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

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              <pb o="115" file="0167" n="167" rhead="PARS SECUNDA."/>
            ſum mæ diſtantiarum punctorum jacentium ultra, demitur horum
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            poſt eriorum punctorum ſumma itidem ducta in O, & </s>
            <s xml:space="preserve">proin-
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            de exceſſui ſummæ citeriorum ſupra ſummam ulteriorum ac-
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            cedit ſumma omnium punctorum harum duarum claſſium ducta
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            in eandem O.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">245. </s>
            <s xml:space="preserve">Quod ſi planum parallelum plano diſtantiarum æqualium
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              <note position="right" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">Theoremata
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              pro plano po
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                <lb/>
              ſito ultra omnia
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              puncta: eorum
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              extenſio ad quæ
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                <lb/>
              vis plana.</note>
            jaceat ultra omnia puncta; </s>
            <s xml:space="preserve">jam habebitur hoc theorema: </s>
            <s xml:space="preserve">Sum-
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            ma omnium diſtantiarum punctorum omnium ab eo plano œqua-
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            bitur diſtantiœ planorum ductœ in omnium punctorum ſummam,
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            & </s>
            <s xml:space="preserve">ſi fuerint duo plana parallela ejuſmodi, ut alterum jaceat ul-
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            tra omnia puncta, & </s>
            <s xml:space="preserve">ſumma omnium diſtantiarum ab ipſo œ-
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            quetur diſtantiœ planorum ductœ in omnium punctorum nume-
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            rum; </s>
            <s xml:space="preserve">alterum illud planum erit planum diſtantiarum œqualium.
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            </s>
            <s xml:space="preserve">Id fane patet ex eo, quod jam ſecunda ſumma pertinens ad
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            puncta ulteriora, quæ nulla ſunt, evaneſcat, & </s>
            <s xml:space="preserve">exceſſus totus
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            ſit ſola prior ſumma. </s>
            <s xml:space="preserve">Quin immo idem theorema habebit
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            locum pro quovis plano habente etiam ulteriora puncta, ſi
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            citeriorum diſtantiæ habeantur pro poſitivis, & </s>
            <s xml:space="preserve">ulteriorum pro
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            negativis; </s>
            <s xml:space="preserve">cum nimirum ſumma conſtans poſitivis, & </s>
            <s xml:space="preserve">nega-
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            tivis ſit ipſe exceſſus poſitivorum ſupra negativa; </s>
            <s xml:space="preserve">quo quidem
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            pacto licebit conſiderare planum diſtantiarum æqualium, ut
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            planum, in quo ſumma omnium diſtantiarum ſit nulla, nega-
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            tivis nimirum diſtantiis elidentibus poſitivas.</s>
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          </p>
          <p>
            <s xml:space="preserve">246. </s>
            <s xml:space="preserve">Hinc autem facile jam patet, dato cuivis plano babe-
              <lb/>
              <note position="right" xlink:label="note-0167-02" xlink:href="note-0167-02a" xml:space="preserve">Cuivis plan
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                <lb/>
              inveniri poſſe
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              parallelum pla.
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              num diſtantia-
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              rum æqualium.</note>
            ri aliquod planum parallelum, quod ſit planum diſtantiarum œ-
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            qualium; </s>
            <s xml:space="preserve">quin immo data poſitione punctorum, & </s>
            <s xml:space="preserve">plano illo
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            ipſo, facile id alterum definitur. </s>
            <s xml:space="preserve">Satis eſt ducere a ſingulis
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            punctis datis rectas in data directione ad planum datum, quæ
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            dabuntur: </s>
            <s xml:space="preserve">tum a ſumma omnium, quæ jacent ex parte al-
              <lb/>
            tera, demere ſummam omnium, ſi quæ ſunt, jacentium ex
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            oppoſita, ac reſiduum dividere per numerum punctorum. </s>
            <s xml:space="preserve">Ad
              <lb/>
            eam diſtantiam ducto plano priori parallelo, id erit planum
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            quæſitum diſtantiarum æqualium. </s>
            <s xml:space="preserve">Patet autem admodum fa-
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            cile & </s>
            <s xml:space="preserve">illud ex eadem demonſtratione, & </s>
            <s xml:space="preserve">ex ſolutione ſupe-
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            rioris problematis, dato cuivis plano non niſi unicum eſſe poſ-
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            ſe planum diſtantiarum æqualium, quod quidem per ſe ſatis
              <lb/>
            patet.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">247. </s>
            <s xml:space="preserve">Hiſce accuratiſſime demonſtratis, atque explicatis,
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              <note position="right" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">Theorema præ
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              cipuum ſi tria
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              plana diſtantia-
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              rum æqualium
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              habeant uni-
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              cum punctum
                <lb/>
              commune; re-
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              liqua omnia per
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              id tranſeuntia
                <lb/>
              erunt ejuſmodi.</note>
            progrediar ad demonſtrandum, haberi aliquod gravitatis cen-
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            trum in quavis punctorum congerie, utcunque diſperſorum, & </s>
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              <lb/>
            in quotcunque maſſas ubicunque ſitas coaleſcentium. </s>
            <s xml:space="preserve">Id fiet
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            ope ſequentis theorematis: </s>
            <s xml:space="preserve">ſi per quoddam punctum tranſeant
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            tria plana diſtantiarum œqualium ſe non in eadem communi ali-
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            qua recta ſecantia; </s>
            <s xml:space="preserve">omnia alia plana tranſeuntia per illud idem
              <lb/>
            punctum erunt itidem diſtantiarum œqualium plana. </s>
            <s xml:space="preserve">Sit enim
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            in fig. </s>
            <s xml:space="preserve">37. </s>
            <s xml:space="preserve">ejuſmodi punctum c, per quod tranſeant tria pla-
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              <note position="right" xlink:label="note-0167-04" xlink:href="note-0167-04a" xml:space="preserve">Fig. 37.</note>
            na GABH, XABY, ECDF, quæ omnia ſint plana di-
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            ſtantiarum æqualium, ac ſit quodvis aliud planum KICL </s>
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