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-s10350" xml:space="preserve">
              <pb o="287" file="0389" n="425" rhead="MATHEMATICA. LIB. II. CAP. XII."/>
            hoc agunt: </s>
            <s xml:id="echoid-s10351" xml:space="preserve">ergo æqualiter eundem motum ejuſdem corporis mutare poſſunt; </s>
            <s xml:id="echoid-s10352" xml:space="preserve">eſt-
              <lb/>
            que retardatio, quam corpus in fluido patitur in primo momento, æqualis
              <lb/>
            velocitati, quam in momento æquali corpus adſcendens, & </s>
            <s xml:id="echoid-s10353" xml:space="preserve">quod gravitas
              <lb/>
            retardat, amittit.</s>
            <s xml:id="echoid-s10354" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10355" xml:space="preserve">Sit nunc C c retardatio quam corpus patitur percurrendo AD, erit C c
              <lb/>
            velocitas quam corpus amittit, adſcendendo ad altitudinem AD, quando gra-
              <lb/>
            vitate retardatur. </s>
            <s xml:id="echoid-s10356" xml:space="preserve">Concipiamus nunc parabolam deſcriptam, cujus axis ſit
              <lb/>
            AB, & </s>
            <s xml:id="echoid-s10357" xml:space="preserve">quæ per puncta C & </s>
            <s xml:id="echoid-s10358" xml:space="preserve">E tranſeat, id eſt eandem habeat tangentem
              <lb/>
            AT cum logarithmica, quæ per C & </s>
            <s xml:id="echoid-s10359" xml:space="preserve">E tranſit, & </s>
            <s xml:id="echoid-s10360" xml:space="preserve">cujus Aſymtos eſt
              <lb/>
            AB.</s>
            <s xml:id="echoid-s10361" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10362" xml:space="preserve">Ordinatæ logarithmicæ hujus deſignabunt velocitates corporis in fluido mo-
              <lb/>
            ti, cujus velocitas in A eſt AC: </s>
            <s xml:id="echoid-s10363" xml:space="preserve">& </s>
            <s xml:id="echoid-s10364" xml:space="preserve">AX axis parabolæ, cujus vertex eſt
              <note symbol="*" position="right" xlink:label="note-0389-01" xlink:href="note-0389-01a" xml:space="preserve">998.</note>
            demonſtrabit altitudinem ad quam corpus, velocitate AC in altum proje-
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0389-02" xlink:href="note-0389-02a" xml:space="preserve">995.</note>
            ctum, & </s>
            <s xml:id="echoid-s10365" xml:space="preserve">ſola gravitate retardatum, poteſt adſcendere ; </s>
            <s xml:id="echoid-s10366" xml:space="preserve">igitur XA,
              <note position="right" xlink:label="note-0389-03" xlink:href="note-0389-03a" xml:space="preserve">1006.</note>
            dium ſubtangentis AT, deſignat altitudinem a qua corpus in vacuo cadendo
              <note symbol="*" position="right" xlink:label="note-0389-04" xlink:href="note-0389-04a" xml:space="preserve">la Hire
                <lb/>
              ſect. con.
                <lb/>
              lib. 2.
                <lb/>
              prop 20.</note>
            quirit velocitatem, qua ſi corpus per fluidum moveatur, reſiſtentiam patitur pon-
              <lb/>
            deri ipſius corporis æqualem, quæ altitudo datur .</s>
            <s xml:id="echoid-s10367" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">930.</note>
          <p>
            <s xml:id="echoid-s10368" xml:space="preserve">Hiſce poſitis ſequentia ſponte ſequuntur.</s>
            <s xml:id="echoid-s10369" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10370" xml:space="preserve">Ut altitudo, à qua corpus in vacuo cadendo, acquirit velocitatem, quæ dat re-
              <lb/>
              <note position="right" xlink:label="note-0389-06" xlink:href="note-0389-06a" xml:space="preserve">1007.</note>
            ſiſtentiam pondericorporis æqualem, ad ſpatium à corpore in fluido percurſum, ita
              <lb/>
            dimidium ſubtangentis tabularum, 0, 21714. </s>
            <s xml:id="echoid-s10371" xml:space="preserve">72409. </s>
            <s xml:id="echoid-s10372" xml:space="preserve">, ad logarihtmum rationis
              <note symbol="*" position="right" xlink:label="note-0389-07" xlink:href="note-0389-07a" xml:space="preserve">987.</note>
            ter velocitates in initio & </s>
            <s xml:id="echoid-s10373" xml:space="preserve">in fine ſpatii .</s>
            <s xml:id="echoid-s10374" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">938.</note>
          <p>
            <s xml:id="echoid-s10375" xml:space="preserve">Numeri quicunque in tabulis, quorum logarihtmorum differentia eſt lo-
              <lb/>
              <note position="right" xlink:label="note-0389-09" xlink:href="note-0389-09a" xml:space="preserve">1008.</note>
            garithmus rationis detectus, ſunt inter ſe ut hæ velocitates .</s>
            <s xml:id="echoid-s10376" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">982. 980.</note>
          <p>
