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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[641.] EXPERIMENTUM CCXXVI.
Page: 672 (655)
[642.] EXPERIMENTUM CCXXVII.
Page: 672 (655)
[643.] EXPERIMENTUM CCXXVIII.
Page: 673 (656)
[644.] EXPERIMENTUM CCXXIX.
Page: 673 (656)
[645.] EXPERIMENTUM CCXXX.
Page: 673 (656)
[646.] EXPERIMENTUM CCXXXI.
Page: 673 (656)
[647.] EXPERIMENTUM CCXXXII.
Page: 673 (656)
[648.] EXPERIMENTUM CCXXXIII.
Page: 673 (656)
[649.] EXPERIMENTUM CCXXXIV.
Page: 673 (656)
[650.] EXPERIMENTUM CCXXXV.
Page: 674 (657)
[651.] EXPERIMENTUM CCXXXVI.
Page: 674 (657)
[652.] EXPERIMENTUM CCXXXVII.
Page: 674 (657)
[653.] EXPERIMENTUM CCXXXVIII.
Page: 674 (657)
[654.] EXPERIMENTUM CCXXXIX.
Page: 674 (657)
[655.] EXPERIMENTUM CCXL.
Page: 674 (657)
[656.] EXPERIMENTUM CCXLI.
Page: 674 (657)
[657.] EXPERIMENTUM CCXLII.
Page: 674 (657)
[658.] EXPERIMENTUM CCXLIII.
Page: 675 (658)
[659.] PROPOSITIO CXVIII.
Page: 675 (658)
[660.] PROPOSITIO CXIX.
Page: 677 (660)
[661.] Regula prima.
Page: 682 (665)
[662.] Regula Secunda.
Page: 683 (666)
[663.] Regula Tertia.
Page: 683 (666)
[664.] TABULA
Page: 684 (667)
[665.] CAPUT DECIMUM. Tentamen de corporum Duritie.
Page: 685 (668)
[666.] EPHEMERIDES METEOROLOGICÆ ULTRAJECTINÆ ANNI MDCCXXVIII.
Page: 690 (673)
[667.] FINIS.
Page: 705 (685)
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              <pb o="624" file="0640" n="641" rhead="INTRODUCTIO AD COHÆRENTIAM"/>
            compoſita latitudinis C B, & </s>
            <s xml:id="echoid-s15638" xml:space="preserve">altitudinis E C duplicatâ, ſive B C
              <lb/>
            X
              <emph style="ol">E C</emph>
              <emph style="super">q</emph>
            . </s>
            <s xml:id="echoid-s15639" xml:space="preserve">ſed eſt E C X
              <emph style="ol">CB</emph>
              <emph style="super">q</emph>
            ad B C X
              <emph style="ol">E C</emph>
              <emph style="super">q</emph>
            :</s>
            <s xml:id="echoid-s15640" xml:space="preserve">: CB, EC, quare
              <lb/>
            erit Cohærentia hujus parallelopipedi, ad eam, cujus latus inferius
              <lb/>
            eſt A F C B, uti C B ad E C.</s>
            <s xml:id="echoid-s15641" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15642" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s15643" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15644" xml:space="preserve">Ergo aſſeris Lignei vel parallelopipedi firmitas poteſt
              <lb/>
            eſſe admodum variâ, pro diverſo ſitu, quem ſupra fulcra accepit: </s>
            <s xml:id="echoid-s15645" xml:space="preserve">ſi
              <lb/>
            enim E C ſit major C B, erit firmitas aſſeris in ſitu ſecundo major
              <lb/>
            quam in primo.</s>
            <s xml:id="echoid-s15646" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15647" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s15648" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15649" xml:space="preserve">Et datis duobus aſſeribus æque longis, æque firmis,
              <lb/>
            diverſarum baſium & </s>
            <s xml:id="echoid-s15650" xml:space="preserve">utrimque fulcro impoſitis, erunt eorum lati-
              <lb/>
            tudines reciproce uti ſunt quadrata altitudinum.</s>
            <s xml:id="echoid-s15651" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15652" xml:space="preserve">Ponatur enim altitudo B C = A latitudo E C = B. </s>
            <s xml:id="echoid-s15653" xml:space="preserve">erit Cohærentia
              <lb/>
            = A A X B. </s>
            <s xml:id="echoid-s15654" xml:space="preserve">vocetur alterius altitudo a. </s>
            <s xml:id="echoid-s15655" xml:space="preserve">latitudo b. </s>
            <s xml:id="echoid-s15656" xml:space="preserve">erit hujus Co-
              <lb/>
            hærentia = aa X b. </s>
            <s xml:id="echoid-s15657" xml:space="preserve">ponuntur firmitates æquales, adeoque</s>
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          <p>
            <s xml:id="echoid-s15658" xml:space="preserve">A A X B = aa X b. </s>
