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

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          <p>
            <s xml:id="echoid-s10461" xml:space="preserve">
              <pb o="289" file="0391" n="427" rhead="MATHEMATICA. LIB. II. CAP. XII."/>
            tatem in A exprimit ex ſecunda cauſa ſola patitur. </s>
            <s xml:id="echoid-s10462" xml:space="preserve">Si igitur concipia-
              <lb/>
            mus logarithmicam IR cujus aſymtos ſit BN, & </s>
            <s xml:id="echoid-s10463" xml:space="preserve">quæ tranſeat per I & </s>
            <s xml:id="echoid-s10464" xml:space="preserve">n,
              <lb/>
            deſignabit PR velocitatem quam corpus, ſi ex ſola ſecunda cauſa retarda-
              <lb/>
            retur ſuperſtitem haberet, percurrendo ſpatium experimento detectum AQ,
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0391-01" xlink:href="note-0391-01a" xml:space="preserve">998.</note>
            aut BP , poteſtque ratio inter BI & </s>
            <s xml:id="echoid-s10465" xml:space="preserve">PR detegi .</s>
            <s xml:id="echoid-s10466" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">1007.</note>
          <p>
            <s xml:id="echoid-s10467" xml:space="preserve">Subtangens logarithmicæ IR eſt BN, aut AM dupla AO, quæ eſt ſub-
              <lb/>
            tangens logarithmicæ IP.</s>
            <s xml:id="echoid-s10468" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10469" xml:space="preserve">Si ergo AQ, æqualis BP, logarithmo rationis BI ad PR, in duas partes
              <lb/>
            æquales dividatur in V, & </s>
            <s xml:id="echoid-s10470" xml:space="preserve">VS detur perpendicularis ad AQ, erit BI ad PR,
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0391-03" xlink:href="note-0391-03a" xml:space="preserve">986.</note>
            ut AI ad VS . </s>
            <s xml:id="echoid-s10471" xml:space="preserve">Sunt autem in continuâ proportione AI, VS, QP ; </s>
            <s xml:id="echoid-s10472" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0391-04" xlink:href="note-0391-04a" xml:space="preserve">980.</note>
            go A I
              <emph style="super">q</emph>
            ad V S
              <emph style="super">q</emph>
            , id eſt B I
              <emph style="super">q</emph>
            ad P R
              <emph style="super">q</emph>
            , ut AI ad QP, aut AB; </s>
            <s xml:id="echoid-s10473" xml:space="preserve">& </s>
            <s xml:id="echoid-s10474" xml:space="preserve">divi-
              <lb/>
            dendo</s>
          </p>
        </div>
        <div xml:id="echoid-div1486" type="section" level="1" n="358">
          <head xml:id="echoid-head493" xml:space="preserve">B I
            <emph style="super">q</emph>
          - PR
            <emph style="super">q</emph>
          , PR
            <emph style="super">q</emph>
          :: AI-AB = BI, AB.</head>
          <p>
            <s xml:id="echoid-s10475" xml:space="preserve">Quod ſic enuntiari poteſt: </s>
            <s xml:id="echoid-s10476" xml:space="preserve">Quadratum velocitatis corporis ininitio minus qua-
              <lb/>
              <note position="right" xlink:label="note-0391-05" xlink:href="note-0391-05a" xml:space="preserve">1015.</note>
            drato velocitatis, quam, ſi corpus ex ſola ſecunda cauſa retardaretur, ſuperſtitem ha-
              <lb/>
            beret, poſt percurſum ſpatium, in quo, dum ex ambabus cauſis retardatur, totum
              <lb/>
            motum amittit, ad hoc ultimum quadrarum, ita retardatio ex ſecunda ad retar-
              <lb/>
            dationem ex prima, in primo momento motus.</s>
            <s xml:id="echoid-s10477" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10478" xml:space="preserve">His præmiſſis, computatione detegimus velocitatem in puncto quocunque
              <lb/>
              <note position="right" xlink:label="note-0391-06" xlink:href="note-0391-06a" xml:space="preserve">1016.</note>
            dato lineæ AQ, ut C.</s>
            <s xml:id="echoid-s10479" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10480" xml:space="preserve">Quærimus in numeris tabularum logarithmum rationis BI ad PR ,
              <note symbol="*" position="right" xlink:label="note-0391-07" xlink:href="note-0391-07a" xml:space="preserve">1007.</note>
            eſt logarithmus rationis AI ad VS; </s>
            <s xml:id="echoid-s10481" xml:space="preserve">ſi hic duplicetur habemus numerum
              <lb/>
            qui repræſentat AQ, ſi ponamus ISP eſſe logarithmicam tabularum;
              <lb/>
            </s>
            <s xml:id="echoid-s10482" xml:space="preserve">demonſtrata enim ad logarithmicam quamcunque applicari poſſunt; </s>
