Bošković, Ruđer Josip, Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium
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              <pb o="147" file="0199" n="199" rhead="PARS SECUNDA."/>
            riore tantum. </s>
            <s xml:space="preserve">Nam ob latera proportionalia ſinubus angulorum
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            oppoſitorum, erit AC x ſin CAD = CD x ſin CDA;
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pariter CB x ſin CBA = CD x ſin CDB. </s>
            <s xml:space="preserve">Quare ob
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            CD communem, ſola ratio ſinuum ADC, BDC, quibus di-
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            rectiones AD, BD inclinantur ad CD, æquatur compoſitæ
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            ex rationibus ſinuum CAD, CBD, & </s>
            <s xml:space="preserve">diſtantiarum CA,
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            CB, quæ ingrediebantur rationem virium B, & </s>
            <s xml:space="preserve">A; </s>
            <s xml:space="preserve">ac eodem
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            pacto AC x ſin ACD = AD x ſin ADC, & </s>
            <s xml:space="preserve">AB x ſin
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            ABD = AD x ſin ADB, adeoque AC x ſin ACD ad
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            AB x ſin ABD, ut ſinus ADC ad ſinum ADB, quibus
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            directiones CD, BD inclinantur ad AD; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eadem eſt demon-
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            ſtratio pro ſinubus ADB, EDB aſſumpto communi latere BD.</s>
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          <p>
            <s xml:space="preserve">317. </s>
            <s xml:space="preserve">Si ducatur MO parallela DA, occurrens BD, CD in
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              <note position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">Alia expreſſio
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              tam virium mo-
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              tricium, quam
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              acceleratricium
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              in eodem caſu.</note>
            M, O, & </s>
            <s xml:space="preserve">compleatur parallelogrammum DMON; </s>
            <s xml:space="preserve">erunt vires
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            motrices in C, B, A ad ſe invicem, ut rectæ DO, DM, DN,
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            & </s>
            <s xml:space="preserve">vires acceleratrices præterea in ratione maſſarum reciproca. </s>
            <s xml:space="preserve">Eſt
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            enim ex præcedenti vis motrix in C ad vim in B, ut ſin BDA
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            ad ſin CDA, vel ob AD, OM parallelas, ut ſin DMO ad
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            ſin DOM, nimirum ut DO ad DM, & </s>
            <s xml:space="preserve">ſimili argumento vis
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            in C ad vim in A, ut DO ad DN. </s>
            <s xml:space="preserve">Vires autem motrices
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            diviſæ per maſſas evadunt acceleratrices. </s>
            <s xml:space="preserve">Quamobrem ſi tres vi-
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            res agerent in idem punctum cum directionibus, quas babent eæ
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            vires motrices, & </s>
            <s xml:space="preserve">eſſent iis proportionales; </s>
            <s xml:space="preserve">binæ componerent vim
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            oppoſitam, & </s>
            <s xml:space="preserve">æqualem tertiæ, ac eſſent in æquilibrio. </s>
            <s xml:space="preserve">Id autem
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            etiam directe patet: </s>
            <s xml:space="preserve">nam vires BQ, AH componuntur ex
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            quatuor viribus BR, BP, AI, AG, quæ ſi ducantur in maſ-
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            ſas ſuas, ut fiant motrices; </s>
            <s xml:space="preserve">evadit prima æqualis, & </s>
            <s xml:space="preserve">contraria
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            tertiæ, quam idcirco elidit, ubi deinde AH, BQ componan-
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            tur ſimul, & </s>
            <s xml:space="preserve">in ejuſmodi compoſitione remanent BP, AG,
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            ex quarum oppoſitis, & </s>
            <s xml:space="preserve">æqualibus CV, Cd componitur ter-
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            tia CT.</s>
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          <p>
            <s xml:space="preserve">318. </s>
            <s xml:space="preserve">Hinc in hiſce viribus motricibus habebuntur omnia,
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              <note position="right" xlink:label="note-0199-02" xlink:href="note-0199-02a" xml:space="preserve">Hic debere ha-
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              beri ea, quæ
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              habentur in
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              compoſitione,
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              & reſolution
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                <lb/>
              virium.</note>
            quæ habentur in compoſitione virium; </s>
            <s xml:space="preserve">dummodo capiatur com-
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            poſitæ contraria. </s>
            <s xml:space="preserve">Si nimirum reſolvantur ſingulæ componentes
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            in duas, alteram ſecundum directionem tertiæ alteram ipſi per-
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            pendicularem, hæ poſteriores elidentur, illæ priores conficient
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            ſummam æqualem tertiæ ubi ambæ eandem directionem habent,
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            uti ſunt binæ, quæ ſimul ingrediantur, vel ſimul evitent trian-
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            gulum; </s>
            <s xml:space="preserve">nam in iis, quarum altera ingreditur, altera evitat,
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            tertia æquaretur differentiæ & </s>
            <s xml:space="preserve">facile tam hic, quam in ratione
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            compoſita, res traducitur ad reſolutionem in aliam quamcunque
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            directionem datam, præter directionem tertiæ, binis ſemper eli-
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            ſis, & </s>
            <s xml:space="preserve">reliquarum accepta ſumma; </s>
            <s xml:space="preserve">ſi rite habeatur ratio poſiti-
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            vorum, & </s>
            <s xml:space="preserve">negativorum.</s>
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          <p>
            <s xml:space="preserve">319. </s>
            <s xml:space="preserve">Eſt & </s>
            <s xml:space="preserve">illud utile: </s>
            <s xml:space="preserve">tres vires motrices in C, B, A ſunt
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              <note position="right" xlink:label="note-0199-03" xlink:href="note-0199-03a" xml:space="preserve">Alia expreſſio
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              rationum ea-
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              rundem virium.</note>
            inter ſe, ut {AB x ED/AD x BD}, {AE/AD}, {BE/BD}, & </s>
            <s xml:space="preserve">acceleratrices </s>
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