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

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              <pb o="146" file="0198" n="198" rhead="THEORIÆ"/>
            nimirum ex directa ſinuum angulorum, quos continet recta jun-
              <lb/>
            gens ipſarum centra gravitatis cum rectis ductis ab iiſdem centris
              <lb/>
            ad centrum tertiæ maſſæ; </s>
            <s xml:space="preserve">reciproca ſinuum angulorum, quos dire-
              <lb/>
            ctiones ipſarum virium continent cum iiſdem rectis illas jungenti-
              <lb/>
            bus cum tertia; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">reciproca maſſarum.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Nam eſt BQ ad AH aſſumptis terminis mediis BR, AI
              <lb/>
              <note position="left" xlink:label="note-0198-01" xlink:href="note-0198-01a" xml:space="preserve">Ejus demon-
                <lb/>
              ſtratio expedi-
                <lb/>
              tiſſima.</note>
            in ratione compoſita ex rationibus BQ, ad BR, & </s>
            <s xml:space="preserve">BR ad
              <lb/>
            AI, & </s>
            <s xml:space="preserve">AI ad AH. </s>
            <s xml:space="preserve">Prima ratio eſt ſinus QRB, ſive CBA
              <lb/>
            ad ſinum BQR, ſive PBQ, vel CBD: </s>
            <s xml:space="preserve">ſecunda maſſæ A
              <lb/>
            ad maſſam B: </s>
            <s xml:space="preserve">tertia ſinus IHA, ſive HAG, vel CAD,
              <lb/>
            ad ſinum HIA, ſive CAB: </s>
            <s xml:space="preserve">eæ rationes, permutato ſolo
              <lb/>
            ordine antecedentium, & </s>
            <s xml:space="preserve">conſequentium, ſunt rationes ſinus
              <lb/>
            CBA ad ſinum CAB, quæ eſt illa prima e rationibus pro-
              <lb/>
            poſitis directa; </s>
            <s xml:space="preserve">ſinus CAD ad ſinum CBD, quæ eſt ſecunda
              <lb/>
            reciproca: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">maſſæ A ad maſſam B, quæ eſt tertia itidem re-
              <lb/>
            ciproca. </s>
            <s xml:space="preserve">Eadem autem eſt prorſus demonſtratio; </s>
            <s xml:space="preserve">ſi compare-
              <lb/>
            tur BQ, vel AH cum CT, ac in hac demonſtratione, ut & </s>
            <s xml:space="preserve">
              <lb/>
            alibi ubique, ubi de ſinubus angulorum agitur, angulis quibuſvis
              <lb/>
            ſubſtitui poſſunt, uti ſæpe eſt factum, & </s>
            <s xml:space="preserve">fiet impoſterum, eo-
              <lb/>
            rum complementa ad duos rectos, quæ eoſdem habent ſinus.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">314. </s>
            <s xml:space="preserve">Inde conſequitur, eſſe ejuſmodi vires reciproce, ut maſ-
              <lb/>
              <note position="left" xlink:label="note-0198-02" xlink:href="note-0198-02a" xml:space="preserve">Corollarium
                <lb/>
              ſimplex provi-
                <lb/>
              ribus ipſis.</note>
            ſas ductas in ſuas diſtantias a tertia maſſa, & </s>
            <s xml:space="preserve">reciproce, ut ſi-
              <lb/>
            nus, quos earum directiones continent cum iiſdem rectis; </s>
            <s xml:space="preserve">adeoque
              <lb/>
            ubi eæ ad ejuſmodi rectas inclinentur in angulis æqualibus, eſse
              <lb/>
            tantummodo reciproce, ut producta maſſarum per diſtantias a maſ-
              <lb/>
            ſa tertia. </s>
            <s xml:space="preserve">Nam ratio directa ſinuum CBA, CAB eſt ea-
              <lb/>
            dem, ac diſtantiarum AC, BC, ſive reciproca diſtantiarum
              <lb/>
            BC, AC, qua ſubſtituta pro illa, habentur tres rationes reci-
              <lb/>
            procæ, quas exprimit ipſum theorema hic propoſitum. </s>
            <s xml:space="preserve">Porro
              <lb/>
            ubi anguli æquales ſunt, ſinus itidem ſunt æquales, adeoque
              <lb/>
            eorum ſinuum ratio fit 1 ad 1.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">315. </s>
            <s xml:space="preserve">Vires autem motrices ſunt in ratione compoſita ex binis tan-
              <lb/>
              <note position="left" xlink:label="note-0198-03" xlink:href="note-0198-03a" xml:space="preserve">
                <gap/>
              atio virium
                <lb/>
              motricium.</note>
            tummodo, nimirum directa ſinuum angulorum, quos continent di-
              <lb/>
            ſtantiæ a tertia maſſa cum diſtantia a ſe invicem; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">reciproca
              <lb/>
            ſinuum angulorum, quos continent cum iiſdem diſtantiis directio-
              <lb/>
            nes virium; </s>
            <s xml:space="preserve">vel in ratione compoſita ex reciproca illarum diſtan-
              <lb/>
            tiarum, & </s>
            <s xml:space="preserve">reciproca borum poſteriorum ſinuum: </s>
            <s xml:space="preserve">ac ſi inclinatio-
              <lb/>
            nes ad diſtantias ſint æquales, in ſola ratione reciproca diſtantia-
              <lb/>
            rum. </s>
            <s xml:space="preserve">Nam vires motrices ſunt ſummæ omnium virium deter-
              <lb/>
            minantium celeritatem in punctis omnibus ſecundum eam dire-
              <lb/>
            ctionem, ſecundum quam movetur centrum gravitatis commu-
              <lb/>
            ne, quę idcirco ſunt præterea directe, ut maſſæ, ſive ut nu-
              <lb/>
            meri punctorum; </s>
            <s xml:space="preserve">adeoque ratio directa, & </s>
            <s xml:space="preserve">reciproca maſſarum
              <lb/>
            mutuo eliduntur.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">316. </s>
            <s xml:space="preserve">Præterea vires acceleratrices, ſi alicubi earum directio-
              <lb/>
              <note position="left" xlink:label="note-0198-04" xlink:href="note-0198-04a" xml:space="preserve">Ratio virium
                <lb/>
              acceleratrici-
                <lb/>
              um, ubi eæ diri-
                <lb/>
              guntur ad ali-
                <lb/>
              quod commune
                <lb/>
              punctum.</note>
            nes concurrunt, ſunt ad ſe invicem in ratione compoſita ex reci-
              <lb/>
            proca maſſarum, & </s>
            <s xml:space="preserve">reciproca ſinuum angulorum, quibus incli-
              <lb/>
            nantur ad directionem tertiæ & </s>
            <s xml:space="preserve">vires motrices in bac </s>
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