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

Table of handwritten notes

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