of Edinburgh, Session 1880 - 81 . 169 
is a less definite form of the statement 
3c Henry VIII. = ic Catherine of Arragon+ ic Anne Boleyn 
+ ic Jane Seymour. 
Thus S placed before a sum of terms is distributive, but its arith^ 
metical value changes. 
§ 16. Let IV'be used to denote any partial number in the same 
way as 2 is used to denote any complete number. The simplest 
kind of equation is where we have got one term equated to 
one term. Of this kind there are three forms according as, 1st, 
2 occurs on both sides, 2d, 2 on the one, and N on the other side, 
3d, N on both sides. Examples are 
5 c Edward III. = 5 c Philippa of Hainault. 
3 c John of Gaunt, Duke of Lancaster = 3c Blanche, 
lc Margaret Tudor = 1c Archibald, Earl of Angus. 
The first of those equations can be written in the form 
5 
-z c Edward III. = lc Philippa, 
D 
that is, each of the five children of Edward III. was a child of 
Philippa, and conversely. The second can be written in the form 
3 
^ c John of Gaunt = lc Blanche. 
Each of three children of John of Gaunt was a child of Blanche, 
the converse being each of the three children of Blanche was a 
child of John of Gaunt. 
§ 17. The next simplest kind of equation is that in which one 
term is equated to two terms, as 
5 c m A = 3 c f B + 2 c f C 
that is, five children of the man A are identical with three children 
of the woman B together with two children of the woman C . This 
equation can be written in the other two forms 
3 c f B = 5 c m A - 2 c f C , 
and 
2 c f C = 5 c m A - 3c f B . 
