Elements of Algebra

xxviii CONTENTS. Page Chap. VII. Of the Extraction of Roots applied to Compound Quantities - - - 100 VIII. Of the Calculation of Irrational Quantities - 104 IX. Of Cubes, and of the Extraction of Cube Roots 107 X. Of the higher Powers of Compound Quantities 110 XI. Of the Transposition of the Letters, on which the demonstration of the preceding Rule is founded - - - - 115 XII. Of the Expression of Irrational Powers by Infinite Series - - - - 120 XIII. Of the Resolution of Negative Powers - - 123 SECTION III. Of Ratios and Proportions. Chap. I. Of Arithmetical Ratio, or the Difference between two numbers - - - 126 II. Of Arithmetical Proportion - - - 129 III. Of Arithmetical Progressions - - - 131 IV. Of the Summation of Arithmetical Progressions 135 V. Of Figurate, or Polygonal Numbers - - 139 VI. Of Geometrical Ratio - - - - 146 VII. Of the greatest Common Divisor of two given Numbers - - - - - 148 VIII. Of Geometrical Proportions - - - 152 IX. Observations on the Rules of Proportion and their Utility - - - - - 155 X. Of Compound Relations - - - - 159 XI. Of Geometrical Progressions - - - 164 XII. Of Infinite Decimal Fractions - - - 171 XIII. Of the Calculation of Interest - - - 177 SECTION IV. Of Algebraic Equations, and of the Resolution of those Equations. Chap. I. Of the Solution of Problems in General - - 186 II. Of the Resolution of Simple Equations, or Equations of the First Degree - - 189 III. Of the Solution of Questions relating to the preceding Chapter - - - - 194 IV. Of the Resolution of two or more Equations of the First Degree - - - - 206 V. Of the Resolution of Pure Quadratic Equations 216 VI. Of the Resolution of Mixed Equations of the Second Degree - - - - 222 VII. Of the Extraction of the Roots of Polygonal Numbers - - - - - 230 VIII. Of the Extraction of Square Roots of Binomials - - - - - - 234