Mathematics at Work: Practical Applications of Arithmetic, Algebra, Geometry, Trigonometry, and Logarithms to the Step-by-step Solutions of Mechanical Problems, with Formulas Commonly Used in Engineering Practice and a Concise Review of Basic Mathematical PrinciplesThe new fourth edition retains the original purpose which has made this book such a large success through every one of its previous editions: to effectively help its readers solve a wide array of mathematical problems specifically related to mechanical work. Aside from its unique compilation of mathematical problems, this book is renowned for its ability to duplicate, as far as possible, personal instruction. Its usefulness as a self-learning guide for the mathematics of mechanical problems is therefore unexcelled. The entire text has been carefully reviewed and edited where necessary for greater clarity and accuracy. Includes new problem materials. At the request of many users, it now includes trigonometric and common logarithm tables. |
Contents
ArithmeticSome Useful Elements You May Have Forgotten | 1-1 |
AlgebraThe Shorthand of Mathematics | 2-21 |
GeometryDefinitions and Principles Commonly Applied | 2-31 |
TrigonometryFundamentals Utilized in Solving Practical | 18 |
Basic Facts About Common and Hyperbolic Logarithms | 42 |
Rightangled TrianglesFinding Unknown Sides and Angles | 56 |
Obliqueangled TrianglesFinding Unknown Sides and Angles | 74 |
TapersFiguring Angles Diameters and Lengths | 90 |
Problems in MechanicsWhere Forces are in Equilibrium 171 | 15-50 |
Problems in MechanicsWhere Forces are Not in Equilibrium 181 | 18-1 |
Factors in DesignEfficiency Load Torque Strength | 19-1 |
Gear Ratios Obtaining by Exact or Approximate Gear | 19-36 |
Finding Out What Happens in Planetary Gearing 211 | 19-62 |
Trial and Error SolutionsWhen and How They are Used 221 | 22-1 |
Errors Their Appearance and Systematic Handling 231 | 22-23 |
Working Formulas Based Upon Tests and Experience 241 | 22-30 |
Arcs and CirclesBasic ConceptsLength and Location of 111 | 10-11 |
Arcs and CirclesTangent to Circles and Lines | 12-1 |
Arcs and CirclesFixed by Lines and Points | 13-1 |
Vees and ArcsChecking with Cylinders and Spheres | 14-1 |
Circular SegmentsFinding Unknown Elements | 15-1 |
Approximate FormulasWhy and How They are Used 161 | 15-24 |
Common terms and phrases
90 degrees Analysis of Problem axis chord circular segment cologarithms common compound angle computed convergent Cotangent Secant Cosecant cubic decimal Derivation of Formula diagram distance divided divisor draw driver equal Example factor find angle Find Radius fixed gear fraction Free Body Diagram geometrical given number greatest common divisor hence horizontal horsepower hypotenuse intersection Involute Functions Known Analysis Law of Cosines Law of Sines lead angle least common multiple length logarithm method Minutes Cosine multiplied number of teeth pitch circle pitch diameter plane planet gear planetary gearing quadratic equation radians ratio required to find revolutions per minute right-angled triangle rotation shaft shown in Fig side Solution solved square inch Step Substituting the equivalent surface Tangent Cotangent Secant taper thread train arm Trigonometric and Involute vertical W₁ weight