Changes

An illustrious example of a propositional theorem is the ''praeclarum theorema'', the ''admirable'', ''shining'', or ''splendid'' theorem of [[Leibniz]].

An illustrious example of a propositional theorem is the ''praeclarum theorema'', the ''admirable'', ''shining'', or ''splendid'' theorem of [[Leibniz]].

: If ''a'' is ''b'' and ''d'' is ''c'', then ''ad'' will be ''bc''.

: <br>

<p>If ''a'' is ''b'' and ''d'' is ''c'', then ''ad'' will be ''bc''.</p>

: This is a fine theorem, which is proved in this way:

 

: <br>

<p>This is a fine theorem, which is proved in this way:</p>

: ''a'' is ''b'', therefore ''ad'' is ''bd'' (by what precedes),

 

: <br>

<p>''a'' is ''b'', therefore ''ad'' is ''bd'' (by what precedes),</p>

: ''d'' is ''c'', therefore ''bd'' is ''bc'' (again by what precedes),

 

: <br>

<p>''d'' is ''c'', therefore ''bd'' is ''bc'' (again by what precedes),</p>

: ''ad'' is ''bd'', and ''bd'' is ''bc'', therefore ''ad'' is ''bc''.  Q.E.D.

 

: <br>

<p>''ad'' is ''bd'', and ''bd'' is ''bc'', therefore ''ad'' is ''bc''.  Q.E.D.</p>

: ([[Leibniz]], ''Logical Papers'', p. 41).

 

<p>([[Leibniz]], ''Logical Papers'', p. 41).</p>

Under the existential interpretation, the praeclarum theorema is represented by means of the following logical graph.

Under the existential interpretation, the praeclarum theorema is represented by means of the following logical graph.