Thus he devoted some attention to the quadrature of surfaces and the **cubature** of solids, which he accomplished, in some of the simpler cases, by an original method which he called the "Method of Indivisibles"; but he lost much of the credit of the discovery as he kept his method for his own use,while Bonaventura Cavalieri published a similar method which he himself had invented.

Mensuration, then, is mainly concerned with quadratureformulae and **cubature** formulae, and, to a not very clearly defined extent, with the methods of obtaining such formulae; a quadrature-formula being a formula for calculating the numerical representation of an area, and a **cubature-formula** being a formula for calculating the numerical representation of a volume, in terms, in each case, of the numerical representations of particular data which determine the area or the volume.

On the other hand, it is worth noticing that the words " quadrature " and " **cubature** " are originally due to geometrical rather than numerical considerations; the former implying the construction of a square whose area shall be equal to that of a given surface, and the latter the construction of a cube whose volume shall be equal to that of a given solid.

Quadrature-formulae or **cubature-formulae** may sometimes be conveniently replaced by formulae giving the mean ordinate or mean section.

The terms quadratureformula and **cubature-formula** are sometimes restricted to formulae for expressing the area of a trapezette, or the volume of a briquette, in terms of such data.

Thus a quadrature-formula is a formula for expressing [A x .24] or fudx in terms of a series of given values of u, while a **cubature-formula** is a formula for expressing [[Vx, 0 .

In mensuration, "**cubature**" is sometimes used to denote the volume of a solid; the word is parallel with "quadrature," to determine the area of a surface (see Mensuration; Infinitesimal Calculus) .