GRAPHICAL REPRESENTATION OF SOLUTIONS OF SYSTEMS OF SIMULTANEOUS QUADRATIC EQUATIONS Graph of ar+ bx + c Type I, Graphs of Ax2+2 B xy + Cy2+ 2 Dx + 2 Ey +F=0 488 489 491 493 Solution of Numerical Problems by Logarithms, Powers, Roots, etc. 557 558 560 563 565 571 575 578 585 588 Proof of the Binomial Theorem for Positive Integral Exponents CHAPTER II ARRANGEMENTS AND COMBINATIONS The Problem of the Number of Arrangements of n Things taken r at a time and n at a time Permutations Circular Permutation Combinations and Special Theorems Problems CHAPTER III FORMULA FOR THE EXPANSION OF A BINOMIAL 591 592 593 595 598 599 600 601 606 Summation of the Same Powers of Numbers which are in A. P. Convergence of Series whose Terms are Positive-Graphical Repre sentations 631 Fundamental Theorems 632 Standard Series for Comparison Tests of Convergence, 1+, EXPONENTIAL SERIES, LOGARITHMIC SERIES, AND DE MOIVRE'S THEOREM 662 665 667 De Moivre's Theorem and Certain Series which may be deduced from it 681 Value of Calculated by means of Gregory's Series - Euler's Series 686 CHAPTER VII THE SUMMATION OF SERIES Recurring Series, Definition-Scale of Relation Order of a Recurring Series - To Find the Scale of Relation. Summation by Undetermined Coefficients Series which may be given the Form of the Alternating Series Miscellaneous Series BOOK VIII INTRODUCTORY CHAPTER ON THE THEORY OF DETEMINANTS Determinants of Three Rows - Determinants of Nine Elements Relation between Determinants of the Second and Third Orders Solution of Equations of the First Degree in Three Unknown Quantities 723 Principle of Addition of Rows or Columns Definition of the General Equation of the nth Degree― A Root. Definition of Cubic Equation-Cube Roots of Unity The Equation a-a-Symmetrical Cubic Equation - Cubic Equation |