The conceptions of space and of number are the subject matter of mathematical investigations. These investigations accordingly diverge into two main branches: Geometry and Analysis. It thus appears that Mathematics are of fundamental importance to all our knowledge of Nature: for our representations of space contain the simplest properties which are common to all things in the surrounding world; and accu rate comparison or measurement of quantities leads always to concrete numbers of the units employed: in order to understand the result, we require a knowledge of numbers and of their combinations.

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