or, a - b : b ∷ c - d : d ,
| if | a | be greater than 1. |
|---|---|---|
| b | ||
| Again, since | a + b | = | c + d |
|---|---|---|---|
| b | d |
| and | a - b | = | c - d | ( | a | being greater than 1 ) |
|---|---|---|---|---|---|---|
| b | d | b |
dividing the first by the second we have
| a + b | = | c + d | |
|---|---|---|---|
| a - b | c - d |
or a + b : a - b ∷ c + d : c - d
and also a + b : b - a ∷ c + d : d - c,
| if | a | be less than 1. |
|---|---|---|
| b | ||
- Many other proportions might be obtained in the same manner. We will, however, content ourselves with writing down a few which can be obtained by combining