The work which is here presented to the public, is an abridgment of Bourdon, from the translation of Lt. Ross; with such modifications, as experience in teaching it, and a very careful comparison with other standard works, have suggested. It has been the intention to unite in this work, the scientific discussions of the French, with the practical methods of the English school; that theory and practice, science and art, may mutually aid and illustrate each other. Many of the examples have been selected from the Algebra of Bonnycastle. It has been thought best, in the present edition, to transfer the general discussion of the Common Divisor to Chapter VII, and to arrange the subject of Proportions and Progressions directly after Equations of the second degree. It is hoped that these alterations may be regarded as improve ments. Hartford, September 1, 1838. CONTENTS. Preliminary Definition and Remarks. ARTICLES Equations involving but One Unknown Quantity, Transformation of Equations-First and Second, Resolution of Equations of the First Degree-Rule, Questions involving Equations of the First Degree, Equations of the First Degree involving Two Unknown Elimination By Addition-By Subtraction-By Comparison,. Resolution of Questions involving Two or more Unknown Geometrical Progression. Reciprocal Proportion Defined, Product of Extremes Equal to the Product of the Means, To make a Proportion from Four Quantities, Proportion by Equality of Ratios, Four Proportionals are Proportional Inversely, . Equi-multiples have the same Ratio as the Quantities, Proportion by Augmenting Antecedent and Consequent, Proportion by Multiplying Ratios, The Powers of Proportionals are in Proportion, The Products of Proportionals are in Proportion, To Extract the nth Root of a Whole Number, Extraction of Roots by Approximation, Cube Root of Decimal Fractions, Calculus of Radicals-Transformation of Radicals. |