Changes

Table 39 exhibits another method that happens to work quickly in this particular case, using distributive laws to multiply things out in an algebraic manner, arranging the notations of feature and fluxion according to a scale of simple character and degree.  Proceeding this way leads through an intermediate step which, in chiming the changes of ordinary calculus, should take on a familiar ring.  Consequential properties of exclusive disjunction then carry us on to the concluding line.

Table 39 exhibits another method that happens to work quickly in this particular case, using distributive laws to multiply things out in an algebraic manner, arranging the notations of feature and fluxion according to a scale of simple character and degree.  Proceeding this way leads through an intermediate step which, in chiming the changes of ordinary calculus, should take on a familiar ring.  Consequential properties of exclusive disjunction then carry us on to the concluding line.

<pre>

<font face="courier new">

Table 39.  Computation of EJ (Method 2)

o-------------------------------------------------------------------------------o

|+ Table 39.  Computation of E''J'' (Method 2)

|                                                                               |

| EJ  = <u + du> <v + dv>                                                      |

{| align="left" border="0" cellpadding="0" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:left; width:100%"

|                                                                               |

| width="8%"  | E''J''

|     =       u v       +       u dv      +       v du      +     du dv    |

| colspan="2" | = ‹''u'' + d''u''› <math>\cdot</math> ‹''v'' + d''v''›

|                                                                               |

| EJ =   u v (du)(dv) +   u (v)(du) dv  + (u) v du (dv) + (u)(v) du  dv |

|                                                                               |

</pre>

|-

| width="8%"  | &nbsp;

| colspan="2" | = ''u'' ''v'' + ''u'' d''v'' + ''v'' d''u'' + d''u'' d''v''

| width="23%" | &nbsp;

| width="23%" | &nbsp;

|-

| width="8%" | E''J''

| width="23%" | = ''u'' ''v'' (d''u'')(d''v'')

| width="23%" | + ''u'' (''v'') (d''u'')d''v''

| width="23%" | + (''u'') ''v'' d''u'' (d''v'')

| width="23%" | + (''u'')(''v'') d''u'' d''v''

|}

|}

</font><br>

Figures&nbsp;40-a through 40-d present several views of the enlarged proposition EJ.

Figures&nbsp;40-a through 40-d present several views of the enlarged proposition EJ.