            <s xml:id="echoid-s10483" xml:space="preserve">Dica-
              <lb/>
            tur hic numerus L.</s>
            <s xml:id="echoid-s10484" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10485" xml:space="preserve">Ut ſpatium AQ, in quo corpus totum motum amittit, ad ſpatium da-
              <lb/>
            tum AC, id eſt AQ ad AC, ita L ad logarithmum rationis AI ad CD aut
              <lb/>
            AI ad AE: </s>
            <s xml:id="echoid-s10486" xml:space="preserve">qui ergo datur, poteſtque deſignari littera M.</s>
            <s xml:id="echoid-s10487" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10488" xml:space="preserve">Sumto nunc ad libitum numero qui deſignat AI, Log. </s>
            <s xml:id="echoid-s10489" xml:space="preserve">AI - M erit
              <lb/>
            log. </s>
            <s xml:id="echoid-s10490" xml:space="preserve">numeri qui deſignat CD , aut AE. </s>
            <s xml:id="echoid-s10491" xml:space="preserve">Log. </s>
            <s xml:id="echoid-s10492" xml:space="preserve">A I - L eſt log.</s>
            <s xml:id="echoid-s10493" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0391-08" xlink:href="note-0391-08a" xml:space="preserve">982.</note>
            numeri qui deſignat QP, aut AB: </s>
            <s xml:id="echoid-s10494" xml:space="preserve">quos numeros determinamus:
              <lb/>
            </s>
            <s xml:id="echoid-s10495" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0391-09" xlink:href="note-0391-09a" xml:space="preserve">1012.</note>
            dantur ergo tres numeri, qui ſunt inter ſe ut AI, AE, AB; </s>
            <s xml:id="echoid-s10496" xml:space="preserve">quare ex
              <lb/>
              <note position="right" xlink:label="note-0391-10" xlink:href="note-0391-10a" xml:space="preserve">la Hire
                <lb/>
              ſect. con.
                <lb/>
              lib. 3.</note>
            primis duobus ſubtracto ultimo, reſtant numeri, qui ſunt ut BI
              <lb/>
            ad BE, ut id eſt quadrata velocitatum in A & </s>
            <s xml:id="echoid-s10497" xml:space="preserve">C , in initio & </s>
            <s xml:id="echoid-s10498" xml:space="preserve">puncto dato.</s>
            <s xml:id="echoid-s10499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10500" xml:space="preserve">Operatione contraria, datis velocitatibus GI & </s>
            <s xml:id="echoid-s10501" xml:space="preserve">FE, & </s>
            <s xml:id="echoid-s10502" xml:space="preserve">ſpa-
              <lb/>
            tio AQ, in quo corpus totam amittit velocitatem, detegi-
              <lb/>
              <note position="right" xlink:label="note-0391-11" xlink:href="note-0391-11a" xml:space="preserve">1017.</note>
            tur punctum C. </s>
            <s xml:id="echoid-s10503" xml:space="preserve">Nam data AQ detegitur ratio inter BI & </s>
            <s xml:id="echoid-s10504" xml:space="preserve">BA ; </s>
            <s xml:id="echoid-s10505" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0391-12" xlink:href="note-0391-12a" xml:space="preserve">1015.</note>
            que numero qui velocitatem GI, æqualem BI, exprimit datur BA;
              <lb/>
            </s>
            <s xml:id="echoid-s10506" xml:space="preserve">ſed ut GI
              <emph style="super">q</emph>
            ad FE
              <emph style="super">q</emph>
            ita BI ad BE, datur ergo numerus qui lineam hanc ex-
              <lb/>
            primit; </s>
            <s xml:id="echoid-s10507" xml:space="preserve">ideoque numeros determinamus, qui ſunt inter ſe ut AB, AE,
              <lb/>
            AI. </s>
            <s xml:id="echoid-s10508" xml:space="preserve">Ex demonſtratis autem conſtat differentiam log. </s>
            <s xml:id="echoid-s10509" xml:space="preserve">AI, AB, ad
              <note symbol="*" position="right" xlink:label="note-0391-13" xlink:href="note-0391-13a" xml:space="preserve">1013.</note>
            ferentiam log. </s>
            <s xml:id="echoid-s10510" xml:space="preserve">AI, AE, ita AQ ad AC, ſpatium percurſum, quod ergo
              <lb/>
            detegitur.</s>
            <s xml:id="echoid-s10511" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10512" xml:space="preserve">Determinatur etiam CQ ſpatium in quo corpus amittit totum motum da-
              <lb/>
              <note position="right" xlink:label="note-0391-14" xlink:href="note-0391-14a" xml:space="preserve">1018.</note>
            ta velocitate FE in initio, ſubtrahendo nempe AC ex AQ.</s>
            <s xml:id="echoid-s10513" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10514" xml:space="preserve">Si nunc concipiamus, datâ velocitate GI, ſolam locum habere </s>
          </p>
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