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

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            <s xml:id="echoid-s3420" xml:space="preserve">
              <pb o="81" file="0135" n="147" rhead="MATHEMATICA. LIB. I. CAP. XX."/>
            punctis B & </s>
            <s xml:id="echoid-s3421" xml:space="preserve">b coincidentibus in Q, puncto medio arcus
              <lb/>
            LQA, a quo puncto ſemper æqualiter diſtant puncta B
              <lb/>
            & </s>
            <s xml:id="echoid-s3422" xml:space="preserve">b.</s>
            <s xml:id="echoid-s3423" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3424" xml:space="preserve">Si AI ſit horizontalis arcus AQL, eſt ſemicirculus, & </s>
            <s xml:id="echoid-s3425" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">336.</note>
            in hoc caſu amplitudo, manente celeritate, cum qua pro-
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            jectio fit, eſt omnium maxima, quando directio projectionis
              <lb/>
            cum borizonte efficit angulum ſemirectum.</s>
            <s xml:id="echoid-s3426" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3427" xml:space="preserve">Si celeritas mutetur, & </s>
            <s xml:id="echoid-s3428" xml:space="preserve">corpus ſecundum eandem dire-
              <lb/>
            ctionem projiciatur, amplitudo in eodem plano mutatur in ea-
              <lb/>
            dem ratione cum altitudine A L; </s>
            <s xml:id="echoid-s3429" xml:space="preserve">id eſt, amplitudines, manente
              <lb/>
              <note position="right" xlink:label="note-0135-02" xlink:href="note-0135-02a" xml:space="preserve">337.</note>
            eâdem directione, ſunt ut altitudines ad quas corpora, iiſ-
              <lb/>
            dem celeritatibus, in altum projecta adſcendere poſſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s3430" xml:space="preserve">ſunt ergo ut quadrata celeritatum .</s>
            <s xml:id="echoid-s3431" xml:space="preserve"/>
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          <note symbol="*" position="right" xml:space="preserve">262.</note>
          <p>
            <s xml:id="echoid-s3432" xml:space="preserve">Sit iterum
              <emph style="sc">La</emph>
            altitudo a qua cadendo corpus acquirit
              <lb/>
              <note position="right" xlink:label="note-0135-04" xlink:href="note-0135-04a" xml:space="preserve">338.</note>
            velocitatem cum qua projicitur per
              <emph style="sc">A</emph>
            B; </s>
            <s xml:id="echoid-s3433" xml:space="preserve">punctum altiſſi-
              <lb/>
              <note position="right" xlink:label="note-0135-05" xlink:href="note-0135-05a" xml:space="preserve">TAB XIII.
                <lb/>
              fig. 1.</note>
            mum viæ percurſæ determinatur, ſi deſcripto ſemicirculo
              <lb/>
            cujus diameter eſt AL, per punctum B in quo a directio-
              <lb/>
            ne projectionis ſecatur ducatur horizontalis linea MBG,
              <lb/>
            & </s>
            <s xml:id="echoid-s3434" xml:space="preserve">fiat BG æqualis BM; </s>
            <s xml:id="echoid-s3435" xml:space="preserve">punctum quæſitum erit G.</s>
            <s xml:id="echoid-s3436" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3437" xml:space="preserve">Hujus patebit demonſtratio ſi ad ſequentia attendamus;
              <lb/>
            </s>
            <s xml:id="echoid-s3438" xml:space="preserve">
              <note position="right" xlink:label="note-0135-06" xlink:href="note-0135-06a" xml:space="preserve">339.</note>
            ductâ AI horizontali, corpus ut dictum projectum cadet in
              <lb/>
            I, poſitâ AI quadrupla MB aut AR .</s>
            <s xml:id="echoid-s3439" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">134.</note>
          <p>
            <s xml:id="echoid-s3440" xml:space="preserve">Dum corpus per AB projicitur motus hicce coincidit
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            cum duplici motu horizontali uno & </s>
            <s xml:id="echoid-s3441" xml:space="preserve">æquabili, altero
              <lb/>
            verticali . </s>
            <s xml:id="echoid-s3442" xml:space="preserve">Ultimo motu corpus adſcendit & </s>
            <s xml:id="echoid-s3443" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0135-08" xlink:href="note-0135-08a" xml:space="preserve">246.</note>
            dit, tempuſque adſcenſus æquale eſt tempori deſcenſus;
              <lb/>
            </s>
            <s xml:id="echoid-s3444" xml:space="preserve">ideò aſcenſus terminatur ubi corpus motu horizontali dimi-
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            dium AI, id eſt MG, percurrit; </s>
            <s xml:id="echoid-s3445" xml:space="preserve">punctum ergo altiſſimum
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            datur in verticali lineâ SC quæ per G tranſit. </s>
            <s xml:id="echoid-s3446" xml:space="preserve">Dentur IE
              <lb/>
            verticalis, AB continuatam ſecans in E, ut & </s>
            <s xml:id="echoid-s3447" xml:space="preserve">verticalis
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            BR; </s>
            <s xml:id="echoid-s3448" xml:space="preserve">quia MG dupla eſt MB, id eſt
              <emph style="sc">A</emph>
            S dupla
              <emph style="sc">A</emph>
            R; </s>
            <s xml:id="echoid-s3449" xml:space="preserve">
              <lb/>
            eſt etiam CS dupla BR, id eſt CG æqualis GS: </s>
            <s xml:id="echoid-s3450" xml:space="preserve">Sed
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            AI dupla eſt AS; </s>
            <s xml:id="echoid-s3451" xml:space="preserve">ergo EI dupla CS, & </s>
            <s xml:id="echoid-s3452" xml:space="preserve">quadrupla CG; </s>
            <s xml:id="echoid-s3453" xml:space="preserve">
              <lb/>
            etiam AE dupla AC. </s>
            <s xml:id="echoid-s3454" xml:space="preserve">Dum Corpus motu projectitio per-
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            currit
              <emph style="sc">A</emph>
            E, cadit per EI; </s>
            <s xml:id="echoid-s3455" xml:space="preserve">dum percurrit AC, cadendo quar-
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            tam partem EI id eſt CG percurrit ; </s>
            <s xml:id="echoid-s3456" xml:space="preserve">tranſit idcirco
              <note symbol="*" position="right" xlink:label="note-0135-09" xlink:href="note-0135-09a" xml:space="preserve">255.</note>
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