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

Table of figures

< >
< >
page |< < (161) of 389 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="0" n="0">
          <p>
            <s xml:space="preserve">
              <pb o="161" file="0213" n="213" rhead="PARS SECUNDA."/>
            mit. </s>
            <s xml:space="preserve">Exprimat in fig. </s>
            <s xml:space="preserve">68. </s>
            <s xml:space="preserve">AD diſtantiam quandam, & </s>
            <s xml:space="preserve">aſ-
              <lb/>
              <note position="right" xlink:label="note-0213-01" xlink:href="note-0213-01a" xml:space="preserve">Fig. 68.</note>
            ſumpta BD ad AB in quacunque ratione utcunque parva, vel
              <lb/>
            utcunque ſenſibili, capiantur rectæ perpendiculares DE, BF
              <lb/>
            itidem in quacunque ratione minoris inæqualitatis utcunque
              <lb/>
            magna: </s>
            <s xml:space="preserve">poterit utique arcus MN curvæ exprimentis mutuas
              <lb/>
            particularum vi
              <lb/>
            res tranſire per illa puncta E, F, & </s>
            <s xml:space="preserve">exhibere
              <lb/>
            quodcunque preſſionis incrementum cum quacunque preſſione
              <lb/>
            utcunque magna, vel utcunque inſenſibili.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">352. </s>
            <s xml:space="preserve">Compreſſionem ingentem experimur in aere, quæ in
              <lb/>
              <note position="right" xlink:label="note-0213-02" xlink:href="note-0213-02a" xml:space="preserve">Compreſſio a
                <gap/>
                <gap/>
                <lb/>
              ris a qua vi pro-
                <lb/>
              veniat: aquæ
                <lb/>
              compreſſio cur
                <lb/>
              ad ſenſum nul-
                <lb/>
              la: unde muta-
                <lb/>
              tio in vapores
                <lb/>
              tam elaſtices
                <unsure/>
              .</note>
            eo eſt proportionalis vi comprimenti. </s>
            <s xml:space="preserve">Pro eo caſu demon-
              <lb/>
            ſtravit Newtonus Princ. </s>
            <s xml:space="preserve">Lib. </s>
            <s xml:space="preserve">3. </s>
            <s xml:space="preserve">prop. </s>
            <s xml:space="preserve">23, vim particularum
              <lb/>
            repulſivam mutuam debere eſſe in ratione reciproca ſimplici
              <lb/>
            diſtantiarum. </s>
            <s xml:space="preserve">Quare in iis diſtantiis, quas habere poſſunt par-
              <lb/>
            ticulæ aeris perſeverantis cum ejuſmodi proprietate, & </s>
            <s xml:space="preserve">formam
              <lb/>
            aliam non inducentis (nam & </s>
            <s xml:space="preserve">aerem poſſe e volatili fieri fi-
              <lb/>
            xum, Newtonus innuit, ac Haleſius inprimis uberrime demon-
              <lb/>
            ſtravit), oportet, arcus MN accedat ad formam arcus hy-
              <lb/>
            perbolæ conicæ Apollonianæ. </s>
            <s xml:space="preserve">At in aqua compreſſio ſenſibi-
              <lb/>
            lis habetur nulla, utcunque magnis ponderibus comprimatur.
              <lb/>
            </s>
            <s xml:space="preserve">Inde aliqui inferunt, ipſam elaſtica vi carere, ſed perperam; </s>
            <s xml:space="preserve">
              <lb/>
            quin immo vires habere debet ingentes diſtantiis utcunque pa-
              <lb/>
            rum imminutis; </s>
            <s xml:space="preserve">quanquam eædem particulæ debent eſſe prope
              <lb/>
            limites, nam & </s>
            <s xml:space="preserve">diſtractioni reſiſtit aqua. </s>
            <s xml:space="preserve">Infinita ſunt curva-
              <lb/>
            rum genera, quæ poſſunt rei ſatisſacere, & </s>
            <s xml:space="preserve">ſatis eſt, ſi arcus
              <lb/>
            EF directionem habeat fere perpendicularem axi AC. </s>
            <s xml:space="preserve">Si cur-
              <lb/>
            vam cognitam adhibere libeat; </s>
            <s xml:space="preserve">ſatis eſt, ut arcus EF accedat
              <lb/>
            plurimum ad logiſticam, cujus ſubtangens ſit perquam exigua
              <lb/>
            reſpectu diſtantiæ AD. </s>
            <s xml:space="preserve">Demonſtratur paſſim, ſubtangentem. </s>
            <s xml:space="preserve">
              <lb/>
            logiſticæ ad intervallum ordinatarum exhibens rationem duplam
              <lb/>
            eſſe proxime ut 14 ad 10; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eadem ſubtangens ad intervallum,
              <lb/>
            quod exhibeat ordinatas in quacunque magna ratione inæqua-
              <lb/>
            litatis, habet in omnibus logiſticis rationem eandem. </s>
            <s xml:space="preserve">Si igi-
              <lb/>
            tur minuatur fubtangens logiſticæ, quantum libuerit; </s>
            <s xml:space="preserve">minuetur
              <lb/>
            utique in eadem ratione intervallum BD reſpondens cuicunque
              <lb/>
            rationi ordinatarum BF, DE, & </s>
            <s xml:space="preserve">accedet ad æqualitatem,
              <lb/>
            quantum libuerit, ratio AB ad AD, a qua pendet compreſ-
              <lb/>
            ſio; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cujus ratio reciproca triplicata eſt ratio denſitatum,
              <lb/>
            cum ſpatia ſimilia ſint in ratione triplicata laterum homolo-
              <lb/>
            gorum, & </s>
            <s xml:space="preserve">maſſa compreſſa poſſit cum eadem nova denſitate
              <lb/>
            redigi ad formam ſimilem. </s>
            <s xml:space="preserve">Quare poterit haberi incremen-
              <lb/>
            tum vis comprimentis in quacunque ingenti ratione auctæ cum
              <lb/>
            compreſſione utcunque exigua, & </s>
            <s xml:space="preserve">ratione denſitatum utcunque
              <lb/>
            accedente ad æqualitatem. </s>
            <s xml:space="preserve">Verum ubi ordinata ED jam ſatis
              <lb/>
            exigua fuerit, debet curva recedere plurimum ab arcu logiſti-
              <lb/>
            cæ, ad quem acceſſerat, & </s>
            <s xml:space="preserve">qui in infinitum protenditur ex par-
              <lb/>
            te eadem, ac debet accedere ad axem AC, & </s>
            <s xml:space="preserve">ipſum ſecare, ut
              <lb/>
            habeantur deinde vires attractivæ, quæ ingentes etiam eſſe poſ-
              <lb/>
            ſunt; </s>
            <s xml:space="preserve">tum poſt exiguum intervallum debet haberi alius </s>
          </p>
        </div>
      </text>
    </echo>
Impressum