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-s3394" xml:space="preserve">
              <pb o="80" file="0134" n="146" rhead="PHYSICES ELEMENTA"/>
            malis plano A I, ſecans L N in N; </s>
            <s xml:id="echoid-s3395" xml:space="preserve">centro puncto medio li-
              <lb/>
            neæ
              <emph style="sc">A</emph>
            N per
              <emph style="sc">A</emph>
            deſcribatur circulus, qui etiam per L tranſ-
              <lb/>
            ibit; </s>
            <s xml:id="echoid-s3396" xml:space="preserve">ſit
              <emph style="sc">A</emph>
            R pars quarta lineæ
              <emph style="sc">A</emph>
            I; </s>
            <s xml:id="echoid-s3397" xml:space="preserve">per R ducatur, hori-
              <lb/>
            zonti perpendicularis, id eſt parallela lineæ
              <emph style="sc">A</emph>
            L, linea R b,
              <lb/>
            quæ circulum ſecat in B & </s>
            <s xml:id="echoid-s3398" xml:space="preserve">b; </s>
            <s xml:id="echoid-s3399" xml:space="preserve">ſi corpus projiciatur per
              <emph style="sc">A</emph>
            B
              <lb/>
            aut A b cadet in I. </s>
            <s xml:id="echoid-s3400" xml:space="preserve">Qua methodo directio jactus determi-
              <lb/>
            natur, ſi punctum ſit in linea horizontali per A tranſeunti
              <lb/>
            (in quo caſu L & </s>
            <s xml:id="echoid-s3401" xml:space="preserve">N coincidunt), aut in plano quocunque
              <lb/>
            inclinato ſive ſupra ſive infra lineam hanc horizontalem.</s>
            <s xml:id="echoid-s3402" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3403" xml:space="preserve">Motu æ quabili celeritate, cum qua projectio fit, corpus
              <lb/>
              <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">334.</note>
            poteſt percurrere
              <emph style="sc">A</emph>
            E, dum cadit per EI Quia corpus pro-
              <lb/>
            jicitur velocitate per
              <emph style="sc">La</emph>
            cadendo acquiſita, eodem motu
              <lb/>
            æ quabili poteſt percurrere duplam
              <emph style="sc">La</emph>
            in tempore in quo
              <lb/>
            ab altitudine
              <emph style="sc">La</emph>
            cadit . </s>
            <s xml:id="echoid-s3404" xml:space="preserve">Spatia, velocitate eâdem & </s>
            <s xml:id="echoid-s3405" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">257.</note>
            quabili percurſa, ſunt ut tempora in quibus percurruntur;</s>
            <s xml:id="echoid-s3406" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0134-03" xlink:href="note-0134-03a" xml:space="preserve">95.</note>
            ergo tempus caſus per
              <emph style="sc">La</emph>
            ad tempus caſus per EI, ut
              <lb/>
            dupla
              <emph style="sc">La</emph>
            ad
              <emph style="sc">A</emph>
            E. </s>
            <s xml:id="echoid-s3407" xml:space="preserve">Ideo 2
              <emph style="sc">La</emph>
              <emph style="super">9</emph>
            ad
              <emph style="sc">A</emph>
            E
              <emph style="super">9</emph>
            ut,
              <emph style="sc">La</emph>
            ad
              <lb/>
            EI , Quam ergo proportionem ſi demonſtremus dari
              <note symbol="*" position="left" xlink:label="note-0134-04" xlink:href="note-0134-04a" xml:space="preserve">255.</note>
            conſtructione præ cedenti, directionem benè fuiſſe determi-
              <lb/>
            natam conſtabit.</s>
            <s xml:id="echoid-s3408" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3409" xml:space="preserve">Ducatur LB, & </s>
            <s xml:id="echoid-s3410" xml:space="preserve">habemus angulum
              <emph style="sc">Ba</emph>
            R a tangente
              <emph style="sc">A</emph>
            R,
              <lb/>
            eſt enim perpendicularis radio
              <emph style="sc">A</emph>
            O, & </s>
            <s xml:id="echoid-s3411" xml:space="preserve">a linea circulum ſe-
              <lb/>
            cante
              <emph style="sc">A</emph>
            B formatum æ qualem angulo
              <emph style="sc">A</emph>
            MB in ſegmento
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0134-05" xlink:href="note-0134-05a" xml:space="preserve">32 EI. III.</note>
            oppoſito ; </s>
            <s xml:id="echoid-s3412" xml:space="preserve">anguli etiam alterni
              <emph style="sc">RBa</emph>
            ,
              <emph style="sc">La</emph>
            B, ſunt æ quales ;</s>
            <s xml:id="echoid-s3413" xml:space="preserve">
              <note symbol="*" position="left" xlink:label="note-0134-06" xlink:href="note-0134-06a" xml:space="preserve">29. EI. 1.</note>
            ergo ſunt ſimilia triangula
              <emph style="sc">A</emph>
            BR,
              <emph style="sc">A</emph>
            LB, & </s>
            <s xml:id="echoid-s3414" xml:space="preserve">lineæ
              <emph style="sc">La</emph>
            ,
              <lb/>
              <emph style="sc">A</emph>
            B,
              <emph style="sc">Br</emph>
            , proportionales; </s>
            <s xml:id="echoid-s3415" xml:space="preserve">ergo
              <emph style="sc">La</emph>
              <emph style="super">9</emph>
            ad
              <emph style="sc">A</emph>
            B
              <emph style="super">9</emph>
            ut
              <emph style="sc">La</emph>
            ad
              <lb/>
            BR; </s>
            <s xml:id="echoid-s3416" xml:space="preserve">ideo 2
              <emph style="sc">La</emph>
              <emph style="super">9</emph>
            ad 2
              <emph style="sc">A</emph>
            B
              <emph style="super">9</emph>
            , aut
              <emph style="sc">A</emph>
            C
              <emph style="super">9</emph>
            ut
              <emph style="sc">La</emph>
            ad BR:
              <lb/>
            </s>
            <s xml:id="echoid-s3417" xml:space="preserve">multiplicando conſequentia per quatuor, habemus 2
              <emph style="sc">La</emph>
              <emph style="super">9</emph>
              <lb/>
            ad
              <emph style="sc">A</emph>
            C
              <emph style="super">9</emph>
            multiplicatum per quatuor, id eſt 2
              <emph style="sc">A</emph>
            C
              <emph style="super">9</emph>
            , aut
              <lb/>
              <emph style="sc">A</emph>
            E
              <emph style="super">9</emph>
            , ut
              <emph style="sc">La</emph>
            ad 4 BR, aut EI, quod demonſtrandum
              <lb/>
            erat.</s>
            <s xml:id="echoid-s3418" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3419" xml:space="preserve">Demonſtratio ſimilis eſt, ſi corpus per A b projiciatur. </s>
            <s xml:id="echoid-s3420" xml:space="preserve">Un-
              <lb/>
              <note position="left" xlink:label="note-0134-07" xlink:href="note-0134-07a" xml:space="preserve">335.</note>
            de ſequitur corpus per duas directiones poſſe projici ut in
              <lb/>
            idem punctum cadat, ſi autem diſtantia ſit omnium maxima
              <lb/>
            ad quam corpus, data velocitate, in plano dato, poteſt pro-
              <lb/>
            jici, unica eſt directio per quam projiciendum eſt </s>
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