equations in one variable. The whole of chapter12 is devoted to an explanation of linearequations in two variables.ARITHMETICThe common arithmetical operations areaddition, subtraction, multiplication, and divi-sion. Arithmetical operations with positivewhole numbers are explained in chapter 2of NAVEDTRA 10069-D1, and arithmeticaloperations with signed numbers, in chapter 3.Arithmetical operations with common fractionsare explained in chapter 4, and arithmeticaloperations with decimal fractions, in chapter 5.ALGEBRAIC NOTATION ANDALGEBRAIC OPERATIONSAlgebraic notation—meaning generally thesubstitution of symbols (usually letters) fornumerical values-is explained in chapter 9 ofNAVEDTRA 10069-D1. Algebraic fundamentals,such as the meanings of terms; systems ofgroupings; and the addition, subtraction,multiplication,and division of algebraicmonomials and polynomials are explained inthe same chapter. The factoring of algebraicexpressions is explained in chapter 10.GEOMETRYSince geometry is the branch of mathematicsthat investigates the relations, properties, andmeasurement of solids, surfaces, lines, and angles,it follows that just about everything a surveyordoes involves geometry in some way or other.Whenever you establish a point, chain a lineardistance, measure a vertical distance, turn anangle, or determine an area or a volume, you areworking with geometry.To begin with, you must know how torecognize the common types of geometrical planeand solid figures and how to compute the areasof the plane figures and the volumes of the solids.SURFACES AND FIGURESThere is a surface on this sheet of paper. Ageometrical surface has length and breadth. It hasFigure 1-3.-Intersecting planes.no thickness. A surface may be either a planesurface or a curved surface. When this page is heldperfectly level at every point, the surface is thena plane surface. When the page is rolled toresemble a tube, the plane surface becomes acurved surface.A plane is a real or imaginary surfacein which a straight line between any twopoints lies wholly on that surface. Figure 1-3shows two intersecting planes. Plane ABCDis shown to be a horizontal plane; planeabed is a vertical plane perpendicular toABCD.A plane surface is a surface on which everypoint lies in the same plane.Plane figures are plane surfaces bounded byeither straight lines or curved lines.POLYGONSA plane figure that is bounded by straight-linesides is called a polygon. The smallest possiblenumber of sides for a polygon is three, and athree-sided polygon is called a triangle.Some terms and definitions relating topolygons are as follows:SidesThe boundary lines of a polygonPerimeterThe sum of the sides1-8
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