equations in one variable. The whole of chapter 12  is  devoted  to  an  explanation  of  linear equations  in  two  variables. ARITHMETIC 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  OPERATIONS Algebraic   notation—meaning   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, multiplication, and   division   of   algebraic monomials   and   polynomials   are   explained   in the   same   chapter.   The   factoring   of   algebraic expressions is explained in chapter 10. GEOMETRY 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 curved  surface. 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 ABCD. 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. POLYGONS 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: Sides The boundary lines of a  polygon Perimeter The  sum  of  the  sides 1-8