Science Fair Project Encyclopedia
I don't really agree with the paragaph:
- One cannot see why the proportion called arithmetical is any more arithmetical than that which is called geometrical, nor why the latter is more geometrical than the former. On the contrary, the primitive idea of geometrical proportion is based on arithmetic, for the notion of ratios springs essentially from the consideration of numbers
That seems a rationalisation based on number, but it is not certain that mathematics started as number.
- It is "not certain" that it did? Indeed, isn't it certain that it did not? The notion of real number grew out of geometry!
For example, take a square, double the length of its sides, double again, and again. Clearly the side lengths are in geometric progression; so too are the areas. Take a different square, add 2 to the length of the sides (2 what?), add 2 again, and again. This time the side lengths are in arithmetic progression, but the areas are not. It seems natural to call the former geometric, leaving arithmetic to the latter. In the medieval quadrivium, arithmetic was pure number, geometry was number in space, music number in time, and astronomy number in space and time; but I doubt that was the order in pre-history.--Henrygb 13:13, 21 Mar 2004 (UTC)
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