This applies not only to the geometrical principles but also to the arithmetical principles, and it is therefore of importance, in the earlier stages, to keep geometry, mensuration and arithmetic in close association with one another; mensuration forming, in fact, the link between arithmetic and geometry.
All exact relations pertaining to the mensuration of the circle involve the ratio of the circumference to the diameter.
General aspects of the subject are considered under Mensuration; Vector Analysis; Infinitesimal Calculus.
This use of formulae for dealing with numbers, which express magnitudes in terms of units, constitutes the broad difference between mensuration and ordinary geometry, which knows nothing of units.
Similarly, analytical plane geometry deals with the curve described by a point moving in a particular way, while analytical plane mensuration deals with the figure generated by an ordinate moving so that its length varies in a particular manner depending on its position.