| Line 4,058: |
Line 4,058: |
| | Figures 46-a through 46-d illustrate the proposition d''J'', rounded out in our usual array of prospects. This proposition of E''U''<sup> •</sup> is what we refer to as the (first order) differential of ''J'', and normally regard as ''the'' differential proposition corresponding to ''J''. | | Figures 46-a through 46-d illustrate the proposition d''J'', rounded out in our usual array of prospects. This proposition of E''U''<sup> •</sup> is what we refer to as the (first order) differential of ''J'', and normally regard as ''the'' differential proposition corresponding to ''J''. |
| | | | |
| − | <pre> | + | <br> |
| − | o---------------------------------------o
| + | <p>[[Image:Diff Log Dyn Sys -- Figure 46-a -- Differential of J.gif|center]]</p> |
| − | | | | + | <p><center><font size="+1">'''Figure 46-a. Differential of ''J'' (Areal)'''</font></center></p> |
| − | | o |
| |
| − | | / \ |
| |
| − | | / \ |
| |
| − | | / \ |
| |
| − | | o o |
| |
| − | | /%\ /%\ |
| |
| − | | /%%%\ /%%%\ |
| |
| − | | /%%%%%\ /%%%%%\ |
| |
| − | | o%%%%%%%o%%%%%%%o |
| |
| − | | /%\%%%%%/ \%%%%%/%\ |
| |
| − | | /%%%\%%%/ \%%%/%%%\ |
| |
| − | | /%%%%%\%/ \%/%%%%%\ |
| |
| − | | o%%%%%%%o o%%%%%%%o |
| |
| − | | / \%%%%%/%\ /%\%%%%%/ \ |
| |
| − | | / \%%%/%%%\ /%%%\%%%/ \ |
| |
| − | | / \%/%%%%%\ /%%%%%\%/ \ |
| |
| − | | o o%%%%%%%o%%%%%%%o o |
| |
| − | | |\ / \%%%%%/ \%%%%%/ \ /| |
| |
| − | | | \ / \%%%/ \%%%/ \ / | |
| |
| − | | | \ / \%/ \%/ \ / | |
| |
| − | | | o o o o | |
| |
| − | | | |\ / \ / \ /| | |
| |
| − | | | | \ / \ / \ / | | |
| |
| − | | | u | \ / \ / \ / | v | |
| |
| − | | o---+---o o o---+---o |
| |
| − | | | \ / \ / | |
| |
| − | | | \ / \ / | |
| |
| − | | | du \ / \ / dv | |
| |
| − | | o-------o o-------o |
| |
| − | | \ / |
| |
| − | | \ / |
| |
| − | | \ / |
| |
| − | | o |
| |
| − | | |
| |
| − | o---------------------------------------o
| |
| − | Figure 46-a. Differential of J (Areal) | |
| − | </pre> | |
| | | | |
| − | <pre> | + | <br> |
| − | o-----------------------------o
| + | <p>[[Image:Diff Log Dyn Sys -- Figure 46-b -- Differential of J.gif|center]]</p> |
| − | | |
| + | <p><center><font size="+1">'''Figure 46-b. Differential of ''J'' (Bundle)'''</font></center></p> |
| − | | o-----o o-----o |
| |
| − | | / \ / \ |
| |
| − | | / o \ |
| |
| − | | / / \ \ |
| |
| − | | o o o o |
| |
| − | @ | du | | dv | |
| |
| − | /| o o o o |
| |
| − | / | \ \ / / |
| |
| − | / | \ o / |
| |
| − | / | \ / \ / |
| |
| − | / | o-----o o-----o |
| |
| − | / | |
| |
| − | / o-----------------------------o
| |
| − | /
| |
| − | o----------------------------------------/----o o-----------------------------o
| |
| − | | / | | |
| |
| − | | @ | | o-----o o-----o |
| |
| − | | | | /%%%%%%%\ / \ |
| |
| − | | o---------o o---------o | | /%%%%%%%%%o \ |
| |
| − | | / \ / \ | | /%%%%%%%%%/%\ \ |
| |
| − | | / o \ | | o%%%%%%%%%o%%%o o |
| |
| − | | / /`\ @------\-----------@ |%% du %%%|%%%| dv | |
| |
| − | | / /```\ \ | | o%%%%%%%%%o%%%o o |
| |
| − | | / /`````\ \ | | \%%%%%%%%%\%/ / |
| |
| − | | / /```````\ \ | | \%%%%%%%%%o / |
| |
| − | | o o`````````o o | | \%%%%%%%/ \ / |
| |
| − | | | |````@````| | | | o-----o o-----o |
| |
| − | | | |`````\```| | | | |
| |
| − | | | |``````\``| | | o-----------------------------o
| |
| − | | | u |```````\`| v | |
| |
| − | | | |````````\| | | o-----------------------------o
| |
| − | | | |`````````| | | | |
| |
| − | | | |`````````|\ | | | o-----o o-----o |
