Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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          <pb o="108" file="0166" n="180" rhead="PHYSICES ELEMENTA"/>
        </div>
        <div xml:id="echoid-div664" type="section" level="1" n="186">
          <head xml:id="echoid-head263" xml:space="preserve">SCHOLIUM. 6</head>
          <head xml:id="echoid-head264" xml:space="preserve">De Computatione motuum Apſidum in curvis parum
            <lb/>
          cum circulo differentibus.</head>
          <p>
            <s xml:id="echoid-s4526" xml:space="preserve">Apſides dicuntur extremitates axeos majoris Ellipſeos in qua movetur cor-
              <lb/>
            pus, quod vi ad focum tendente retinetur. </s>
            <s xml:id="echoid-s4527" xml:space="preserve">Agitur hìc de motus Apſidum
              <lb/>
            determinatione, id eſt de motu angulari Ellipſeos, poſitâ vi, quæ ſequatur
              <lb/>
            rationem poteſtatis cujuſcunque diſtantiæ, in quo caſu motus ad Elliptin
              <lb/>
            mobilem referri non poterit, niſi agatur de curvâ à circulo parum diffe-
              <lb/>
            rente .</s>
            <s xml:id="echoid-s4528" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">425.</note>
          <p>
            <s xml:id="echoid-s4529" xml:space="preserve">Lemmatica autem propoſitio præmittenda eſt. </s>
            <s xml:id="echoid-s4530" xml:space="preserve">Quadratum hujus quanti-
              <lb/>
              <note position="left" xlink:label="note-0166-02" xlink:href="note-0166-02a" xml:space="preserve">428.</note>
            tatis a-b eſt aa-2ab + bb, ut cubus formetur ſingulæ quanti-
              <lb/>
            tates hujus quadrati per a-b multiplicari debent, productum duarum prima-
              <lb/>
            rum per has eſt a
              <emph style="super">3</emph>
            - 3aab + 2abb & </s>
            <s xml:id="echoid-s4531" xml:space="preserve">in reliqua parte producti adſcendit b
              <lb/>
            ad majorem quàm ad primam poteſtatem.</s>
            <s xml:id="echoid-s4532" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4533" xml:space="preserve">Ut ex cubo formetur quarta poteſtas, ſingulæ cubi quantitates per a-b
              <lb/>
            multiplicari debent; </s>
            <s xml:id="echoid-s4534" xml:space="preserve">multiplicatis duabus primis, habemus a
              <emph style="super">4</emph>
            - 4a
              <emph style="super">3</emph>
            b + 3aabb
              <lb/>
            & </s>
            <s xml:id="echoid-s4535" xml:space="preserve">in reliquis quantitatibus totius poteſtatis elevatur b ultra primam poteſta-
              <lb/>
            tem.</s>
            <s xml:id="echoid-s4536" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4537" xml:space="preserve">Siccontinuando clarè patet: </s>
            <s xml:id="echoid-s4538" xml:space="preserve">Siagatur de poteſtate quantitatis a-b, cujus index ſit
              <lb/>
              <note position="left" xlink:label="note-0166-03" xlink:href="note-0166-03a" xml:space="preserve">429.</note>
            n, primos terminos eſſe a
              <emph style="super">n</emph>
            - na
              <emph style="super">n-1</emph>
            b, & </s>
            <s xml:id="echoid-s4539" xml:space="preserve">in reliquis omnibus dabitur b ad poteſta-
              <lb/>
            tem magis elevatam.</s>
            <s xml:id="echoid-s4540" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4541" xml:space="preserve">Poſitis nunc quæ in Scholio præcedenti ſunt demonſtrata; </s>
            <s xml:id="echoid-s4542" xml:space="preserve">dicatur H di-
              <lb/>
              <note position="left" xlink:label="note-0166-04" xlink:href="note-0166-04a" xml:space="preserve">430.</note>
            ſtantia omnium maxima AF; </s>
            <s xml:id="echoid-s4543" xml:space="preserve">& </s>
            <s xml:id="echoid-s4544" xml:space="preserve">X difterentia indeterminata inter H & </s>
            <s xml:id="echoid-s4545" xml:space="preserve">D;
              <lb/>
            </s>
            <s xml:id="echoid-s4546" xml:space="preserve">reducendo duas fractiones {NN/D
              <emph style="super">q</emph>
            } + {RMM-RNN/D
              <emph style="super">c</emph>
            } ad unicam habemus
              <lb/>
            {DNN + RMM - RNN/D
              <emph style="super">c</emph>
            }, ſubſtituendo in numeratore pro D valorem
              <lb/>
            H-X, vis in Ellipſi mobili proportionalis eſt {RMM-RNN - HNN-NNX/D
              <emph style="super">c</emph>
            }. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">
              <lb/>
            Detur nunc vis quæ ſequatur rationem cujuſcunque poteſtatis diſtantiæ, cu-
              <lb/>
            jus poteſtatis index ſit n-3, id eſt vis eſt ut D
              <emph style="super">n-3</emph>
            = {D
              <emph style="super">n</emph>
            /D
              <emph style="super">c</emph>
            } = {
              <emph style="ol">H-X</emph>
              <emph style="super">n</emph>
            /D
              <emph style="super">c</emph>
            } =
              <lb/>
            {H
              <emph style="super">n</emph>
            -nH
              <emph style="super">n-1</emph>
            X + &</s>
            <s xml:id="echoid-s4548" xml:space="preserve">c/D
              <emph style="super">c</emph>
            } in reliquis terminis numeratoris ultra primam
              <note symbol="*" position="left" xlink:label="note-0166-05" xlink:href="note-0166-05a" xml:space="preserve">429.</note>
            adſcendit X; </s>
            <s xml:id="echoid-s4549" xml:space="preserve">ideò hi omnes exigui ſunt reſpectu illorumqui hìc ponuntur, quia X
              <lb/>
            exigua eſt reſpectu H: </s>
            <s xml:id="echoid-s4550" xml:space="preserve">ponimus enim curvam cum circulo parum differrre.
              <lb/>
            </s>
            <s xml:id="echoid-s4551" xml:space="preserve">Si nunc motus corporis quod vi hac in curva retinetur referri debeat ad mo-
              <lb/>
            tum in Ellipſi mobili, vis hæc analoga ponenda eſt cum vi qua corpus
              <lb/>
            in tali Ellipſi revera retinetur, ſunt ergo analogæ quantitates </s>
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