Mensuration
2 of the 6 encyclopedias on this shelf carry an entry for Mensuration. Both are reproduced below, so you can see where they agree and where they differ.
Aiton's Encyclopedia (1910)
the art of measuring. Properly speaking mensuration is an application of geometry. Some of the common principles are the following: The area of a triangle is equal to half the product of its base by its altitude. The area of a square, rectangle, or parallelogram, is equal to the product of the base and altitude. The area of a trapezoid is equal to half the product of the sum of the two parallel sides by the altitude. To find the circumference of a circle, multiply the diameter by 3.1416. To find the diameter of a circle, divide the circumference by 3.1416. To find the area of a circle, multiply the square of the radius by 3.1416. To find the surface of a sphere, multiply the square of the diameter by 3.1416. To find the volume or contents of a sphere, multiply the surface by the diameter, and divide the product by 6. To find the volume or contents of a cylinder, multiply the area of the base by the altitude. To find the volume or contents of a pyramid, multiply the area of the base by the altitude, and divide the product by 3. To find the volume or contents of a cone, multiply the area of the base by the altitude, and divide the product by 3.
Collier's New Encyclopedia (1921)
that branch of applied geometry which gives the rules for finding the lengths of lines, the areas of surfaces, and the volumes of solids. In medicine the term denotes a means for exploring the state of the thoracic and other cavities. MENTAL DEFECTIVES. See IN- SANITY.
What Has Changed in the Last Century
Every formula Aiton's set out in 1910 is still exactly right: the area of a triangle is still half base times height, and a circle's circumference is still its diameter times 3.1416. What has faded is the word itself — "mensuration" was a standard heading in Victorian and Edwardian arithmetic texts, and it survives today mainly in Indian and British school syllabuses rather than in American classrooms, where the same material is simply taught as geometry. Collier's second sense in 1921, mensuration as a medical technique for "exploring the state of the thoracic and other cavities" by measuring the chest, has vanished from practice, displaced by X-ray and later imaging. The cross-reference Collier's printed immediately after — "MENTAL DEFECTIVES. See INSANITY" — is a reminder of how much the surrounding vocabulary has moved even where the arithmetic has not.
Written for this edition, 2026.