Definitions and units in mechanics

Foundations of Physics 6 (2):209-219 (1976)
With displacement, time, and force as basic undefined physical quantities, other physical quantities are defined as combinations of two vector quantities and one scalar quantity. Combinations include multiplication and division of vectors by vectors, scalars by vectors, and scalars by scalars. Defined quantities are vectors, scalars or quaternions, depending on directions of vectors in the definitions. Division of a vector by a vector is equivalent to multiplication of vectors divided by a scalar. The unit of a vector (or scalar) is itself a vector (or scalar) quantity. Thesquare meter (a vector) differs from meter 2 (a scalar), and the cubic meter (a scalar) is different frommeter 3 . The characteristics of displacement, time, and force are considered known from experience
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DOI 10.1007/BF00708961
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The Nature of Physical Theory.Victor Fritz Lenzen - 1931 - London: Chapman & Hall.

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