            <s xml:id="echoid-s15659" xml:space="preserve">unde B. </s>
            <s xml:id="echoid-s15660" xml:space="preserve">b:</s>
            <s xml:id="echoid-s15661" xml:space="preserve">: aa. </s>
            <s xml:id="echoid-s15662" xml:space="preserve">A A.</s>
            <s xml:id="echoid-s15663" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15664" xml:space="preserve">Corol 3. </s>
            <s xml:id="echoid-s15665" xml:space="preserve">Quare datâ altitudine duorum præcedentium aſſerum
              <lb/>
            & </s>
            <s xml:id="echoid-s15666" xml:space="preserve">unius latitudine, invenitur latitudo alterius: </s>
            <s xml:id="echoid-s15667" xml:space="preserve">nam erit B = {aab.</s>
            <s xml:id="echoid-s15668" xml:space="preserve">/AA}
              <lb/>
            & </s>
            <s xml:id="echoid-s15669" xml:space="preserve">data latitudine amborum aſſerum & </s>
            <s xml:id="echoid-s15670" xml:space="preserve">altitudine unius, invenitur
              <lb/>
            altitudo alterius, cum {aab/B} = A.</s>
            <s xml:id="echoid-s15671" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15672" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s15673" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15674" xml:space="preserve">Si igitur aſſer fuerit longus, & </s>
            <s xml:id="echoid-s15675" xml:space="preserve">erigatur ſecundum
              <lb/>
            ſuam longitudinem, ut fiat, a b c d, in Tab. </s>
            <s xml:id="echoid-s15676" xml:space="preserve">XXIV. </s>
            <s xml:id="echoid-s15677" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s15678" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s15679" xml:space="preserve">at-
              <lb/>
            que utrimque imponatur fulcro, b c & </s>
            <s xml:id="echoid-s15680" xml:space="preserve">e. </s>
            <s xml:id="echoid-s15681" xml:space="preserve">firmiſſimus erit, pote-
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            ritque ex ſui medio pondus maximum appenſum gerere.</s>
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            <s xml:id="echoid-s15683" xml:space="preserve">Corol. </s>
            <s xml:id="echoid-s15684" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15685" xml:space="preserve">Ex his diſcimus Trabium oneribus ſuſtinendis deſtina-
              <lb/>
            tarum firmitates poſſe augeri, non augendo earum pretium, nec
              <lb/>
            quantitatem Ligni, nec pondus proprium.</s>
            <s xml:id="echoid-s15686" xml:space="preserve"/>
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            <s xml:id="echoid-s15687" xml:space="preserve">Sit enim Trabs alta & </s>
            <s xml:id="echoid-s15688" xml:space="preserve">lata 12 pollices, adeoque cujus ſectio eſt
              <lb/>
            144 pollic. </s>
            <s xml:id="echoid-s15689" xml:space="preserve">quadratorum: </s>
            <s xml:id="echoid-s15690" xml:space="preserve">detur alia trabs altitudinis 14 pollic. </s>
            <s xml:id="echoid-s15691" xml:space="preserve">la-
              <lb/>
            titudinis 10 poll: </s>
            <s xml:id="echoid-s15692" xml:space="preserve">erit hujus ſectio 140 pollic. </s>
            <s xml:id="echoid-s15693" xml:space="preserve">quadratorum, adeo-
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            que erit ſoliditas prioris Trabis ad eam poſterioris uti 144 ad 140.
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            </s>
            <s xml:id="echoid-s15694" xml:space="preserve">ſed firmitas primæ eſt ut 144 X 12. </s>
            <s xml:id="echoid-s15695" xml:space="preserve">& </s>
            <s xml:id="echoid-s15696" xml:space="preserve">ſecundæ uti 196 X 10, quæ
              <lb/>
            ſunt inter ſe uti 1728 ad 1960. </s>
            <s xml:id="echoid-s15697" xml:space="preserve">quare poſterior Trabs erit fortior
              <lb/>
            & </s>
            <s xml:id="echoid-s15698" xml:space="preserve">minoris pretii, cum minus ligni in ſe contineat.</s>
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