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Revision as of 15:54, 24 June 2007

1,277 bytes added ,  15:54, 24 June 2007
→‎Table 55. Synopsis of Terminology: Restrictive and Alternative Subtypes
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:left; width:96%"
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:left; width:96%"
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|+ '''Table 54.  Cast of Characters:  Expansive Subtypes of Objects and Operators'''
+
|+ '''Table 55.  Synopsis of Terminology:  Restrictive and Alternative Subtypes'''
 
|- style="background:paleturquoise"
 
|- style="background:paleturquoise"
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! Item
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!  
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! Notation
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! Operator
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! Description
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! Proposition
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! Type
+
! Map
 
|-
 
|-
 
| valign="top" |
 
| valign="top" |
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|-
 
|-
 
|  
 
|  
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|-
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|
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{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
  −
| <math>\epsilon</math>
  −
|-
  −
| <math>\eta</math>
  −
|-
  −
| E
  −
|-
  −
| D
  −
|-
  −
| d
  −
|}
  −
| valign="top" | &nbsp;
  −
| colspan="2"  |
  −
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:60%"
  −
| Tacit Extension Operator || <math>\epsilon</math>
  −
|-
  −
| Trope Extension Operator || <math>\eta</math>
  −
|-
  −
| Enlargement Operator    || E
  −
|-
  −
| Difference Operator      || D
  −
|-
  −
| Differential Operator    || d
   
|}
 
|}
 
|-
 
|-
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|-
 
|-
 
| &nbsp;
 
| &nbsp;
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{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
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| <font face=georgia>'''e'''</font>
  −
|-
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| <font face=georgia>'''E'''</font>
  −
|-
  −
| <font face=georgia>'''D'''</font>
  −
|-
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| <font face=georgia>'''T'''</font>
  −
|}
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| valign="top" | &nbsp;
  −
| colspan="2"  |
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{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:60%"
  −
| Radius Operator || <font face=georgia>'''e'''</font>&nbsp;=&nbsp;‹<math>\epsilon</math>,&nbsp;<math>\eta</math>›
  −
|-
  −
| Secant Operator || <font face=georgia>'''E'''</font>&nbsp;=&nbsp;‹<math>\epsilon</math>,&nbsp;E›
  −
|-
  −
| Chord Operator  || <font face=georgia>'''D'''</font>&nbsp;=&nbsp;‹<math>\epsilon</math>,&nbsp;D›
  −
|-
  −
| Tangent Functor || <font face=georgia>'''T'''</font>&nbsp;=&nbsp;‹<math>\epsilon</math>,&nbsp;d›
   
|}
 
|}
 
|}<br>
 
|}<br>
 +
 +
<pre>
 +
 +
| Tacit        | !e! :                | !e!J :            | !e!J :              |
 +
| Extension    | U%->EU%, X%->EX%,    | <|u,v,du,dv|> -> B | [u,v,du,dv]->[x]    |
 +
|              | (U%->X%)->(EU%->X%)  | B^2 x D^2 -> B    | [B^2 x D^2]->[B^1]  |
 +
 +
--------------o
 +
 +
| Trope        | !h! :                | !h!J :            | !h!J :              |
 +
| Extension    | U%->EU%, X%->EX%,    | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx]    |
 +
|              | (U%->X%)->(EU%->dX%) | B^2 x D^2 -> D    | [B^2 x D^2]->[D^1]  |
 +
 +
--------------o
 +
 +
| Enlargement  | E :                  | EJ :              | EJ :                |
 +
| Operator    | U%->EU%, X%->EX%,    | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx]    |
 +
|              | (U%->X%)->(EU%->dX%) | B^2 x D^2 -> D    | [B^2 x D^2]->[D^1]  |
 +
 +
--------------o
 +
 +
| Difference  | D :                  | DJ :              | DJ :                |
 +
| Operator    | U%->EU%, X%->EX%,    | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx]    |
 +
|              | (U%->X%)->(EU%->dX%) | B^2 x D^2 -> D    | [B^2 x D^2]->[D^1]  |
 +
 +
--------------o
 +
 +
| Differential | d :                  | dJ :              | dJ :                |
 +
| Operator    | U%->EU%, X%->EX%,    | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx]    |
 +
|              | (U%->X%)->(EU%->dX%) | B^2 x D^2 -> D    | [B^2 x D^2]->[D^1]  |
 +
 +
--------------o
 +
 +
| Remainder    | r :                  | rJ :              | rJ :                |
 +
| Operator    | U%->EU%, X%->EX%,    | <|u,v,du,dv|> -> D | [u,v,du,dv]->[dx]    |
 +
|              | (U%->X%)->(EU%->dX%) | B^2 x D^2 -> D    | [B^2 x D^2]->[D^1]  |
 +
 +
--------------o
 +
 +
| Radius      | $e$ = <!e!, !h!> :  |                    | $e$J :              |
 +
| Operator    | U%->EU%, X%->EX%,    |                    | [u,v,du,dv]->[x, dx] |
 +
|              | (U%->X%)->(EU%->EX%) |                    | [B^2 x D^2]->[B x D] |
 +
 +
--------------o
 +
 +
| Secant      | $E$ = <!e!, E> :    |                    | $E$J :              |
 +
| Operator    | U%->EU%, X%->EX%,    |                    | [u,v,du,dv]->[x, dx] |
 +
|              | (U%->X%)->(EU%->EX%) |                    | [B^2 x D^2]->[B x D] |
 +
 +
--------------o
 +
 +
| Chord        | $D$ = <!e!, D> :    |                    | $D$J :              |
 +
| Operator    | U%->EU%, X%->EX%,    |                    | [u,v,du,dv]->[x, dx] |
 +
|              | (U%->X%)->(EU%->EX%) |                    | [B^2 x D^2]->[B x D] |
 +
 +
--------------o
 +
 +
| Tangent      | $T$ = <!e!, d> :    | dJ :              | $T$J :              |
 +
| Functor      | U%->EU%, X%->EX%,    | <|u,v,du,dv|> -> D | [u,v,du,dv]->[x, dx] |
 +
|              | (U%->X%)->(EU%->EX%) | B^2 x D^2 -> D    | [B^2 x D^2]->[B x D] |
 +
 +
--------------o
 +
</pre>
    
===Figure 56-a1.  Radius Map of the Conjunction J = uv===
 
===Figure 56-a1.  Radius Map of the Conjunction J = uv===
Jon Awbrey
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