In 1764 he published his first work, The Schoolmaster's Guide, or a Complete System of Practical Arithmetic, which in 1770 was followed by his Treatise on Mensuration both in Theory and Practice.
As a result of the importance both of the formulae obtained by elementary methods and of those which have involved the previous use of analysis, there is a tendency to dissociate the former, like the latter, from the methods by which they have been obtained, and to regard mensuration as consisting of those mathematical formulae which are concerned with the measurement of geometrical magnitudes (including lengths), or, in a slightly wider sense, as being the art of applying these formulae to specific cases.
The circle, for instance, is regarded geometrically as a line described in a particular way, while from the point of view of mensuration it is a figure of a particular shape.
The statement that, if the adjacent sides of a rectangle are represented numerically by 3 and 4, the diagonal is represented by 5, is as much a matter of mensuration as the statement that the area is represented by 12.
Lambert, Computation and Mensuration (1907).
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.
There are also cases in which graphics and mensuration are used jointly; a variable numerical quantity is represented by a graph, and the principles of mensuration are then applied to determine related numerical quantities.
The province of mensuration is to express the final result of such an elimination in terms of the data, without the necessity of going through the intermediate processes.
All exact relations pertaining to the mensuration of the circle involve the ratio of the circumference to the diameter.
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.