**TABLE OF CONTENTS**

**NUMBERS, FRACTIONS, AND DECIMALS**

3 Fractional Inch, Decimal, Millimeter Conversion

4 Numbers

4 Positive and Negative Numbers

5 Sequence of Operations

5 Ratio and Proportion

7 Percentage

8 Fractions

8 Common Fractions

8 Reciprocals

9 Addition, Subtraction, Multiplication, Division

10 Decimal Fractions

11 Continued Fractions

12 Conjugate Fractions

13 Using Continued Fraction

14 Powers and Roots

14 Powers of Ten Notation

15 Converting to Power of Ten

15 Multiplication

16 Division

16 Constants Frequently Used in Mathematical Expressions

17 Imaginary and Complex Numbers

18 Factorial

18 Permutations

18 Combinations

19 Prime Numbers and Factors

**ALGEBRA AND EQUATIONS**

29 Rearrangement of Formulas

30 Principle Algebraic Expressions

31 Solving First Degree Equations

31 Solving Quadratic Equations

32 Factoring a Quadratic Expression

33 Cubic Equations

33 Solving Numerical Equations

34 Series

34 Derivatives and Integrals

**GEOMETRY
**

36 Arithmetical & Geometrical Progression

39 Analytical Geometry

39 Straight Line

42 Coordinate Systems

45 Circle

47 Ellipse

50 Spherical Areas and Volumes

53 Parabola

53 Hyperbola

65 Areas and Volumes

65 The Prismoidal Formula

65 Pappus or Guldinus Rules

66 Area of Revolution Surface

66 Area of Irregular Plane Surface

67 Areas of Cycloidal Curves

67 Contents of Cylindrical Tanks

69 Areas and Dimensions of Figures

75 Formulas for Regular Polygons

76 Circular Segments

79 Circles and Squares of Equal Area

80 Diagonals of Squares & Hexagons

81 Volumes of Solids

87 Circles in Circles and Rectangles

92 Circles within Rectangles

93 Rollers on a Shaft

**SOLUTION OF TRIANGLES**

94 Functions of Angles

95 Laws of Sines and Cosines

95 Trigonometric Identities

97 Right-angled Triangles

100 Obtuse-angled Triangles

102 Degree-radian Conversion

104 Functions of Angles, Graphic

105 Trig Function Tables

109 Versed Sine and Versed Cosine

109 Sevolute and Involute Functions

110 Involute Functions Tables

114 Spherical Trigonometry

114 Right Spherical Trigonometry

116 Oblique Spherical Trigonometry

118 Compound Angles

120 Interpolation

**LOGARITHMS**

121 Common Logarithms

122 Inverse Logarithm

123 Natural Logarithms

123 Powers of Number by Logarithms

124 Roots of Number by Logarithms

125 Tables of Logarithms

*Machinery’s Handbook 28th Edition*