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

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              <pb o="145" file="0197" n="197" rhead="PARS SECUNDA."/>
            Cd. </s>
            <s xml:space="preserve">Prima vocando A, B, C maſſas, quarum ea puncta ſunt
              <lb/>
            centra gravitatum, eſt ex actione, & </s>
            <s xml:space="preserve">reactione æqualibus ratio
              <lb/>
            maſſæ B ad C: </s>
            <s xml:space="preserve">ſecunda ſin PQB, ſive AB D ad ſin PBQ,
              <lb/>
            ſive CBD: </s>
            <s xml:space="preserve">tertia A ad B: </s>
            <s xml:space="preserve">quarta ſin HAG, ſive CAD ad
              <lb/>
            ſin GHA, ſive BAD: </s>
            <s xml:space="preserve">quinta C ad A. </s>
            <s xml:space="preserve">Tres rationes, in
              <lb/>
            quibus habentur maſſæ, componunt rationem B x A x C ad
              <lb/>
            C x B x A, quæ eſt 1 ad 1, & </s>
            <s xml:space="preserve">remanet ratio ſin ABD x ſin
              <lb/>
            CAD ad ſin CBD x ſin BAD. </s>
            <s xml:space="preserve">Pro ſin ABD, & </s>
            <s xml:space="preserve">ſin BAD,
              <lb/>
            ponantur AD, & </s>
            <s xml:space="preserve">BD ipſis proportionales; </s>
            <s xml:space="preserve">ac pro ſinu CAD,
              <lb/>
            & </s>
            <s xml:space="preserve">ſin CBD ponantur {ſin ACD x CD/AD}, & </s>
            <s xml:space="preserve">{ſin BCD x CD/BD},
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            ipſis æquales ex Trigonometria, & </s>
            <s xml:space="preserve">habebitur ratio ſin ACD x
              <lb/>
            CD ad ſin BCD x CD, ſive ſin ACD, vel CTV, qui i-
              <lb/>
            pſi æquatur ob VT, CA parallelas, ad ſin BCD, ſive VCT,
              <lb/>
            nimirum ratio ejuſdem illius CV ad VT. </s>
            <s xml:space="preserve">Quare VT æqua-
              <lb/>
            tur Cd, CVTd eſt parallelogrammum, & </s>
            <s xml:space="preserve">vis pertinens ad
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            C, habet directionem itidem tranſeuntem per D.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Secunda pars patet ex iis, quæ demonſtrata ſunt de directio-
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            ne duarum virium, ubi tertia triangulum ingreditur, & </s>
            <s xml:space="preserve">ſex ca-
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            ſus, qui haberi poſſunt, exhibentur totidem figuris. </s>
            <s xml:space="preserve">In fig. </s>
            <s xml:space="preserve">57,
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            & </s>
            <s xml:space="preserve">58 cadit D extra triangulum ultra baſim AB, in 59, & </s>
            <s xml:space="preserve">60
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            intra triangulum, in 61, & </s>
            <s xml:space="preserve">62 extra triangulum citra verticem
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            ad partes baſi oppoſitas, ac in ſingulorum binariorum priore vis
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            CT tendit verſus baſim, in poſteriore ad partes ipſi oppoſitas.
              <lb/>
            </s>
            <s xml:space="preserve">In iis omnibus demonſtratio eſt communis juxta leges transfor-
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            mationis locorum geometricorum, quas diligenter expoſui, & </s>
            <s xml:space="preserve">
              <lb/>
            fuſius perſecutus ſum in diſſertatione adjecta meis Sectionum Co-
              <lb/>
            nicarum Elementis, Elementorum tomo 3.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">311. </s>
            <s xml:space="preserve">Quoniam evadentibus binis HA, QB parallelis, pun-
              <lb/>
              <note position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">Corollarium
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              pro caſu dire-
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              ctionum para
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              l-
                <lb/>
              lelarum.</note>
            ctum D abit in infinitum, & </s>
            <s xml:space="preserve">tertia CT evadit parallela reliquis
              <lb/>
            binis etiam ipſa juxta eaſdem leges; </s>
            <s xml:space="preserve">patet illud: </s>
            <s xml:space="preserve">Sibinæ ex ejuſmo-
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            di directionibus fuerint parallelæ inter ſe; </s>
            <s xml:space="preserve">erit iiſdem parallela & </s>
            <s xml:space="preserve">
              <lb/>
            tertia: </s>
            <s xml:space="preserve">ac illa, quæ jacet inter directiones virium tranſeuntes per re-
              <lb/>
            liquas binas, quæ idcirco in eo caſu appellari poteſt media, babebit
              <lb/>
            directionem oppoſitam directionibus reliquarum conformibus inter ſe.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">312. </s>
            <s xml:space="preserve">Patet autem, datis binis directionibus virium, dari ſem
              <lb/>
              <note position="right" xlink:label="note-0197-02" xlink:href="note-0197-02a" xml:space="preserve">Aliud generale
                <lb/>
              tertiæ directio-
                <lb/>
              nis datæ datis
                <lb/>
              binis.</note>
            per & </s>
            <s xml:space="preserve">tertiam. </s>
            <s xml:space="preserve">Si enim illæ ſint parallelæ; </s>
            <s xml:space="preserve">erit illis parallela
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            & </s>
            <s xml:space="preserve">tertia: </s>
            <s xml:space="preserve">ſi autem concurrant in aliquo puncto; </s>
            <s xml:space="preserve">tertiam deter-
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            minabit recta ad idem punctum ducta: </s>
            <s xml:space="preserve">ſed oportet, habeant il-
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            lam conditionem, ut tam binæ, quæ triangulum non ingredian-
              <lb/>
            tur, quam quæ ingrediantur, vel ſimul tendant ad illud pun-
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            ctum, vel ſimul ad partes ipſi contrarias.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">313. </s>
            <s xml:space="preserve">Hæc quidem pertinent ad directiones: </s>
            <s xml:space="preserve">nunc ipſas ea-
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              <note position="right" xlink:label="note-0197-03" xlink:href="note-0197-03a" xml:space="preserve">Theorema præ-
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              cipuum de ma-
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              gnitudine, quod
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              toti Operi oc-
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              caſionem dedit.</note>
            rum virium magnitudines inter ſe comparabimus, ubi ſtatim
              <lb/>
            occurret elegantiſſimum illud theorema, de quo mentionem
              <lb/>
            feci num 225: </s>
            <s xml:space="preserve">Vires acceleratrices binarum quarumvis e tribus
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            maſſis in ſe mutuo agentibus ſunt in ratione compoſita ex </s>
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