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

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              <pb o="307" file="0359" n="359" rhead="ADP. SCHERFFER."/>
            piantur omnes diſtantiæ perpendiculares omnium maſſarum A
              <lb/>
            ab ejuſmodi plano, æquales nimirum ſuis a Q: </s>
            <s xml:space="preserve">ſingularum qua-
              <lb/>
            drata ducantur in ſuas maſſas, & </s>
            <s xml:space="preserve">factorum ſumma dividatur
              <lb/>
            per ſummam maſſarum, tum in recta G Q producta capia-
              <lb/>
            tur G P æqualis; </s>
            <s xml:space="preserve">ei quoto diviſo per ipſam Q G, & </s>
            <s xml:space="preserve">celeri-
              <lb/>
            tas puncti P revolventis circa axem inventum in circulo, cu-
              <lb/>
            jus radius G P, erit æqualis celeritati inventæ centri gravi-
              <lb/>
            tatis, directio autem motus contraria eidem. </s>
            <s xml:space="preserve">Unde habetur
              <lb/>
            directio, & </s>
            <s xml:space="preserve">celeritas motus punctorum reliquorum ſyſtema-
              <lb/>
            tis.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">126. </s>
            <s xml:space="preserve">Patet conſtructio ex eo, quod ita motu compoſito
              <lb/>
              <note position="right" xlink:label="note-0359-01" xlink:href="note-0359-01a" xml:space="preserve">Demonſtratio.</note>
            movebitur ſyſtema circa axem immotum tranſeuntem per P,
              <lb/>
            qui motus regreſſu ſacto a conſtructione tradita ad inventio-
              <lb/>
            nem præmiſſam centri percuſſionis ſiſteretur impreſſione con-
              <lb/>
            traria, & </s>
            <s xml:space="preserve">æquali impreſſioni datæ.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">127. </s>
            <s xml:space="preserve">Scholium. </s>
            <s xml:space="preserve">Hoc poſtremo corollario definitur motus
              <lb/>
              <note position="right" xlink:label="note-0359-02" xlink:href="note-0359-02a" xml:space="preserve">Aditus ad per-
                <lb/>
              quiſitiones ul-
                <lb/>
              teriores motu
                <lb/>
              impreſſo ſyſte-
                <lb/>
              mati moto.</note>
            vi externa impreſſus ſyſtemati quieſcenti. </s>
            <s xml:space="preserve">Quod ſi jam ſyſtema
              <lb/>
            habuerit aliquem motum progreſſivum, & </s>
            <s xml:space="preserve">circularem, novus
              <lb/>
            motus externa vi inductus juxta corollarium ipſum compo-
              <lb/>
            nendus erit cum priore, quod, quo pacto fieri debeat, hic
              <lb/>
            non inquiram, ubi centrum percuſſionis perſequor tantummo-
              <lb/>
            do. </s>
            <s xml:space="preserve">Ea perqu iſitio ex iiſdem principiis perfici poteſt, & </s>
            <s xml:space="preserve">ejus
              <lb/>
            ope patet, aperiri aditum ad inquirendas etiam mutationes,
              <lb/>
            quæ ab inæquali actione Solis, & </s>
            <s xml:space="preserve">Lunæ in partes ſupra globi
              <lb/>
            formam extantes inducuntur in diurnum motum, adeoque ad
              <lb/>
            definiendam ex genuinis principiis præceſſionem æquinoctio-
              <lb/>
            rum, & </s>
            <s xml:space="preserve">nutationem axis: </s>
            <s xml:space="preserve">ſed ea inveſtigatio peculiarem tra-
              <lb/>
            ctationem requirit.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">128. </s>
            <s xml:space="preserve">Interea gradum hic faciam ad aliam notionem quandam
              <lb/>
              <note position="right" xlink:label="note-0359-03" xlink:href="note-0359-03a" xml:space="preserve">Tranſitus ad a-
                <lb/>
              liam notionem
                <lb/>
              ejus centri.</note>
            centri percuſſionis, nihilo minus, imo etiam magis aptam ipſi
              <lb/>
            nomini. </s>
            <s xml:space="preserve">Ad eam perquiſitionem ſic progrediar.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">129. </s>
            <s xml:space="preserve">Problema. </s>
            <s xml:space="preserve">Si ſyſtema datum gyrans data velocitate cir-
              <lb/>
              <note position="right" xlink:label="note-0359-04" xlink:href="note-0359-04a" xml:space="preserve">Problema con-
                <lb/>
              tinens hanc i-
                <lb/>
              deam.</note>
            ca axem datum externa vi immotum incurrat in dato ſuo puncto
              <lb/>
            in maſſam datam, delatam velocitate data in directione motus
              <lb/>
            puncti ejuſdem, quam maſſam debeat abripere ſecum; </s>
            <s xml:space="preserve">quœritur
              <lb/>
            velocitas, quam ei maſſœ imprimet, & </s>
            <s xml:space="preserve">ipſum ſyſtema retinebit
              <lb/>
            poſt impactum.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">130. </s>
            <s xml:space="preserve">Concipiatur totum ſyſtema projectum in planum per-
              <lb/>
              <note position="right" xlink:label="note-0359-05" xlink:href="note-0359-05a" xml:space="preserve">Solutio: for-
                <lb/>
              mulæ continen-
                <lb/>
              tes motum maſ-
                <lb/>
              ſæ in quam in-
                <lb/>
              cidit, & ſuum
                <lb/>
              reliquum.</note>
            pendiculare axi rotationis tranſiens per centrum gravitatis G,
              <lb/>
            in quo plano punctum converſionis ſit P, maſſa autem in re-
              <lb/>
            cta P G in Q. </s>
            <s xml:space="preserve">Velocitas puncti cujuſvis ſyſtematis, quod di-
              <lb/>
            ſtet ab axe per intervallum = 1, ante incurſum ſit = a, velo-
              <lb/>
            citas ab eodem amiſſa ſit = x, adeoque velocitas poſt impa-
              <lb/>
            ctum = a - x, velocitas autem maſſæ Q ante impactum ſit
              <lb/>
            = P Q x b. </s>
            <s xml:space="preserve">Erit ut 1 ad A P, ita x ad velocitatem amiſſam
              <lb/>
            a maſſa A, quæ erit A P x x. </s>
            <s xml:space="preserve">Erit autem ut 1 ad a - x ita
              <lb/>
            P Q ad velocitatem reſiduam in puncto ſyſtematis Q, quæ
              <lb/>
            fiet P Q x (a - x), & </s>
            <s xml:space="preserve">ea erit itidem velocitas maſſæ Q </s>
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