As with definition 3, definition 8 is regarded by some as being a later insertion by Euclid's editors. It defines three terms "p", "q" and "r" to be in proportion when "p"∶"q"∷"q"∶"r". This is extended to 4 terms "p", "q", "r" and "s" as "p"∶"q"∷"q"∶"r"∷"r"∶"s", and so on. Sequences that have the property that the ratios of consecutive terms are equal are called geometric progressions. Definitions 9 and 10 apply this, saying that if "p", "q" and "r" are in proportion then "p"∶"r" is the "duplicate ratio" of "p"∶"q" and if "p", "q", "r" and "s" are in proportion then "p"∶"s" is the "triplicate ratio" of "p"∶"q".