| |
| − | | o o`````````o \ o | | / \ /%%%%%%%\ |
| |
| − | | \ \```````/ \ / | | / o%%%%%%%%%\ |
| |
| − | | \ \`````/ \ / | | / /%\%%%%%%%%%\ |
| |
| − | | \ \```/ \ / | | o o%%%o%%%%%%%%%o |
| |
| − | | \ @------\-/---------\---------------@ | du |%%%|%%% dv %%| |
| |
| − | | \ o \ / | | o o%%%o%%%%%%%%%o |
| |
| − | | \ / \ / | | \ \%/%%%%%%%%%/ |
| |
| − | | o---------o o---------o \ | | \ o%%%%%%%%%/ |
| |
| − | | \ | | \ / \%%%%%%%/ |
| |
| − | | \ | | o-----o o-----o |
| |
| − | | \ | | |
| |
| − | o----------------------------------------\----o o-----------------------------o
| |
| − | \
| |
| − | \ o-----------------------------o
| |
| − | \ | |
| |
| − | \ | o-----o o-----o |
| |
| − | \ | /%%%%%%%\ /%%%%%%%\ |
| |
| − | \ | /%%%%%%%%%o%%%%%%%%%\ |
| |
| − | \ | /%%%%%%%%%/ \%%%%%%%%%\ |
| |
| − | \| o%%%%%%%%%o o%%%%%%%%%o |
| |
| − | @ |%% du %%%| |%%% dv %%| |
| |
| − | | o%%%%%%%%%o o%%%%%%%%%o |
| |
| − | | \%%%%%%%%%\ /%%%%%%%%%/ |
| |
| − | | \%%%%%%%%%o%%%%%%%%%/ |
| |
| − | | \%%%%%%%/ \%%%%%%%/ |
| |
| − | | o-----o o-----o |
| |
| − | | |
| |
| − | o-----------------------------o
| |
| − | Figure 46-b. Differential of J (Bundle) | |
| − | </pre> | |
| | | | |
| − | <pre> | + | <br> |
| − | o---------------------------------------------------------------------o
| + | <p>[[Image:Diff Log Dyn Sys -- Figure 46-c -- Differential of J.gif|center]]</p> |
| − | | | | + | <p><center><font size="+1">'''Figure 46-c. Differential of ''J'' (Compact)'''</font></center></p> |
| − | | |
| |
| − | | o-------------------o o-------------------o |
| |
| − | | / \ / \ |
| |
| − | | / o \ |
| |
| − | | / / \ \ |
| |
| − | | / / \ \ |
| |
| − | | / / \ \ |
| |
| − | | / / @ \ \ |
| |
| − | | / / ^ ^ \ \ |
| |
| − | | o o / \ o o |
| |
| − | | | | / \ | | |
| |
| − | | | | / \ | | |
| |
| − | | | |/ \| | |
| |
| − | | | u (du)/ dv du \(dv) v | |
| |
| − | | | /| |\ | |
| |
| − | | | / | | \ | |
| |
| − | | | / | | \ | |
| |
| − | | o / o o \ o |
| |
| − | | \ / \ / \ / |
| |
| − | | \ v \ du dv / v / |
| |
| − | | \ @<----------------------->@ / |
| |
| − | | \ \ / / |
| |
| − | | \ \ / / |
| |
| − | | \ o / |
| |
| − | | \ / \ / |
| |
| − | | o-------------------o o-------------------o |
| |
| − | | |
| |
| − | | |
| |
| − | o---------------------------------------------------------------------o
| |
| − | Figure 46-c. Differential of J (Compact) | |
| − | </pre> | |
| | | | |
| − | <pre> | + | <br> |
| − | o-----------------------------------------------------------o
| + | <p>[[Image:Diff Log Dyn Sys -- Figure 46-d -- Differential of J.gif|center]]</p> |
| − | | | | + | <p><center><font size="+1">'''Figure 46-d. Differential of ''J'' (Digraph)'''</font></center></p> |
| − | | u v |
| |
| − | | @ |
| |
| − | | ^ ^ |
| |
| − | | / \ |
| |
| − | | / \ |
| |
| − | | / \ |
| |
| − | | / \ |
| |
| − | | (du) dv / \ du (dv) |
| |
| − | | / \ |
| |
| − | | / \ |
| |
| − | | / \ |
| |
| − | | / \ |
| |
| − | | v v |
| |
| − | | u (v) @<--------------------->@ (u) v |
| |
| − | | du dv |
| |
| − | | |
| |
| − | | |
| |
| − | | |
| |
| − | | |
| |
| − | | |
| |
| − | | |
| |
| − | | |
| |
| − | | |
| |
| − | | |
| |
| − | | |
| |
| − | | @ |
| |
| − | | (u) (v) |
| |
| − | | |
| |
| − | o-----------------------------------------------------------o
| |
| − | Figure 46-d. Differential of J (Digraph) | |
| − | </pre> | |
| | | | |
| | =====Remainder of Conjunction===== | | =====Remainder of Conjunction===== |
