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

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              <pb o="142" file="0194" n="194" rhead="THEORIÆ"/>
            plana incurvabitur motus illis viribus, ſed ita, ut velocitas
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            parallela ab iis nihil turbetur, velocitas autem perpendicularis
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            vel minuatur, vel augeatur; </s>
            <s xml:space="preserve">prout vires tendent verſus planum
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            citerius AB, vel verſus ulterius CD. </s>
            <s xml:space="preserve">Jam vero tres caſus
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            haberi hinc poſſunt; </s>
            <s xml:space="preserve">vel enim iis viribus tota velocitas per-
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            pendicularis ES extinguitur, antequam deveniatur ad planum
              <lb/>
            ulterius CD; </s>
            <s xml:space="preserve">vel perſtat uſque ad appulſum ad ipſum CD,
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            ſed imminuta, vi contraria prævalente viribus eadem directio-
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            ne agentibus; </s>
            <s xml:space="preserve">vel perſtat potius aucta.</s>
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          <p>
            <s xml:space="preserve">303. </s>
            <s xml:space="preserve">In primo caſu, ubi primum velocitas perpendicularis
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              <note position="left" xlink:label="note-0194-01" xlink:href="note-0194-01a" xml:space="preserve">Primo refle-
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              xionem indu-
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              ci.</note>
            extincta fuerit alicubi in X, punctum mobile reflectet curſum
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            retro per XI, & </s>
            <s xml:space="preserve">iiſdem viribus agentibus in regreſſu, quæ
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            egerant in progreſſu, acquiret velocitatem perpendicularem IL
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            æqualem amiſſæ ES, quæ compoſita cum parallela LM, æquali
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            priori HS, exhibebit obliquam IM in recta nova IK, quam
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            deſcribet poſt egreſſum, & </s>
            <s xml:space="preserve">erunt æquales anguli HIL, MES,
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            adeoque & </s>
            <s xml:space="preserve">anguli KIB, GEA; </s>
            <s xml:space="preserve">quod congruit cum iis, quæ
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            in fig. </s>
            <s xml:space="preserve">54. </s>
            <s xml:space="preserve">ſunt exhibita, & </s>
            <s xml:space="preserve">pertinent ad reflexionem.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">304. </s>
            <s xml:space="preserve">In ſecundo caſu prodibit ultra ſuperficiem ulteriorem
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              <note position="left" xlink:label="note-0194-02" xlink:href="note-0194-02a" xml:space="preserve">Secundo refra-
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              ctionem cum
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              acceſſu ad ſu-
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              perficiem re-
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              fringentem,
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              tertio itidem
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              refractionem,
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              ſed cum re-
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              ceſſu.</note>
            CD, ſed ob velocitatem perpendicularem OP minorem prio-
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            re ES, parallelam vero PN æqualem priori HS, erit angu-
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            lus ONP minor, quam EHS, adeoque inclinatio VOD ad
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            ſuperficiem in egreſſu minor inclinatione GEA in ingreſſu.
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            </s>
            <s xml:space="preserve">Contra vero in tertio caſu ob op majorem ES, angulus uo D
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            erit major. </s>
            <s xml:space="preserve">In utroque autem hoc caſu differentia quadra-
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            torum velocitatis ES, & </s>
            <s xml:space="preserve">OP vel op, erit conſtans, per num. </s>
            <s xml:space="preserve">
              <lb/>
            177 in adn. </s>
            <s xml:space="preserve">m, quæcunque fuerit inclinatio GE in ingreſſu, a
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            qua inclinatione pendet velocitas perpendicularis SE.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">305. </s>
            <s xml:space="preserve">Inde autem facile demonſtratur, fore ſinum anguli in-
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              <note position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">Ratio conſtans
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              ſinus anguli in-
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              cidentiæ ad
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              ſinum an
                <unsure/>
              guli
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              refracti.</note>
            cidentiæ HES, ad ſinum anguli refracti PON (& </s>
            <s xml:space="preserve">quidquid
              <lb/>
            dicitur de iis, quæ deſignantur litteris PON, erunt commu-
              <lb/>
            nia iis, quæ exprimuntur litteris pon) in ratione conſtanti,
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            quæcunque fuerit inclinatio rectæ incidentis GE. </s>
            <s xml:space="preserve">Sumatur
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            enim HE conſtans, quæ exprimat velocitatem ante inciden-
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            tiam: </s>
            <s xml:space="preserve">exprimet HS velocitatem parallelam, quæ erit æqualis
              <lb/>
            rectæ PN exprimenti velocitatem parallelam poſt refractio-
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            nem; </s>
            <s xml:space="preserve">ac ES, OP expriment velocitates perpendiculares ante,
              <lb/>
            & </s>
            <s xml:space="preserve">poſt, quarum quadrata habebunt differentiam conſtantem.
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            </s>
            <s xml:space="preserve">Sed ob HS, PN ſemper æquales, differentia quadratorum
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            HE, ON æquatur differentiæ quadratorum ES, OP. </s>
            <s xml:space="preserve">Igitur
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            etiam differentia quadratorum HE, ON erit conſtans; </s>
            <s xml:space="preserve">cum-
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            que ob HE conſtantem debeat eſſe conſtans ejus quadratum; </s>
            <s xml:space="preserve">
              <lb/>
            erit conſtans etiam quadratum ON, adeoque conſtans etiam
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            ipſa ON, & </s>
            <s xml:space="preserve">proinde conſtans erit & </s>
            <s xml:space="preserve">ratio HE ad ON; </s>
            <s xml:space="preserve">
              <lb/>
            quæ quidem ratio eſt eadem, ac ſinus anguli NOP ad ſinum
              <lb/>
            HES: </s>
            <s xml:space="preserve">cum enim ſit in quovis triangulo rectangulo radius ad
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            latus utrumvis, ut baſis ad ſinum anguli oppoſiti; </s>
            <s xml:space="preserve">in diverſis
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            triangulis rectangulis ſunt ſinus, ut latera oppoſita diviſa </s>
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