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

Table of Notes

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              <pb o="119" file="0171" n="171" rhead="PARS SECUNDA."/>
            ordine, tum binaria conjungi cum ternariis, denariis, aliiſque, or-
              <lb/>
            dine itidem quocunque, & </s>
            <s xml:space="preserve">ſemper eadem metbodo devenitur ad cen-
              <lb/>
            trum commune gravitatis maſſæ totius. </s>
            <s xml:space="preserve">Id patet, quia quotcun-
              <lb/>
            que maſſæ conſiderari poſſunt pro maſſa unica, cum agatur de
              <lb/>
            numero punctorum maſſæ tantummodo, & </s>
            <s xml:space="preserve">de ſumma diſtantia-
              <lb/>
            rum punctorum omnium: </s>
            <s xml:space="preserve">ſummę maſſarum conſtituunt maſ-
              <lb/>
            ſam, & </s>
            <s xml:space="preserve">ſummæ diſtantiarum ſummam per ſolam conjunctio-
              <lb/>
            nem ipſarum. </s>
            <s xml:space="preserve">Quoniam autem ex generali demonſtratione ſu-
              <lb/>
            perius facta devenitur ſemper ad centrum gravitatis, atque id
              <lb/>
            centrum eſt unicum; </s>
            <s xml:space="preserve">quocunque ordine res peragatur, ad illud
              <lb/>
            utique unicum devenitur.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">255. </s>
            <s xml:space="preserve">Inde vero illud conſequitur, quod eſt itidem commune,
              <lb/>
              <note position="right" xlink:label="note-0171-01" xlink:href="note-0171-01a" xml:space="preserve">Inde & theo-
                <lb/>
              rema, ope cu-
                <lb/>
              jus inveſtigatur
                <lb/>
              id in figuris
                <lb/>
              continuis.</note>
            ſi plurium maſſarum centra gravitatis ſint in eadem aliqua recta,
              <lb/>
            fore etiam in eadem centrum gravitatis ſummæ omnium; </s>
            <s xml:space="preserve">quod
              <lb/>
            viam ſternit ad inveſtiganda gravitatis centra etiam in pluribus
              <lb/>
            figuris continuis. </s>
            <s xml:space="preserve">Sic in fig. </s>
            <s xml:space="preserve">38 centrum commune gravitatis to.
              <lb/>
            </s>
            <s xml:space="preserve">
              <note position="right" xlink:label="note-0171-02" xlink:href="note-0171-02a" xml:space="preserve">F. 38.</note>
            tius trianguli eſt in illo puncto, quod a recta ducta a vertice an-
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            guli cujuſvis ad mediam baſim oppoſitam relinquit trientem ver-
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            ſus baſim ipſam. </s>
            <s xml:space="preserve">Nam omnium rectarum baſi parallelarum,
              <lb/>
            quæ omnes a recta BD ſecantur bifariam, ut FH, centra gra-
              <lb/>
            vitatis ſunt in eadem recta, adeoque & </s>
            <s xml:space="preserve">areæ ab iis contextæ
              <lb/>
            centrum gravitatis eſt tam in recta BD, quam in recta GE
              <lb/>
            ob eandem rationem, nempe in illo puncto C. </s>
            <s xml:space="preserve">Eadem metho-
              <lb/>
            dus applicatur aliis Figuris ſolidis, ut pyramidibus; </s>
            <s xml:space="preserve">at id, ut
              <lb/>
            & </s>
            <s xml:space="preserve">reliqua omnia pertinentia ad inventionem centri gravitatis
              <lb/>
            in diverſis curvis lineis, ſuperficiebus, ſolidis, hinc proſluen-
              <lb/>
            tia, ſed meæ Theoriæ communia jam cum vulgaribus elemen-
              <lb/>
            tis, hic omittam, & </s>
            <s xml:space="preserve">ſolum illud iterum innuam, ea rite pro-
              <lb/>
            cedere, ubi jam ſemel demonſtratum fuerit, haberi in maſſis
              <lb/>
            omnibus aliquod gravitatis centrum, & </s>
            <s xml:space="preserve">eſſe unicum, ex quo
              <lb/>
            nimirum hic & </s>
            <s xml:space="preserve">illud fluit, areas FAGH, FBH licet inæ-
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            quales, habere tamen æquales ſummas diſtantiarum omnium
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            ſuorum punctorum ab eadem recta FH.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">256. </s>
            <s xml:space="preserve">In communi methodo alio modo ſe res habet. </s>
            <s xml:space="preserve">Poſtea-
              <lb/>
              <note position="right" xlink:label="note-0171-03" xlink:href="note-0171-03a" xml:space="preserve">Difficultas de-
                <lb/>
              monſtrationis
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              in communi
                <lb/>
              methodo.</note>
            quam inventum eſt in fig. </s>
            <s xml:space="preserve">40 centrum gravitatis commune maſ-
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            ſis A, & </s>
            <s xml:space="preserve">B, juncta pro tertia maſſa DC, & </s>
            <s xml:space="preserve">ſecta in F in ratio-
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            ne maſſarum D, & </s>
            <s xml:space="preserve">A + B reciproca, habetur F pro centro com-
              <lb/>
              <note position="right" xlink:label="note-0171-04" xlink:href="note-0171-04a" xml:space="preserve">Fig. 40.</note>
            muni omnium trium. </s>
            <s xml:space="preserve">Si prius inventum eſſet centrum com-
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            mune E maſſarum D, B, & </s>
            <s xml:space="preserve">juncta AE, ea ſecta fuiſſet in F
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            in ratione reciproca maſſarum A, & </s>
            <s xml:space="preserve">B + D; </s>
            <s xml:space="preserve">haberetur itidem
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            illud ſectionis punctum pro centro gravitatis. </s>
            <s xml:space="preserve">Niſi generaliter
              <lb/>
            demonſtratum fuiſſet, haberi ſemper aliquod, & </s>
            <s xml:space="preserve">eſſe unicum
              <lb/>
            gravitatis centrum; </s>
            <s xml:space="preserve">oporteret hic iterum demonſtrare, id novum
              <lb/>
            ſectionis punctum fore idem, ac illud prius; </s>
            <s xml:space="preserve">ſed per ſingulos
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            caſus ire, res infinita eſſet, cum diveræ rationes conjungendi
              <lb/>
            maſſas eodem redeant, quo diverſi ordines litterarum conjun-
              <lb/>
            gendarum in voces, de quarum multitudine immenſa in exiguo
              <lb/>
            etiam terminorum numero mentionem ſecimus num. </s>
            <s xml:space="preserve">114.</s>
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