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

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              <pb o="32" file="0084" n="84" rhead="THEORIÆ"/>
            in omnibus diſſertationibus meis globum, qui cum 12 veloci-
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            tatis gradibus aſſequatur alterum præcedentem cum 6; </s>
            <s xml:space="preserve">ut ni-
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            mirum abeundo ad velocitatem aliam quamcunque haberetur
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            ſaltus ab una velocitate ad aliam, in quo evidentius eſſet ab-
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            ſurdum.</s>
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          </p>
          <p>
            <s xml:space="preserve">69. </s>
            <s xml:space="preserve">Jam vero in hiſce caſibus utique haberi deberet ſaltus
              <lb/>
              <note position="left" xlink:label="note-0084-01" xlink:href="note-0084-01a" xml:space="preserve">Quo pacto mu-
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              tata velocitate
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              potentiali per
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              ſaltum, non
                <lb/>
              mutetur per
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              ſaltum actua-
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              lis.</note>
            quidam, & </s>
            <s xml:space="preserve">violatio legis continuitatis, non quidem in velo-
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            citate actuali, ſed in potentiali, ſi ad contactum deveniretur
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            cum velocitatum diſcrimine aliquo determinato quocunque.
              <lb/>
            </s>
            <s xml:space="preserve">In velocitate actuali, ſi eam metiamur ſpatio, quod confici-
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            tur, diviſo per tempus, tranſitus utique fieret per omnes in-
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            termedias, quod ſic facile oſtenditur ope Geometriæ. </s>
            <s xml:space="preserve">In fig. </s>
            <s xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0084-02" xlink:href="note-0084-02a" xml:space="preserve">Fig. 10.</note>
            10 deſignent AB, BC bina tempora ante, & </s>
            <s xml:space="preserve">poſt contactum,
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            & </s>
            <s xml:space="preserve">momento quolibet H ſit velocitas potentialis illa major HI,
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            quæ æquetur velocitati primæ AD; </s>
            <s xml:space="preserve">quovis autem momento
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            Q poſterioris temporis ſit velocitas potentialis minor Q R,
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            quæ æquetur velocitati cuidam datæ CG. </s>
            <s xml:space="preserve">Aſſumpto quovis
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            tempore HK determinatæ magnitudinis, area IHKL diviſa per
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            tempus HK, ſive recta HI, exhibebit velocitatem actualem.
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            </s>
            <s xml:space="preserve">Moveatur tempus HK verſus B, & </s>
            <s xml:space="preserve">donec K adveniat ad B,
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            ſemper eadem habebitur velocitatis menſura; </s>
            <s xml:space="preserve">eo autem pro-
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            greſſo in O ultra B, ſed adhuc H exiſtente in M citra B, ſpa. </s>
            <s xml:space="preserve">
              <lb/>
            tium illi tempori reſpondens componetur ex binis MNEB,
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            BFPO, quorum ſumma ſi dividatur per MO; </s>
            <s xml:space="preserve">jam nec erit
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            MN æqualis priori AD, nec BF, ipſa minor per datam quan-
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            titatem FE; </s>
            <s xml:space="preserve">ſed facile demonſtrari poteſt , capta VE æquali IL, vel HK, ſive MO, & </s>
            <s xml:space="preserve">ducta recta VF, quæ ſecet MN
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            in X, quotum ex illa diviſione prodeuntem fore MX, donec,
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            abeunte toto illo tempore ultra B in QS, jam area QRTS di-
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            viſa per tempus QS exhibeat velocitatem conſtantem Q R.</s>
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          </p>
          <p>
            <s xml:space="preserve">70. </s>
            <s xml:space="preserve">Patet igitur in ea conſideratione a velocitate actuali
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              <note position="left" xlink:label="note-0084-03" xlink:href="note-0084-03a" xml:space="preserve">Irregularitas
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              alia in expreſ-
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              ſione actualis
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              velocitatis.</note>
            præcedente HI ad ſequentem QR tranſiri per omnes interme-
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            dias MX, quas continua recta VF definiet; </s>
            <s xml:space="preserve">quanquam ibi
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            etiam irregulare quid oritur inde, quod velocitas actualis XM
              <lb/>
            diverſa obvenire debeat pro diverſa magnitudine temporis aſſum-
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            pti HK, quo nimirum aſſumpto majore, vel minore remo-
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            vetur magis, vel minus V ab E, & </s>
            <s xml:space="preserve">decreſcit, vel creſcit XM.
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            </s>
            <s xml:space="preserve">Id tamen accidit in motibus omnibus, in quibus velocitas non
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            manet eadem toto tempore, ut nimirum tum etiam, ſi velocitas
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            aliqua actualis debeat agnoſci, & </s>
            <s xml:space="preserve">determinari ſpatio diviſo per
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            tempus; </s>
            <s xml:space="preserve">pro aliis, atque aliis temporibus aſſumptis pro men-
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            ſura aliæ, atque aliæ velocitatis actualis menſuræ ob-
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              <note symbol="(b)" position="foot" xlink:label="note-0084-04" xlink:href="note-0084-04a" xml:space="preserve">Si enim producatur OP uſque ad NE in γ, erit Eγ = VN, ob
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              VE = MO = Nγ. Eſt autem VE : VN :: EF : NX; quare VN x EF =
                <lb/>
              VE x NX, ſive poſito Eγ pro VN, & MO pro VE, erit Eγ x EF =
                <lb/>
              MO x NX. Totum MNγO eſt MO x MN, pars FEγP eſt = Eγ x EF.
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              Quare reſiduus gnomon NMOPFE eſt MO x (MN - NX), ſive eſt MO
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              x MX, quo diviſo per MO babetur MX.</note>
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