoque
              <lb/>
            omnes vires in unam ſummam addendæ ſunt, ut habeatur tota
              <lb/>
            vis reſpectiva Cohærentiæ. </s>
            <s xml:id="echoid-s12456" xml:space="preserve">Hæc ſumma ſequenti modo cognoſce-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s12457" xml:space="preserve">capiatur NR æqualis AB, in quâ fiat NP æqualis A H: </s>
            <s xml:id="echoid-s12458" xml:space="preserve">dein-
              <lb/>
            de ut NP
              <emph style="super">q</emph>
            ad NR
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s12459" xml:space="preserve">ita ſit quæcunque PQ ad RS, quæ ad angulos
              <lb/>
            rectos inſiſtant ipſi NR, per puncta NQS deſcribatur parabola A-
              <lb/>
            polloniana, cujus vertex ſit in N, & </s>
            <s xml:id="echoid-s12460" xml:space="preserve">compleatur rectangulum NR
              <lb/>
            ST. </s>
            <s xml:id="echoid-s12461" xml:space="preserve">Tum ſi R S exponat vim Cohærentiæ puncti B, PQ exponet
              <lb/>
            eam puncti H, omnesque parallelæ ad RS utrimque terminatæ </s>
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