c , and d , being proportionals, we may obtain other proportions, thus:
| Let | a | = | c |
|---|---|---|---|
| b | d |
| Then (114) 1 + | a | = | 1 + | c |
|---|---|---|---|---|
| b | d |
| or | a + b | = | c + d |
|---|---|---|---|
| b | d | ||
| or | a + b : b ∷ c + d : d |
That is, the sum of the first and second is to the second as the sum of the third and fourth is to the fourth. For brevity, we shall not state in words any more of these proportions, since the pupil will easily supply what is wanting.
Resuming the proportion a: b ∷ c: d
| or | a | = | c |
|---|---|---|---|
| b | d |
| 1 - | a | = | 1 - | c | , if | a | be less than 1 , |
|---|---|---|---|---|---|---|---|
| b | d | b |
| or | b - a | = | d - c |
|---|---|---|---|
| b | d |
that is, b - a : b ∷ d - c : d