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

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              <pb o="116" file="0168" n="168" rhead="THEORIÆ"/>
            ſiens itidem per C, ac ſecans primum ex iis recta CI quacun-
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            que; </s>
            <s xml:space="preserve">oportet oſtendere, hoc quoque fore planum diſtantia-
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            rum æqualium, ſi illa priora ejuſmodi fint. </s>
            <s xml:space="preserve">Concipiatur quod-
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            cunque punctum P; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per ipſum P concipiantur tria plana
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            parallela planis DCEF, ABYX, GABH, quorum ſibi
              <lb/>
            priora duo mutuo occurrant in recta PM, poſtrema duo in re-
              <lb/>
            cta PV, primum cum tertio in recta PO; </s>
            <s xml:space="preserve">ac primum occurrat
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            plano GA BH in MN, ſecundum vero eidem in MS, pla-
              <lb/>
            no DC EF in QR, ac plano CIKL in SV, ducaturque ST
              <lb/>
            parallela rectis QR, MP, quas, utpote parallelorum plano-
              <lb/>
            rum interſectiones, patet fore itidem parallelas inter ſe, uti & </s>
            <s xml:space="preserve">
              <lb/>
            MN, PO, DC inter ſe, ac MS, PTV, BA inter ſe.</s>
            <s xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Demonftratio
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            <gap/>
          juſdem.</note>
          <p>
            <s xml:space="preserve">248. </s>
            <s xml:space="preserve">Jam vero ſumma omnium diſtantiarum a plano KICL
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            fecundum datam directionem BA erit ſumma omnium PV,
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            quæ reſolvitur in tres ſummas, omnium PR, omnium RT,
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            omnium T V, ſive eæ, ut figura exhibet, in unam colligendæ
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            ſint, ſive, quod in aliis plani novi inclinationibus poſſet ac-
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            cidere, una ex iis demenda a reliquis binis, ut habeatur omnium
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            PV ſumma. </s>
            <s xml:space="preserve">Porro quævis PR eſt diſtantia a plano DCE F
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            ſecundum eandem eam directionem; </s>
            <s xml:space="preserve">quævis RT eſt æqualis
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            QS ſibi reſpondenti, quæ ob datas directiones laterum trian-
              <lb/>
            guli SCQ eſt ad CQ, æqualem MN, ſive PO, diſtantiæ a
              <lb/>
            plano XA BY ſecundum datam directionem DC, in ratione
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            data; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quævis VT eſt itidem in ratione data ad TS æqua-
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            lem P M, diſtantiæ a plano GA BH ſecundum datam dire-
              <lb/>
            ctionem EC; </s>
            <s xml:space="preserve">ac idcirco etiam nulla ex ipſis PR, RT, TV
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            poterit evaneſcere, vel directione mutata abire e poſitiva in
              <lb/>
            negativam, aut vice verſa, mutato ſitu puncti P, niſi ſua ſibi
              <lb/>
            reſpondens ipſius puncti P diſtantia ex iis PR, PO, PM e-
              <lb/>
            vaneſcat fimul, aut directionem mutet. </s>
            <s xml:space="preserve">Quamobrem & </s>
            <s xml:space="preserve">ſumma
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            omnium poſitivarum vel PR, vel RT, vel TV ad ſummam
              <lb/>
            omnium poſitivarum vel PR, vel PO, vel PM, & </s>
            <s xml:space="preserve">ſumma
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            omnium negativarum prioris directionis ad ſummam omnium
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            negativarum poſterioris ſibi reſpondentis, erit itidem in ratio-
              <lb/>
            ne data: </s>
            <s xml:space="preserve">ac proinde ſi omnes poſitivæ directionum P R, P O,
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            PM a ſuis negativis deſtruuntur in illis tribus æqualium diſtan-
              <lb/>
            tiarum planis, etiam omnes poſitivæ PR, RT, TV a ſuis ne-
              <lb/>
            gativis deſtruentur, adeoque & </s>
            <s xml:space="preserve">omnes PV poſitivæ a ſuis ne-
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            gativis. </s>
            <s xml:space="preserve">Quamobrem planum LC IK erit planum diſtantia-
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            rum æqualium. </s>
            <s xml:space="preserve">Q. </s>
            <s xml:space="preserve">E. </s>
            <s xml:space="preserve">D.</s>
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          </p>
          <p>
            <s xml:space="preserve">249. </s>
            <s xml:space="preserve">Demonſtrato hoc theoremate jam ſponte illud conſe-
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            quitur, in quavis punctorum congerie, adeoque maſſarum utcun-
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            que diſperſarum ſumma, baberi ſemper aliquod gravitatis cen-
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            trum, atque id eſſe unicum, quod quidem data omnium puncto-
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            rum poſitione facile determinabitur. </s>
            <s xml:space="preserve">Nam aſſumpto puncto quo-
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            vis ad arbitrium ubicunque, ut puncto P, poterunt duci per
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            ipſum tria plana quæcunque, ut OPM, RPM, RPO.
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            </s>
            <s xml:space="preserve">Tum ſingulis poterunt per num. </s>
            <s xml:space="preserve">246 inveniri plana </s>
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