section_path: Properties
section_name: Properties
paragraph_text: Properties
  
  As a measure of the Euclidean three-dimensional space, volume cannot be physically measured as a negative value, similar to length and area. Like all continuous monotonic (order-preserving) measures, volumes of bodies can be compared against each other and thus can be ordered. Volume can also be added together and be decomposed indefinitely; the latter property is integral to Cavalieri's principle and to the infinitesimal calculus of three-dimensional bodies. A 'unit' of infinitesimally small volume in integral calculus is the volume element; this formulation is useful when working with different coordinate systems, spaces and manifolds.