The first original definition of the metre, presented by the French Academy of Sciences in 1795 is:
The length of the metre is one ten-millionth of the Earth quadrant, the distance from the North Pole to the Equator, measured along a meridian through Paris.
Roughly speaking, this definition is equivalent to the following one:
The length of the metre is 1/40,000,000'th of the circumference of the Earth.
It makes sense sense to define the length of the metre in terms of the entire circumference of the Earth, not its one-fourth, with the deiniftion only featuring a "pure" power of 10 like 100,000,000.
Why was the original definition for the metre chosen? If the original definition is just the paraphrased second definition, the question becomes: where does the '4' come from?