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

Table of Notes

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              <pb o="89" file="0141" n="141" rhead="PARS SECUNDA."/>
            currunt, & </s>
            <s xml:space="preserve">quadratum velocitatis vel augent, vel minuunt
              <lb/>
            quantitate ſibi proportionali.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">195. </s>
            <s xml:space="preserve">Utcunque magna ſit velocitas, qua dimoveantur a di-
              <lb/>
              <note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">Acceſſum de-
                <lb/>
              bere ſiſti ſaltem
                <lb/>
              a primo arcu
                <lb/>
              repulſivo, re.
                <unsure/>
                <lb/>
              ceſſum poſſe
                <lb/>
              haberi in inſi-
                <lb/>
              nitum: caſus
                <lb/>
              notabilis exi-
                <lb/>
              guæ differen.
                <lb/>
              tiæ velocitatis
                <lb/>
              ingentis.</note>
            ſtantia limitum illa duo puncta, utcunque validos inveniant
              <lb/>
            arcus conſpirantes cum velocitatis directione, ſi ad ſe invicem
              <lb/>
            accedunt, debebunt utique alicubi motum retro reſlectere, vel
              <lb/>
            ſaltem ſiſ
              <unsure/>
            tere, quia ſaltem advenient ad diſtantias illas mini-
              <lb/>
            mas, quæ reſpondent arcui aſymptotico, cujus area eſt capax
              <lb/>
            extinguendæ cujuſcunque velocitatis utcunque magnæ. </s>
            <s xml:space="preserve">At ſi re-
              <lb/>
            cedant a ſe invicem, ſieri poteſt, ut deveniant ad arcum ali-
              <lb/>
            quem repulſivum validiſſimum, cujus area ſit major, quam o-
              <lb/>
            mnis exceſſus ſequentium arearum attractivarum ſupra repulſi-
              <lb/>
            vas, uſque ad languidiſſimum illum arcum poſtremi
              <lb/>
              <unsure/>
            cruris gra-
              <lb/>
            vitatem exhibentis. </s>
            <s xml:space="preserve">Tum vero motus acquiſitus ab illo arcu
              <lb/>
            nunquam poterit a ſequentibus ſiſti, & </s>
            <s xml:space="preserve">puncta illa recedent a ſe
              <lb/>
            invicem in immenſum; </s>
            <s xml:space="preserve">quin immo ſi ille arcus repulſivus cum
              <lb/>
            ſequentibus repulſivis ingentem habeat areæ exceſſum ſupra ar-
              <lb/>
            cus ſequentes attractivos; </s>
            <s xml:space="preserve">cum ingenti velocitate pergent pun-
              <lb/>
            cta in immenſum recedere a ſe invicem; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">licet ad initium e-
              <lb/>
            jus tam validi arcus repulſivi deveniant puncta cum velocitati-
              <lb/>
            bus non parum diverſis; </s>
            <s xml:space="preserve">tamen velocitates receſſuum poſt no-
              <lb/>
            vum ingens illud augmentum erunt parum admodum diſcrepan-
              <lb/>
            tes a ſe invicem: </s>
            <s xml:space="preserve">nam ſi ingentis radicis quadrato addatur
              <lb/>
            quadratum radicis multo minoris, quamvis non exiguæ; </s>
            <s xml:space="preserve">ra-
              <lb/>
            dix extracta
              <gap/>
            x ſumma parum admodum differet a radice prio-
              <lb/>
            re.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">196. </s>
            <s xml:space="preserve">Id quidem ex Euclidea etiam Geometria manifeſtum
              <lb/>
              <note position="right" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">Demonſtratio
                <lb/>
              admcdum ſim-
                <lb/>
              plex.</note>
            ſit. </s>
            <s xml:space="preserve">Sit in ſig. </s>
            <s xml:space="preserve">20 A B linea longior, cui addatur ad perpen-
              <lb/>
            diculum BC, multo minor, quam ſit ipſa; </s>
            <s xml:space="preserve">tum centro A,
              <lb/>
            intervallo AC, ſiat ſemicirculus occurrens AB hinc, & </s>
            <s xml:space="preserve">inde
              <lb/>
              <note position="right" xlink:label="note-0141-03" xlink:href="note-0141-03a" xml:space="preserve">Fig. 20.</note>
            in E, D. </s>
            <s xml:space="preserve">Quadrato AB addendo quadratum BC habetur
              <lb/>
            quadratum AC, ſive AD; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">tamen hæc excedit præceden-
              <lb/>
            tem radicem A B per ſolam B D, quæ ſemper eſt minor,
              <lb/>
            quam BC, & </s>
            <s xml:space="preserve">eſt ad ipſam, ut eſt ipſa ad totam BE. </s>
            <s xml:space="preserve">Ex-
              <lb/>
            primat AB velocitatem, quam in punctis quieſcentibus gigne-
              <lb/>
            ret arcus ille repulſivus per ſuam aream, una cum differentia o-
              <lb/>
            mnium ſequentium arcuum repulſivorum ſupra omnes ſequentes
              <lb/>
            attractivos: </s>
            <s xml:space="preserve">exprimat autem BC velocitatem, cum qua adveni-
              <lb/>
            tur ad diſtantiam reſpondentem initio ejus arcus: </s>
            <s xml:space="preserve">exprimet AC
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            velocitatem, quæ habebitur, ubi jam diſtantia evaſit major, & </s>
            <s xml:space="preserve">
              <lb/>
            vis inſenſibilis, ac ejus exceſſus ſupra priorem AB erit BD,
              <lb/>
            exiguus ſane etiam reſpectu BC, ſi BC fuerit exigua reſpe-
              <lb/>
            ctu AB, adeoque multo magis reſpectu EB; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ob eandem
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            rationem perquam exigua area ſequentis cruris attractivi in-
              <lb/>
            gentem illam jam acquiſitam velocitatem nihil ad ſenſum mu-
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            tabit, quæ permanebit ad ſenſum eadem poſt receſſum in im-
              <lb/>
            menſum.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">197. </s>
            <s xml:space="preserve">Hæc accident binis punctis ſibi relictis, vel impulſis
              <lb/>
              <note position="right" xlink:label="note-0141-04" xlink:href="note-0141-04a" xml:space="preserve">Quid accidat</note>
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