THE

PRACTICE

OF

MENSURATION,

SHEWING THE USES

OF THE

MOST PRINCIPAL RULES

Applied to Measuring the

SEVERAL ARTIFICER'S WORKS,

CONCERNED IN

BUILDING.

MENSURATION

OF

SUPERFICIES:

***

EVERY

DEFINITION.

quantity is measured by some other quantity of the same kind; as a line by a line, a surface by a surface, and a solid by a solid: and the number which shows how often the lesser, called the measuring unit, is contained in the greater, or quantity measured, is called the content of the quantity so measured. Thus, if the quantity to be measured be the rectangle ABCD, and the little square E, whose side is one inch, be the measuring unit propounded, then, as often as the said little square is contained in the rectangle, so many square inches the rectangle is said to contain: so that if the length DC be supposed 5 inches, and the breadth AD 3 inches, the content of the rectangle will be 3 times 5, or 15 square inches: because, if lines be drawn parallel to the sides, at an inch distance one from another, they will. divide the whole rectangle ABCD into 3 times 5, or 15 equal parts, of one inch each. And, generally, whatever the measures of the two sides may be, it is evident that the rectangle

VOL. I.

X

angle will contain the square E, as many times as the base AB contains the base of the square, repeated as often as the altitude AD contains the altitude of the square.

Hence we have the following rule for any parallelogram whatever.

PROBLEM I.

To find the area of a parallelogram, whether it be a square, a rectangle, a rhombus, or a rhomboides.

Multiply the length by the perpendicular height, and the product will be the area.

EXAMPLE I.

What is the area of a square ABCD, whose side AB or BC