Changes

<p>'''The Signs for Multiplication''' (cont.)</p>

<p>'''The Signs for Multiplication''' (cont.)</p>

<p>A conjugative term like 'giver' naturally requires two correlates, one denoting the thing given, the other the recipient of the gift.</p>

<p>A conjugative term like ''giver'' naturally requires two correlates, one denoting the thing given, the other the recipient of the gift.</p>

<p>We must be able to distinguish, in our notation, the giver of ''A'' to ''B'' from the giver to ''A'' of ''B'', and, therefore, I suppose the signification of the letter equivalent to such a relative to distinguish the correlates as first, second, third, etc., so that "giver of --- to ---" and "giver to --- of ---" will be expressed by different letters.</p>

<p>We must be able to distinguish, in our notation, the giver of <math>\mathrm{A}\!</math> to <math>\mathrm{B}\!</math> from the giver to <math>\mathrm{A}\!</math> of <math>\mathrm{B}\!</math>, and, therefore, I suppose the signification of the letter equivalent to such a relative to distinguish the correlates as first, second, third, etc., so that "giver of&nbsp;&mdash;&mdash; to&nbsp;&mdash;&mdash;" and "giver to&nbsp;&mdash;&mdash; of&nbsp;&mdash;&mdash;" will be expressed by different letters.</p>

<p>Let `g` denote the latter of these conjugative terms.  Then, the correlates or multiplicands of this multiplier cannot all stand directly after it, as is usual in multiplication, but may be ranged after it in regular order, so that:</p>

<p>Let <math>\mathfrak{g}</math> denote the latter of these conjugative terms.  Then, the correlates or multiplicands of this multiplier cannot all stand directly after it, as is usual in multiplication, but may be ranged after it in regular order, so that:</p>

<p>will denote a giver to <math>\mathit{x}\!</math> of <math>\mathit{y}\!</math>.</p>

<p>But according to the notation, <math>\mathit{x}\!</math> here multiplies <math>\mathit{y}\!</math>, so that if we put for <math>\mathit{x}\!</math> owner (<math>\mathit{o}\!</math>), and for <math>\mathit{y}\!</math> horse (<math>\mathrm{h}\!</math>),</p>

 

| align="center" | <math>\mathfrak{g}\mathit{o}\mathrm{h}</math>

 

<p>But according to the notation, ''x'' here multiplies ''y'', so that if we put for ''x'' owner ('o'), and for ''y'' horse (h),</p>

 

<p>appears to denote the giver of a horse to an owner of a horse.  But let the individual horses be <math>\mathrm{H}, \mathrm{H}^{\prime}, \mathrm{H}^{\prime\prime}</math>, etc.</p>

<p>`g`'o'h</p>

 

<p>appears to denote the giver of a horse to an owner of a horse.  But let the individual horses be ''H'', ''H''&prime;, ''H''&Prime;, etc.</p>

<p>Then:</p>

<p>Then:</p>

 

<p>''h'' = ''H'' +, ''H''&prime; +, ''H''&Prime; +, etc.</p>

 

<math>\mathrm{h} = \mathrm{H} ~+\!\!,~ \mathrm{H}^{\prime} ~+\!\!,~ \mathrm{H}^{\prime\prime} ~+\!\!,~ \text{etc.}</math>

<p>`g`'o'h = `g`'o'(''H'' +, ''H''&prime; +, ''H''&Prime; +, etc.)</p>

 

<p>= `g`'o' ''H'' +, `g`'o' ''H''&prime; +, `g`'o' ''H''&Prime; +, etc.</p>

<math>\mathfrak{g}\mathit{o}\mathrm{h} = \mathfrak{g}\mathit{o}(\mathrm{H} ~+\!\!,~ \mathrm{H}^{\prime} ~+\!\!,~ \mathrm{H}^{\prime\prime} ~+\!\!,~ \text{etc.}) = \mathfrak{g}\mathit{o}\mathrm{H} ~+\!\!,~ \mathfrak{g}\mathit{o}\mathrm{H}^{\prime} ~+\!\!,~ \mathfrak{g}\mathit{o}\mathrm{H}^{\prime\prime} ~+\!\!,~ \text{etc.}</math>

 

<p>Now this last member must be interpreted as a giver of a horse to the owner of 'that' horse, and this, therefore must be the interpretation of `g`'o'h.</p>

 

<p>Now this last member must be interpreted as a giver of a horse to the owner of ''that'' horse, and this, therefore must be the interpretation of <math>\mathfrak{g}\mathit{o}\mathrm{h}</math>.  This is always very important. ''A term multiplied by two relatives shows that the same individual is in the two relations.''</p>

<p>This is always very important.</p>

 

<p>'A term multiplied by two relatives shows that the same individual is in the two relations.'</p>

<p>If we attempt to express the giver of a horse to a lover of a woman, and for that purpose write:</p>

<p>If we attempt to express the giver of a horse to a lover of a woman, and for that purpose write:</p>