equations in one variable. The whole of chapter
12 is devoted to an explanation of linear
equations in two variables.
The common arithmetical operations are
addition, subtraction, multiplication, and divi-
sion. Arithmetical operations with positive
whole numbers are explained in chapter 2
of NAVEDTRA 10069-D1, and arithmetical
operations with signed numbers, in chapter 3.
Arithmetical operations with common fractions
are explained in chapter 4, and arithmetical
operations with decimal fractions, in chapter 5.
ALGEBRAIC NOTATION AND
Algebraic notationmeaning generally the
substitution of symbols (usually letters) for
numerical values-is explained in chapter 9 of
NAVEDTRA 10069-D1. Algebraic fundamentals,
such as the meanings of terms; systems of
groupings; and the addition, subtraction,
and division of algebraic
monomials and polynomials are explained in
the same chapter. The factoring of algebraic
expressions is explained in chapter 10.
Since geometry is the branch of mathematics
that investigates the relations, properties, and
measurement of solids, surfaces, lines, and angles,
it follows that just about everything a surveyor
does involves geometry in some way or other.
Whenever you establish a point, chain a linear
distance, measure a vertical distance, turn an
angle, or determine an area or a volume, you are
working with geometry.
To begin with, you must know how to
recognize the common types of geometrical plane
and solid figures and how to compute the areas
of the plane figures and the volumes of the solids.
SURFACES AND FIGURES
There is a surface on this sheet of paper. A
geometrical surface has length and breadth. It has
Figure 1-3.-Intersecting planes.
no thickness. A surface may be either a plane
surface or a curved surface. When this page is held
perfectly level at every point, the surface is then
a plane surface. When the page is rolled to
resemble a tube, the plane surface becomes a
A plane is a real or imaginary surface
in which a straight line between any two
points lies wholly on that surface. Figure 1-3
shows two intersecting planes. Plane ABCD
is shown to be a horizontal plane; plane
abed is a vertical plane perpendicular to
A plane surface is a surface on which every
point lies in the same plane.
Plane figures are plane surfaces bounded by
either straight lines or curved lines.
A plane figure that is bounded by straight-line
sides is called a polygon. The smallest possible
number of sides for a polygon is three, and a
three-sided polygon is called a triangle.
Some terms and definitions relating to
polygons are as follows:
The boundary lines of a polygon
The sum of the sides