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

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              <pb o="291" file="0343" n="343" rhead="SUPPLEMENTA. §. IV."/>
            cumvolvatur circa punctum P, nec tamen in ipſum unquam
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            deſinat: </s>
            <s xml:space="preserve">ſi autem ducatur ex P recta perpendicularis ad A P,
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            quæ tangenti A B occurrat in B, tota ſpiralis ACDEFGH
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            in inſinitum continuata ad menſuram longitudinis A B ac-
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            cedat ultra quoſcunque limites, nec unquam ei æqualis fiat:
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            </s>
            <s xml:space="preserve">velocitas autem in ejuſmodi curva in continuo acceſſu ad cen-
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            trum virium P perpetuo creſcat. </s>
            <s xml:space="preserve">Quare finito tempore, & </s>
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            ſane breviore, quam ſit illud, quo velocitate initiali percurre-
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            ret A B, deberet id mobile devenire ad centrum P, in quo
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            bina graviſſima abſurda habentur. </s>
            <s xml:space="preserve">Primo quidem, quod habe-
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            retur tota illa ſpiralis, quæ in centrum deſineret, contra id,
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            quod ex ejus natura deducitur, cum nimirum in centrum ca-
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            dere nequaquam poſſit: </s>
            <s xml:space="preserve">deinde vero, quod elapſo eo finito tem-
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            pore mobile illud nuſquam eſſe deberet. </s>
            <s xml:space="preserve">Nam ea curva, ubi
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            etiam in infinitum continuata intelligitur, nullum habet egreſ-
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            ſum e P Et quidem formulæ analyticæ exhibent ejus locum
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            poſt id tempus impoſſibilem, ſive, ut dicimus, imaginarium ; </s>
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            quo quidem argumento Eulerus in ſua Mechanica affirmavit
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            illud, debere id mobile in appulſu ad centrum virium annihi-
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            lari. </s>
            <s xml:space="preserve">Quanto ſatius fuiſſet inferre, eam legem virium impoſſi-
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            bilem eſſe?</s>
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          </p>
          <p>
            <s xml:space="preserve">83. </s>
            <s xml:space="preserve">Quanto autem majora abſurda in ulterioribus potentiis,
              <lb/>
              <note position="right" xlink:label="note-0343-01" xlink:href="note-0343-01a" xml:space="preserve">Pejus in poten-
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              tiis altioribus:
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              præparatio ad
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              demonſtrandum
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              abſurdum.</note>
            quibus vires alligatæ ſint, conſequentur? </s>
            <s xml:space="preserve">Sit globus in fig. </s>
            <s xml:space="preserve">74
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            ABE, & </s>
            <s xml:space="preserve">intra ipſum alius A be, qui priorem contingat in A,
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            ac in omnia utriuſque puncta agant vires decreſcentes in ra-
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            tione reciproca quadruplicata diſtantiarum, vel majore, & </s>
            <s xml:space="preserve">quæ-
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              <note position="right" xlink:label="note-0343-02" xlink:href="note-0343-02a" xml:space="preserve">Fig. 74.</note>
            ratur ratio vis puncti conſtituti in concurſu A utriuſque ſu-
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            perſiciei. </s>
            <s xml:space="preserve">Concipiatur uterque reſolutus in pyramides infinite
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            arctas, quæ prodeant ex communi puncto A, ut BAD, b A d.
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            </s>
            <s xml:space="preserve">In ſingulis autem pyramidulis diviſis in partes totis proportio-
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            nales ſint particulæ MN, m n ſimiles, & </s>
            <s xml:space="preserve">ſimiliter poſitæ. </s>
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              <lb/>
            Quantitas materiæ in MN, ad quantitatem in mn erit, ut
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            maſſa totius globi majoris ad totum minorem, nimirum, ut
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            cubus radii majoris ad cubum minoris. </s>
            <s xml:space="preserve">Cum igitur vis, qua
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            trahitur punctum A, ſit, ut quantitas materiæ directe, & </s>
            <s xml:space="preserve">ut
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            quarta poteſtas diſtantiarum reciproce, quæ itidem diſtantiæ
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            ſunt, ut radii ſphærarum; </s>
            <s xml:space="preserve">erit vis in partem MN, ad vim in
              <lb/>
            partem mn directe, ut tertia poteſtas radii majoris ad tertiam
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            minoris, & </s>
            <s xml:space="preserve">reciproce, ut quarta poteſtas ipſius. </s>
            <s xml:space="preserve">Quare mane-
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            bit ratio ſimplex reciproca radiorum.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">84. </s>
            <s xml:space="preserve">Minor erit igitur actio ſingularum particularum homo-
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              <note position="right" xlink:label="note-0343-03" xlink:href="note-0343-03a" xml:space="preserve">partem fore
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              majorem toto.</note>
            logarum M N, quam mn, in ipſa ratione radiorum, adeoque
              <lb/>
            punctum A minus trahetur a tota ſphæra ABE, quam a ſphæ-
              <lb/>
            ra A be, quod eſt abſurdum, cum attractio in eam ſphæram
              <lb/>
            minorem debeat eſſe pars attractionis in ſphæram majorem,
              <lb/>
            quæ continet minorem, cum magna materiæ parte ſita extra i-
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            pſam uſque ad ſuperficiem ſphæræ majoris, unde concluditur eſ-
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            ſe partem majorem toto, maximum nimirum abſurdum. </s>
            <s xml:space="preserve">Et </s>
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