one another are in continued proportion, such as
| 1 | 2 | 4 | 8 | 16 | 32 | 64 | &c. |
|---|---|---|---|---|---|---|---|
| 2 | 2 | 2 | 2 | 2 | 2 | 2 | &c. |
| 3 | 9 | 27 | 81 | 243 | 729 |
Which are in continued proportion, since
| 1 | : | 2 | ∷ | 2 | : | 4 | 2 | : | 2 | ∷ | 2 | : | 2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 3 | 9 | ||||||||||||
| 2 | : | 4 | ∷ | 4 | : | 8 | 2 | : | 2 | ∷ | 2 | : | 2 | |
| 3 | 9 | 9 | 27 | |||||||||||
| &c. | &c. |
- Let a, b, c, d, e be in continued proportion; we have then
| a : b ∷ b : c | or | a | = | b | or | ac = bb |
|---|---|---|---|---|---|---|
| b | c | |||||
| b : c ∷ c : d | b | = | c | bd = cc | ||
| c | d | |||||
| c : d ∷ d : e | c | = | d | ce = dd | ||
| d | e |
Each term is