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This, being analysed, consists of two propositions; the one an assumption with respect to a matter of fact, the other a genuine definition. “A figure may exist, having all the points in the line which bounds it equally distant from a single point within it:” “Any figure possessing this property is called a circle.” Let us look at one of the demonstrations which are said to depend on this definition, and observe to which of the two propositions contained in it the demonstration really appeals. “About the centre A, describe the circle BCD.” Here is an assumption, that a figure, such as the definition expresses, may be described; which is no other than the postulate, or covert assumption, involved in the so-called definition.
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