Bošković, Ruđer Josip, Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium

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              <pb o="99" file="0151" n="151" rhead="PARS SECUNDA."/>
            tinent ad diverſas leges binorum punctorum agentium in ter-
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            tium.</s>
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          </p>
          <p>
            <s xml:space="preserve">214. </s>
            <s xml:space="preserve">Si libeat conſiderare illas leges, quæ oriuntur in re-
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              <note position="right" xlink:label="note-0151-01" xlink:href="note-0151-01a" xml:space="preserve">Vis in duo
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              puncta puncti
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              poſi ti in recta
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              jungente ipſa,
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              vel in recta ſe-
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              cante hanc bi-
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              fariam, & ad
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              angulos rectos
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              directa ſecun-
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              dum eandem
                <unsure/>
                <lb/>
              rectam.</note>
            cta perpendiculari ad AB ducta per D, vel in ipſa AB hinc,
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            & </s>
            <s xml:space="preserve">inde producta, inprimis facile eſt videre illud, directionem
              <lb/>
            vis compoſitæ utrobique fore eandem cum ipſa recta ſine ulla
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            vi in latus, & </s>
            <s xml:space="preserve">ſine ulla declinatione a recta, quæ tendit ad
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            ipſum D, vel ab ipſo. </s>
            <s xml:space="preserve">Pro recta AB res conſtat per ſe ſe;
              <lb/>
            </s>
            <s xml:space="preserve">nam vires illæ, quæ ad bina ea puncta pertinent, vel habe-
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            bunt directionem eandem, vel oppoſitas, jacente ipſo tertio
              <lb/>
            puncto in directum cum utroque e prioribus: </s>
            <s xml:space="preserve">unde fit, ut
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            vis compoſita æquetur ſummæ, vel differentiæ virium ſingu-
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            larum componentium, quæ in eadem recta remaneat. </s>
            <s xml:space="preserve">Pro
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            recta perpendiculari facile admodum demonſtratur. </s>
            <s xml:space="preserve">Si enim
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              <note position="right" xlink:label="note-0151-02" xlink:href="note-0151-02a" xml:space="preserve">Fig. 23.</note>
            in fig. </s>
            <s xml:space="preserve">23 recta DC fuerit perpendicularis ad AB ſectam bi-
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            fariam in D, erunt AC, BC æquales inter ſe. </s>
            <s xml:space="preserve">Quare vi-
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            res, quibus C agitatur ab A, & </s>
            <s xml:space="preserve">B, æquales erunt, & </s>
            <s xml:space="preserve">proin-
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            de vel ambæ attractivæ, ut CL, CK, vel ambæ repulſivæ,
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            ut CN, CM. </s>
            <s xml:space="preserve">Quare vis compoſita CF, vel CH, erit dia-
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            meter rhombi, adeoque ſecabit biſariam angulum LCK, vel
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            NC M; </s>
            <s xml:space="preserve">quos angulos cum biſariam ſecet etiam recta DC,
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            ob æqualitatem triangulorum DCA, DCB, patet, ipſas
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            CF, CH debere cum eadem congruere. </s>
            <s xml:space="preserve">Quamobrem in hiſ-
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            ce caſibus evaneſcit vis illa perpendicularis FO, quæ in præ-
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            cedentibus binis figuris habebatur, ac in iis per unicam æqua-
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            tionem res omnis abſolvitur , quarum ea, quæ ad poſte- riorem caſum pertinet, admodum facile invenitur.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">215. </s>
            <s xml:space="preserve">Legem pro recta perpendiculari rectæ jungenti duo
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              <note position="right" xlink:label="note-0151-03" xlink:href="note-0151-03a" xml:space="preserve">Conſtructio
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              curvæ exhiben-
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              tis legem caſus
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              poſterioris.</note>
            puncta, & </s>
            <s xml:space="preserve">æque diſtanti ab utroque exhibet fig. </s>
            <s xml:space="preserve">24, quæ vi-
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            tandæ confuſionis cauſa exhibetur, ubi ſub numero 24 habe-
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            tur littera B, ſed quod ad ejus conſtructionem pertinet, habe-
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              <note position="right" xlink:label="note-0151-04" xlink:href="note-0151-04a" xml:space="preserve">Fig. 24.</note>
            tur ſeparatim, ubi ſub num. </s>
            <s xml:space="preserve">24 habetur littera A; </s>
            <s xml:space="preserve">ex qui-
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            bus binis figuris fit unica; </s>
            <s xml:space="preserve">ſi puncta XY EA E' cenſeantur utro-
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            bique eadem. </s>
            <s xml:space="preserve">In ea X, Y ſunt duo materiæ puncta, & </s>
            <s xml:space="preserve">ipſam
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            XY recta CC' ſecat bifariam in A. </s>
            <s xml:space="preserve">Curva, quæ vires
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            compoſitas ibi exhibet per ordinatas, conſtructa eſt ex fig. </s>
            <s xml:space="preserve">1,
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            quod fieri poteſt, inveniendo vires ſingulas ſingulorum pun-
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            ctorum, tum vim compoſitam ex iis more conſueto juxta
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              <note symbol="(p)" position="foot" xlink:label="note-0151-05" xlink:href="note-0151-05a" xml:space="preserve">Ducta enim LK in Fig. 23. ipſam FC ſecabit alicubi in I bifa-
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              riam, & ad angulos rectos ex rbombi natura. Dicatur CD =x, CF
                <lb/>
              = y, DB =a, & erit CB = √a a + x x, & CD =x. CB =
                <lb/>
              √aa + xx:: CI = {1/2}y. CK = {y/2x} √a a + x x quo valore poſito in æquatio-
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              ne curvæ figuræ I pro valore ordinatæ, & √a a + x x pro valore abſciſſæ,
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              babebitur immediate æquatiu nova per x, y, & conſtantes, quæ ejuſmodi
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              curvam determinabit.</note>
            </s>
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