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

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              <pb o="117" file="0169" n="169" rhead="PARS SECUNDA."/>
            quæ ſint plana diſtantiarum æqualium, quorum priora duo ſi
              <lb/>
            ſint DCE F, XAB Y, ſe ſecabunt in aliqua recta CE pa-
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            rallela illorum interſectioni M P; </s>
            <s xml:space="preserve">tertium autem GAB H
              <lb/>
            ipſam CE debebit alicubi ſecare in C; </s>
            <s xml:space="preserve">cum planum RP O
              <lb/>
            ſecet PM in P: </s>
            <s xml:space="preserve">nam ex hac ſectione conſtat, hanc rectam
              <lb/>
            non eſſe parallelam huic plano, adeoque nec illa illi erit, ſed
              <lb/>
            in ipſum alicubi incurret. </s>
            <s xml:space="preserve">Tranſibunt igitur per punctum C
              <lb/>
            tria plana diſtantiarum æqualium, adeoque per num. </s>
            <s xml:space="preserve">247 & </s>
            <s xml:space="preserve">
              <lb/>
            aliud quodvis planum tranſiens per punctum idem C erit pla-
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            num æqualium diſtantiarum pro quavis directione, & </s>
            <s xml:space="preserve">idcirco
              <lb/>
            etiam pro diſtantiis perpendicularibus; </s>
            <s xml:space="preserve">ac ipſum punctum C
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            juxta definitionem num. </s>
            <s xml:space="preserve">241, erit commune gravitatis centrum
              <lb/>
            omnium maſſarum, ſive omnis congeriei punctorum, quod qui-
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            dem eſſe unicum, facile deducitur ex definitione, & </s>
            <s xml:space="preserve">hac ipſa
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            demonſtratione; </s>
            <s xml:space="preserve">nam ſi duo eſſent, poſſent utique per ipſa
              <lb/>
            duci duo plana parallela directionis cujuſvis, & </s>
            <s xml:space="preserve">eorum utrum-
              <lb/>
            que eſſet planum diſtantiarum æqualium, quod eſt contra id,
              <lb/>
            quod num. </s>
            <s xml:space="preserve">246 demonſtravimus.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">250. </s>
            <s xml:space="preserve">Demonſtrandum neceſſario fuit, haberi aliquod gravi-
              <lb/>
              <note position="right" xlink:label="note-0169-01" xlink:href="note-0169-01a" xml:space="preserve">Neceſſitas de-
                <lb/>
              monſtrandi ha-
                <lb/>
              beri ſemper cen-
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              trum gravitatis.</note>
            tatis centrum, atque id eſſe unicum; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">perperam id quidem
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            a Mechanicis paſſim omittitur: </s>
            <s xml:space="preserve">ſi enim id non ubique adeſſet,
              <lb/>
            & </s>
            <s xml:space="preserve">non eſſet unicum, in paralogiſmum incurrerent quampluri-
              <lb/>
            mæ Mechanicorum ipſorum demonſtrationes, qui ubi in plano
              <lb/>
            duas invenerunt rectas, & </s>
            <s xml:space="preserve">in ſolidis tria plana determinantia
              <lb/>
            æquilibrium, in ipſa interſectione conſtituunt gravitatis cen-
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            trum, & </s>
            <s xml:space="preserve">ſupponunt omnes alias rectas, vel omnia alia pla-
              <lb/>
            na, quæ per id punctum ducantur, eandem æquilibrii proprie-
              <lb/>
            tatem habere, quod utique fuerat non ſupponendum, ſed de-
              <lb/>
            monſtrandum. </s>
            <s xml:space="preserve">Et quidem facile eſt ſimilis paralogiſmi exem-
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            plum præbere in alio quodam, quod magnitudinis centrum ap-
              <lb/>
            pellare liceret, per quod nimirum figura ſectione quavis ſeca-
              <lb/>
            retur in duas partes æquales inter ſe, ſicut per centrum gravi-
              <lb/>
            tatis ſecta, ſecatur in binas partes æquilibratas in hypotheſi gra-
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            vitatis conſtantis, & </s>
            <s xml:space="preserve">certam directionem habentis plano ſecan-
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            ti parallelam.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">251. </s>
            <s xml:space="preserve">Erraret ſane, qui ita definiret centrum magnitudinis,
              <lb/>
              <note position="right" xlink:label="note-0169-02" xlink:href="note-0169-02a" xml:space="preserve">Centrum enim
                <lb/>
              magnitudinis
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              non ſemper ha-
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              beri.</note>
            tum determinaret id ipſum in datis figuris eadem illa me-
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            thodo, quæ pro centro gravitatis adhibetur. </s>
            <s xml:space="preserve">Is ex. </s>
            <s xml:space="preserve">gr. </s>
            <s xml:space="preserve">pro
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            triangulo ABG in fig. </s>
            <s xml:space="preserve">38 ſic ratiocinationem inſtitueret. </s>
            <s xml:space="preserve">Se-
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              <note position="right" xlink:label="note-0169-03" xlink:href="note-0169-03a" xml:space="preserve">Fig. 38.</note>
            cetur AG bifariam in D, ducaturque BD, quæ utique ipſum
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            triangulum ſecabit in duas partes æquales. </s>
            <s xml:space="preserve">Deinde, ſecta AB
              <lb/>
            itidem bifariam in E, ducatur G E, quam itidem conſtat, de-
              <lb/>
            bere ſecare triangulum in partes æquales duas. </s>
            <s xml:space="preserve">In earum igitur
              <lb/>
            concurſu C habebitur centrum magnitudinis. </s>
            <s xml:space="preserve">Hoc invento ſi
              <lb/>
            progrederetur ulterius, & </s>
            <s xml:space="preserve">haberet pro æqualibus partes, quæ
              <lb/>
            alia ſectione quacunque facta per C obtinentur; </s>
            <s xml:space="preserve">erraret peſ-
              <lb/>
            ſime. </s>
            <s xml:space="preserve">Nam ducta ED, jam conſtat, fore ipſam ED paral-
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            lelam BG, & </s>
            <s xml:space="preserve">ejus dimidiam; </s>
            <s xml:space="preserve">adeoque ſimilia fore </s>
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