that is, b-a: b ∷ d-c: d
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 | ||
185. 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 the preceding articles.