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

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              <pb o="113" file="0165" n="165" rhead="PARS SECUNDA."/>
            ſuſpenſo utcunque ex ejuſmodi puncto, quale definivimus gra-
              <lb/>
            vitatis centrum, omni eo ſyſtemate, cujus ſyſtematis puncta
              <lb/>
            viribus quibuſcunque, vel conceptis virgis inflexilibus, & </s>
            <s xml:space="preserve">gra-
              <lb/>
            vitate carentibus, poſitionem mutuam, & </s>
            <s xml:space="preserve">reſpectivum ſtatum,
              <lb/>
            ac diſtantias omnino ſervent, id ſyſtema fore in æquilibrio;
              <lb/>
            </s>
            <s xml:space="preserve">atque illud ipſum requiri, ut in æquilibrio ſit. </s>
            <s xml:space="preserve">Si enim vel
              <lb/>
            unicum planum ductum per id punctum ſit ejuſmodi, ut ſum-
              <lb/>
            mæ illæ diſtantiarum non ſint æquales hinc, & </s>
            <s xml:space="preserve">inde; </s>
            <s xml:space="preserve">conver-
              <lb/>
            ſo ſyſtemate omni ita, ut illud punctum evadat verticale, jam
              <lb/>
            non eſſent æquales inter ſe ſummæ momentorum hinc, & </s>
            <s xml:space="preserve">inde,
              <lb/>
            & </s>
            <s xml:space="preserve">altera pars alteri præponderaret. </s>
            <s xml:space="preserve">Verum hæc quidem, uti
              <lb/>
            ſupra monui, fuit occaſio quædam nominis imponendi; </s>
            <s xml:space="preserve">at i-
              <lb/>
            pſum punctum ea lege determinatum longe ulterius extenditur,
              <lb/>
            quam ad ſolas maſſas animatas viribus æqualibus, & </s>
            <s xml:space="preserve">parallelis,
              <lb/>
            cujuſmodi concipiuntur a nobis in noſtris gravibus, licet ne in
              <lb/>
            ipſis quidem accurate ſint tales. </s>
            <s xml:space="preserve">Quamobrem aſſumpta ſuperio-
              <lb/>
            re definitione, quæ a gravitatis, & </s>
            <s xml:space="preserve">æquilibrii natura non pen-
              <lb/>
            det, progrediar ad deducenda inde corollaria quædam, quæ nos
              <lb/>
            ad ejus proprietates demonſtrandas deducant.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">242. </s>
            <s xml:space="preserve">Primo quidem ſi aliquod fuerit ejuſmodi planum, ut
              <lb/>
              <note position="right" xlink:label="note-0165-01" xlink:href="note-0165-01a" xml:space="preserve">Cor
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              llarium
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              generale perti-
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              nens ad ſum-
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              mas diſtantia-
                <lb/>
              rum omnium
                <lb/>
              punctorum maſ-
                <lb/>
              ſæ a plano tranſ.
                <lb/>
              eunte per cen-
                <lb/>
              trum gravitatis
                <lb/>
              æquales utrin-
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              que.</note>
            binæ ſummæ diſtantiarum perpendicularium punctorum omnium
              <lb/>
            hinc, & </s>
            <s xml:space="preserve">inde acceptorum æquentur inter ſe; </s>
            <s xml:space="preserve">æquabuntur & </s>
            <s xml:space="preserve">
              <lb/>
            ſummæ diſtantiarum acceptarum ſecundum quancunque aliam
              <lb/>
            directionem datam, & </s>
            <s xml:space="preserve">communem pro omnibus. </s>
            <s xml:space="preserve">Erit enim
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            quævis diſtantia perpendicularis ad quanvis in dato angulo in-
              <lb/>
            clinatam ſemper in eadem ratione, ut patet. </s>
            <s xml:space="preserve">Quare & </s>
            <s xml:space="preserve">ſum-
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            mæ illarum ad harum ſummas erunt in eadem ratione, ac æ-
              <lb/>
            qualitas ſummarum alterius binarii utriuslibet ſecum trahet æ-
              <lb/>
            qualitatem alterius. </s>
            <s xml:space="preserve">Quare in ſequentibus, ubi diſtantias no-
              <lb/>
            minavero, niſi exprimam perpendiculares, intelligam generali-
              <lb/>
            ter diſtantias acceptas in quavis directione data.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">243. </s>
            <s xml:space="preserve">Quod ſi aſſumatur planum aliud quodcunque parallelum
              <lb/>
              <note position="right" xlink:label="note-0165-02" xlink:href="note-0165-02a" xml:space="preserve">Bina theore-
                <lb/>
              mata pertinen.
                <lb/>
              tia ad planum
                <lb/>
              parallelum pla-
                <lb/>
              no diſtantia-
                <lb/>
              rum æqualium
                <lb/>
              cum eorum de-
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              monſtrationi-
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              bus.</note>
            plano habenti æquales hinc, & </s>
            <s xml:space="preserve">inde diſtantiarum ſummas;
              <lb/>
            </s>
            <s xml:space="preserve">ſumma diſtantiarum omnium punctorum jacentium ex parte
              <lb/>
            altera ſuperabit ſummam jacentium ex altera, exceſſu æquali di-
              <lb/>
            ſtantiæ planorum acceptæ ſecundum directionem eandem ductæ
              <lb/>
            in numerum punctorum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">vice verſa ſi duo plana parallela
              <lb/>
            ſint, ac is exceſſus alterius ſummæ ſupra ſummam alterius in
              <lb/>
            altero ex iis æquetur eorum diſtantiæ ductæ in numerum pun-
              <lb/>
            ctorum; </s>
            <s xml:space="preserve">planum alterum habebit oppoſitarum diſtantiarum ſum-
              <lb/>
            mas æquales. </s>
            <s xml:space="preserve">Id quidem facile concipitur; </s>
            <s xml:space="preserve">ſi concipiatur,
              <lb/>
            planum diſtantiarum æqualium moveri verſus illud alterum
              <lb/>
            planum motu parallelo ſecundum eam directionem, ſecundum
              <lb/>
            quam ſumuntur diſtantiæ. </s>
            <s xml:space="preserve">In eo motu diſtantiæ ſingulæ ex
              <lb/>
            altera parte creſcunt, ex altera decreſcunt continuo tantum,
              <lb/>
            quantum promovetur planum, & </s>
            <s xml:space="preserve">ſi aliqua diſtantia evane-
              <lb/>
            ſcit interea; </s>
            <s xml:space="preserve">jam eadem deinde incipit tantundem ex parte
              <lb/>
            contraria creſcere. </s>
            <s xml:space="preserve">Quare patet exceſſum omnium </s>
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