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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[521.] PROPOSITIO XLIII.
Page: 585 (568)
[522.] PROPOSITIO XLIV.
Page: 586 (569)
[523.] PROPOSITIO XLV.
Page: 587 (570)
[524.] PROPOSITIO XLVI.
Page: 588 (571)
[525.] PROPOSITIO XLVII.
Page: 589 (572)
[526.] PROPOSITIO XLVIII.
Page: 589 (572)
[527.] PROPOSITIO XLIX.
Page: 590 (573)
[528.] PROPOSITIO L.
Page: 590 (573)
[529.] PROPOSITIO LI.
Page: 591 (574)
[530.] PROPOSITIO LII.
Page: 592 (575)
[531.] EXPERIMENTUM CLXXXV.
Page: 593 (576)
[532.] PROPOSITIO LIII.
Page: 596 (579)
[533.] PROPOSITIO LIV.
Page: 598 (581)
[534.] PROPOSITIO LV.
Page: 599 (582)
[535.] PROPOSITIO LVI.
Page: 600 (583)
[536.] PROPOSITIO LVII.
Page: 601 (584)
[537.] De Conis & Pyramidibus. PROPOSITIO LVIII.
Page: 602 (585)
[538.] PROPOSITIO LIX.
Page: 602 (585)
[539.] PROPOSITIO LX.
Page: 603 (586)
[540.] PROPOSITIO LXI.
Page: 604 (587)
[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)
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          <pb o="513" file="0527" n="527" rhead="CORPORUM FIRMORUM."/>
          <p>
            <s xml:id="echoid-s12051" xml:space="preserve">Angulo c b d increſcente, decreſcit angulus r s q, & </s>
            <s xml:id="echoid-s12052" xml:space="preserve">ideo de-
              <lb/>
            creſcit longirudo lineæ r q, quæ exprimit rationem ponderis P: </s>
            <s xml:id="echoid-s12053" xml:space="preserve">ſed
              <lb/>
            angulo c b d increſcente, repræſentatur funis validius intortus; </s>
            <s xml:id="echoid-s12054" xml:space="preserve">qui-
              <lb/>
            cunque enim duo fila ſecum invicem torquebit, manifeſto obſer-
              <lb/>
            vabit, in initio angulum c b d eſſe parvum, eumque ſemper augeri,
              <lb/>
            quo fila vehementius intorquentur.</s>
            <s xml:id="echoid-s12055" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12056" xml:space="preserve">Ex hac demonſtratione manifeſto patet, quare funis contorſione
              <lb/>
            fibrarum factus, minus virium ad gerendum pondus habeat, quam
              <lb/>
            fibræ eum componentes, ſeorſim ſumtæ, habent: </s>
            <s xml:id="echoid-s12057" xml:space="preserve">tum 2°. </s>
            <s xml:id="echoid-s12058" xml:space="preserve">quare ro-
              <lb/>
            bur funis eo plus decreſcat, quo fibris vehementius intortis con-
              <lb/>
            ſtat: </s>
            <s xml:id="echoid-s12059" xml:space="preserve">Hæc omnia nunc nonnullis Experimentis confirmabo.</s>
            <s xml:id="echoid-s12060" xml:space="preserve"/>
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        <div xml:id="echoid-div446" type="section" level="1" n="446">
          <head xml:id="echoid-head558" xml:space="preserve">EXPERIMENTUM LXXXIII.</head>
          <p>
            <s xml:id="echoid-s12061" xml:space="preserve">Sumſi funiculum tenuem, diametri 0, 03 pollicis Rhenolandici,
              <lb/>
            cui tres quatuorve ulnas longo appendere potui libras 12 {1/2}, ſed a li-
              <lb/>
            bris 13 rumpebatur: </s>
            <s xml:id="echoid-s12062" xml:space="preserve">ambo igitur fragmenta ſuſtinere potuerunt li-
              <lb/>
            bras 12 {1/2}. </s>
            <s xml:id="echoid-s12063" xml:space="preserve">Hæc conjuncta parum intorſi, ut funiculum acceperim
              <lb/>
            ex ambobus compoſitum, cujus extremitati appendi modo potue-
              <lb/>
            runt libræ 24. </s>
            <s xml:id="echoid-s12064" xml:space="preserve">Conatus fui menſurare angulum c b e in fig. </s>
            <s xml:id="echoid-s12065" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12066" xml:space="preserve">quem
              <lb/>
            filum cum alio contorto conſtituebat, eum deprehendi angulum
              <lb/>
            16 {1/2} graduum, quare angulus c b d. </s>
            <s xml:id="echoid-s12067" xml:space="preserve">erat 33 graduum, tum vide fig. </s>
            <s xml:id="echoid-s12068" xml:space="preserve">4,
              <lb/>
            ambo ſimilia fila c b, b d, alligavi duobus clavis c & </s>
            <s xml:id="echoid-s12069" xml:space="preserve">d, & </s>
            <s xml:id="echoid-s12070" xml:space="preserve">ex me-
              <lb/>
            dio b appendi pondus pedetentim auctum uſque ad 24. </s>
            <s xml:id="echoid-s12071" xml:space="preserve">libras, obſer-
              <lb/>
            vans, ut angulus c b d etiam foret 33 graduum, elapſoque horæ minuto,
              <lb/>
            filum c b d diffractum fuit: </s>
            <s xml:id="echoid-s12072" xml:space="preserve">ſi ambo fila non intorta fuiſſent, tu-
              <lb/>
            liſſent ad minimum 25 libras, adeoque intorta evadunt gerendis
              <lb/>
            ponderibus ineptiora: </s>
            <s xml:id="echoid-s12073" xml:space="preserve">Cum autem angulus c b d eſt 33 graduum, eſt
              <lb/>
            in fig. </s>
            <s xml:id="echoid-s12074" xml:space="preserve">3. </s>
            <s xml:id="echoid-s12075" xml:space="preserve">angulus r s q graduum 147: </s>
            <s xml:id="echoid-s12076" xml:space="preserve">ponamus latus r s = s q ſingulum
              <lb/>
            eſſe 12 {1/2} partium, invenietur per regulas Trigonometriæ latus r q
              <lb/>
            24 partium, qui numerus exprimit pondus P, quod funem dif-
              <lb/>
            fregit.</s>
            <s xml:id="echoid-s12077" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12078" xml:space="preserve">Reaumurius filum ſumſit longum, cui appendit pedetentim li-
              <lb/>
            bras 10, a quibus rumpebatur: </s>
            <s xml:id="echoid-s12079" xml:space="preserve">ambo fragmenta in unum contor-
              <lb/>
            ſit mediocriter, tum vero appendere huic novo funi tantum po-
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            tuit libras 16; </s>
            <s xml:id="echoid-s12080" xml:space="preserve">nam a pluribus frangebatur: </s>
            <s xml:id="echoid-s12081" xml:space="preserve">hæc fila non </s>
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