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

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            <s xml:id="echoid-s3456" xml:space="preserve">
              <pb o="82" file="0136" n="148" rhead="PHYSICES ELEMENTA"/>
            motu ſuo per punctum G, quod eſt punctum altiſſimum
              <lb/>
            cùm hoc detur in linea CS.</s>
            <s xml:id="echoid-s3457" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3458" xml:space="preserve">Si detur curvâ à corpore percurſâ, velocitas quam habet
              <lb/>
              <note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">340.</note>
            corpus in puncto quocunque ut F, illa eſt, quam Corpus po-
              <lb/>
            teſt acquirere cadendo à linea horizontali per L ducta ad
              <lb/>
            punctum F. </s>
            <s xml:id="echoid-s3459" xml:space="preserve">Nam Corpus per planum quodcunque ex A,
              <lb/>
            velocitate qua projicitur, adſcendere poteſt ad horizontalem
              <lb/>
            hanc lineam , ſi nunc planum detur ad F uſque cum
              <note symbol="*" position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">274.</note>
            corporis projecti via congruens, in F autem ſurſum defle-
              <lb/>
            xum, corpus in F illam habebit velocitatem qua juxta pla-
              <lb/>
            num hoc ad horizontalem memoratam pervenire poteſt,
              <lb/>
            id eſt quam cadendo ab ipſa horizontali ad F uſque ac-
              <lb/>
            quirere poteſt .</s>
            <s xml:id="echoid-s3460" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">274.</note>
          <p>
            <s xml:id="echoid-s3461" xml:space="preserve">Sit corpus ex A projiciendum per punctum H in I, poſi-
              <lb/>
              <note position="left" xlink:label="note-0136-04" xlink:href="note-0136-04a" xml:space="preserve">341.</note>
            tis tribus hiſce punctis in eodem plano verticali, & </s>
            <s xml:id="echoid-s3462" xml:space="preserve">puncto
              <lb/>
              <note position="left" xlink:label="note-0136-05" xlink:href="note-0136-05a" xml:space="preserve">TAB. XIII.
                <lb/>
              fig. 7.</note>
            medio ſupra lineam quæ reliqua duo jungit. </s>
            <s xml:id="echoid-s3463" xml:space="preserve">Sit AI ho-
              <lb/>
            rizontalis & </s>
            <s xml:id="echoid-s3464" xml:space="preserve">per tria puncta data ad hanc normales TE, FD,
              <lb/>
            AL. </s>
            <s xml:id="echoid-s3465" xml:space="preserve">Ex I per puncta A & </s>
            <s xml:id="echoid-s3466" xml:space="preserve">H ducantur lineæ IA, IH,
              <lb/>
            quarum ultima ſecat AL in P; </s>
            <s xml:id="echoid-s3467" xml:space="preserve">fiat GD æqualis
              <emph style="sc">A</emph>
            P, & </s>
            <s xml:id="echoid-s3468" xml:space="preserve">
              <lb/>
            habetur
              <emph style="sc">A</emph>
            D directio jactus. </s>
            <s xml:id="echoid-s3469" xml:space="preserve">Celeritas detegitur ſi ſumtâ
              <lb/>
              <emph style="sc">A</emph>
            R quartâ parte
              <emph style="sc">A</emph>
            I; </s>
            <s xml:id="echoid-s3470" xml:space="preserve">& </s>
            <s xml:id="echoid-s3471" xml:space="preserve">ductâ verticali RB, quæ
              <emph style="sc">A</emph>
            D
              <lb/>
            ſecat in B, ducatur BL ita, ut angulus
              <emph style="sc">A</emph>
            BL æqualis ſit
              <lb/>
            angulo
              <emph style="sc">A</emph>
            RB, velocitas quæſita eſt quam corpus acquirit
              <lb/>
            cadendo ex L in A,</s>
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          <p>
            <s xml:id="echoid-s3472" xml:space="preserve">Corpus projectum æquabili percurrit velocitate
              <emph style="sc">A</emph>
            E & </s>
            <s xml:id="echoid-s3473" xml:space="preserve">
              <lb/>
            AD, dum cadit per EI & </s>
            <s xml:id="echoid-s3474" xml:space="preserve">DH: </s>
            <s xml:id="echoid-s3475" xml:space="preserve">ut ergo demonſtremus
              <lb/>
            corpus per hæc puncta tranſire, demonſtrandum
              <lb/>
              <emph style="sc">A</emph>
            E
              <emph style="super">9</emph>
            ſe habere ad
              <emph style="sc">A</emph>
            D
              <emph style="super">9</emph>
            , aut EI
              <emph style="super">9</emph>
            ad DG
              <emph style="super">9</emph>
            , ut EI ad
              <lb/>
            DH .</s>
            <s xml:id="echoid-s3476" xml:space="preserve"/>
          </p>
          <note symbol="*" position="left" xml:space="preserve">255.</note>
          <p>
            <s xml:id="echoid-s3477" xml:space="preserve">In triangulis ſimilibus IHG,
              <emph style="sc">IPa</emph>
            ,
              <emph style="sc">A</emph>
            I ad AG, ut
              <lb/>
              <emph style="sc">A</emph>
            P, aut DG, ad DG minus GH, id eſt HD, Sed
              <lb/>
            in triangulis ſimilibus
              <emph style="sc">A</emph>
            EI,
              <emph style="sc">A</emph>
            DG; </s>
            <s xml:id="echoid-s3478" xml:space="preserve">
              <emph style="sc">A</emph>
            I ad
              <emph style="sc">A</emph>
            G, ut EI
              <lb/>
            ad DG; </s>
            <s xml:id="echoid-s3479" xml:space="preserve">ergo EI ad DG, ut DG ad HD; </s>
            <s xml:id="echoid-s3480" xml:space="preserve">idcirco EI
              <emph style="super">9</emph>
              <lb/>
            ad DG
              <emph style="super">9</emph>
            , ut EI ad HD. </s>
            <s xml:id="echoid-s3481" xml:space="preserve">Quod demonſtrandum erat. </s>
            <s xml:id="echoid-s3482" xml:space="preserve">Ve-
              <lb/>
            locitatem autem rite eſſe determinatam conſtabit ex colla-
              <lb/>
            tione fig. </s>
            <s xml:id="echoid-s3483" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3484" xml:space="preserve">cum 6.</s>
            <s xml:id="echoid-s3485" xml:space="preserve">; ſi ad puncta B, L, attendamus, </s>
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