            <s xml:id="echoid-s10377" xml:space="preserve">Eâdem hac regulâ, data ratione inter velocitates in initio & </s>
            <s xml:id="echoid-s10378" xml:space="preserve">fine ſpatii per-
              <lb/>
              <note position="right" xlink:label="note-0389-11" xlink:href="note-0389-11a" xml:space="preserve">1009.</note>
            curſi, detegitur ſpatium hoc.</s>
            <s xml:id="echoid-s10379" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10380" xml:space="preserve">Logarihtmus rationis 2. </s>
            <s xml:id="echoid-s10381" xml:space="preserve">ad I. </s>
            <s xml:id="echoid-s10382" xml:space="preserve">habetur, ſubtrahendo ex log. </s>
            <s xml:id="echoid-s10383" xml:space="preserve">numeri duo
              <lb/>
              <note position="right" xlink:label="note-0389-12" xlink:href="note-0389-12a" xml:space="preserve">1010.</note>
            0, 30102. </s>
            <s xml:id="echoid-s10384" xml:space="preserve">99957. </s>
            <s xml:id="echoid-s10385" xml:space="preserve">log. </s>
            <s xml:id="echoid-s10386" xml:space="preserve">o. </s>
            <s xml:id="echoid-s10387" xml:space="preserve">unitatis, ergo ut o, 21714. </s>
            <s xml:id="echoid-s10388" xml:space="preserve">72409, ad 0, 30102. </s>
            <s xml:id="echoid-s10389" xml:space="preserve">99957,
              <lb/>
            id eſt, ut 10000000000. </s>
            <s xml:id="echoid-s10390" xml:space="preserve">ad 13862945972.</s>
            <s xml:id="echoid-s10391" xml:space="preserve">, ita altitudo, a qua in vacuo caden-
              <lb/>
            do corpus acquirit velocitatem, quæ dat reſiſtentiam ponderi æqualem, ad
              <lb/>
            ſpatium in quo corpus dimidium velocitatis amittit . </s>
            <s xml:id="echoid-s10392" xml:space="preserve">Congruit hoc
              <note symbol="*" position="right" xlink:label="note-0389-13" xlink:href="note-0389-13a" xml:space="preserve">1007.</note>
            indicatis in n. </s>
            <s xml:id="echoid-s10393" xml:space="preserve">962.</s>
            <s xml:id="echoid-s10394" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10395" xml:space="preserve">Si in puncto quocunque retardatio ex ſecunda cauſa fiat æquabilis, ſpatium
              <lb/>
              <note position="right" xlink:label="note-0389-14" xlink:href="note-0389-14a" xml:space="preserve">1011.</note>
            in quo tota deſtruitur velocitas dimidiata ſubtangente repræſentatur, ut ſequi-
              <lb/>
            tur ex demonſtratione n. </s>
            <s xml:id="echoid-s10396" xml:space="preserve">1005, quæ & </s>
            <s xml:id="echoid-s10397" xml:space="preserve">hîc applicari poteſt; </s>
            <s xml:id="echoid-s10398" xml:space="preserve">cum autem ſub-
              <lb/>
            tangens conſtans ſit , ſequitur etiam in fluido homogeneo, quale in his
              <note symbol="*" position="right" xlink:label="note-0389-15" xlink:href="note-0389-15a" xml:space="preserve">984.</note>
            que ponimus, ſpatium illud non mutari, quomodocunque varietur veloci-
              <lb/>
            tas, & </s>
            <s xml:id="echoid-s10399" xml:space="preserve">æquari altitudini a qua in vacuo cadendo corpus acquirit velocitatem, qua
              <lb/>
            poſitâ, reſiſtentia ponderi æqualis eſt.</s>
            <s xml:id="echoid-s10400" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">1006.</note>
        </div>
        <div xml:id="echoid-div1478" type="section" level="1" n="357">
          <head xml:id="echoid-head491" xml:space="preserve">SCHOLIUM 5.</head>
          <head xml:id="echoid-head492" style="it" xml:space="preserve">De ambabus Retardationibus conjunctim.</head>
          <p>
            <s xml:id="echoid-s10401" xml:space="preserve">Sit A M linea, quam corpus in fluido percurrit; </s>
            <s xml:id="echoid-s10402" xml:space="preserve">ſit hæc Aſymtos loga-
              <lb/>
              <note position="right" xlink:label="note-0389-17" xlink:href="note-0389-17a" xml:space="preserve">1012.</note>
            rithmicæ ISP; </s>
            <s xml:id="echoid-s10403" xml:space="preserve">cujus AI eſt ordinata; </s>
            <s xml:id="echoid-s10404" xml:space="preserve">ſit præterea GFB parabola cu-
              <lb/>
              <note position="right" xlink:label="note-0389-18" xlink:href="note-0389-18a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              fig. 4.</note>
            jus axis eſt IB; </s>
            <s xml:id="echoid-s10405" xml:space="preserve">vertex B; </s>
            <s xml:id="echoid-s10406" xml:space="preserve">ordinata GI, parallela AM; </s>
            <s xml:id="echoid-s10407" xml:space="preserve">Parameter BI: </s>
            <s xml:id="echoid-s10408" xml:space="preserve">Si
              <lb/>
            AB fuerit ad BI, ut retardatio ex prima cauſa ad retardationem ex </s>
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