The right angle is considered to be the creation of the human mind, because in nature its presence is not deliberate. In the products of human endeavor, however, whether in architecture, in trades or industry, in civil engineering and even in agricultural activities, the right angle, resulting from the mutual perpendicularity of lines and surfaces, has been present since ancient times. The reasons for that varied and extensive application of the right angle are many. They may be related to technical convenience and practicality, but also to less distinct concepts; they could reflect the human mind's search for the expression of orderliness or mathematically definable regularity.

While the originating circumstances could be a matter of conjecture, the presence of the right angle and its basic role in engineering design are very real. Consequently, perpendicularity represents a condition that must be measured.

There are quite a number of terms in current usage to designate the positional relationship of two or more physically defined elements at right angles to each other. These terms are perpendicularity, normalcy, squareness or, expressed in angular units, 90 degrees. Concepts related to natural forces are also used to specify the mutual position of perpendicularity, namely, plumb in relation to the horizontal. Actually, gravitational force is used to create in measuring instruments a very reliable representation of the horizontal; that is, the surface planes of liquids under the effect of gravity. (Note: Plumb and level can be considered as perpendicular...