Elements of Algebra

CONTENTS. PART I. Containing the Analysis of Determinate Quantities. SECTION I. Of the Different Methods of calculating Simple Quantities. Page Chap. I. Of Mathematics in general - - - - - 1 II. Explanation of the signs $+$ plus and $-$ minus - - 3 III. Of the Multiplication of Simple Quantities - - - 6 IV. Of the nature of whole Numbers, or Integers with respect to their Factors - - - - - 10 V. Of the Division of Simple Quantities - - - - 13 VI. Of the properties of Integers, with respect to their Divisors - - - - - - - - 16 VII. Of Fractions in general - - - - - - 20 VIII. Of the Properties of Fractions - - - - - 24 IX. Of the Addition and Subtraction of Fractions - - 27 X. Of the Multiplication and Division of Fractions - 30 XI. Of Square Numbers - - - - - - - 36 XII. Of Square Roots, and of Irrational Numbers re- sulting from them - - - - - - - 38 XIII. Of Impossible, or Imaginary Quantities, which arise from the same source - - - - - 42 XIV. Of Cubic Numbers - - - - - - - 45 XV. Of Cube Roots, and of Irrational Numbers re- sulting from them - - - - - - - 46 XVI. Of Powers in general - - - - - - - 48 XVII. Of the Calculation of Powers - - - - - 52 XVIII. Of Roots with relation to Powers in general - - 54 XIX. Of the Method of representing Irrational Num- bers by Fractional Exponents - - - - - 56 XX. Of the different Methods of Calculation, and of their Mutual Connexion - - - - - - 60 XXI. Of Logarithms in general - - - - - - 63 XXII. Of the Logarithmic Tables that are now in use - 66 XXIII. Of the Method of expressing Logarithms - - - 69 SECTION II. Of the different Methods of calculating Compound Quantities. Chap. I. Of the Addition of Compound Quantities - - 76 II. Of the Subtraction of Compound Quantities - - 78 III. Of the Multiplication of Compound Quantities - - 79 IV. Of the Division of Compound Quantities - - - 84 V. Of the Resolution of Fractions into Infinite Series 88 VI. Of the Squares of Compound Quantities - - - 97