Elements of Algebra

Table of Contents

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   Book Overview
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   Chapter 1 Of Mathematics in general
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   Chapter 2 Explanation of the Signs + Plus and — Minus
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   Chapter 3 Of the Multiplication of Simple Quantities
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   Chapter 4 Of the Nature of whole Numbers, or Integers, with respect to their Factors
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   Chapter 5 Of the Division of Simple Quantities
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   Chapter 6 Of the Properties of Integers, with respect to their Divisors
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   Chapter 7 Of Fractions in general
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   Chapter 8 Of the Properties of Fractions
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    Chapter 9 Of the Addition and Subtraction of Fractions
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    Chapter 10 Of the Multiplication and Division of Fractions
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    Chapter 11 Of Square Numbers
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    Chapter 12 Of Square roots, and of Irrational Numbers resulting from them
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    Chapter 13 Of Impossible, or Imaginary Quantities, which arise from the same source
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    Chapter 14 Of Cubic Numbers
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    Chapter 15 Of Cube Roots, and of Irrational Numbers resulting from them
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    Chapter 16 Of Powers in general
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    Chapter 17 Of the Calculation of Powers
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    Chapter 18 Of Roots, with relation to Powers in general
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    Chapter 19 Of the Method of representing Irrational Numbers by Fractional Exponents
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    Chapter 20 Of the different Methods of Calculation, and of their mutual Connexion
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    Chapter 21 Of Logarithms in general
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    Chapter 22 Of the Logarithmic Tables now in use
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    Chapter 23 Of the Method of expressing Logarithms
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    Chapter 24 Of the Addition of Compound Quantities
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    Chapter 25 Of the Subtraction of Compound Quantities
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    Chapter 26 Of the Multiplication of Compound Quantities
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    Chapter 27 Of the Division of Compound Quantities
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    Chapter 28 Of the Resolution of Fractions into Infinite Series
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    Chapter 29 Of the Squares of Compound Quantities
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    Chapter 30 Of the Extraction of Roots applied to Compound Quantities
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    Chapter 31 Of the Calculation of Irrational Quantities
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    Chapter 32 Of Cubes, and of the Extraction of Cube Roots
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    Chapter 33 Of the higher Powers of Compound Quantities
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    Chapter 34 Of the Transposition of the Letters, on which the demonstration of the preceding Rule is founded
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    Chapter 35 Of the Expression of Irrational Powers by Infinite Series
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    Chapter 36 Of the Resolution of Negative Powers
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    Chapter 37 Of Arithmetical Ratio, or of the Difference between two Numbers
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    Chapter 38 Of Arithmetical Proportion
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    Chapter 39 Of Arithmetical Progressions
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    Chapter 40 Of the Summation of Arithmetical Progressions
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    Chapter 41 Of Figurate, or Polygonal Numbers
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    Chapter 42 Of Geometrical Ratio
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    Chapter 43 Of the Greatest Common Divisor of two given Numbers
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    Chapter 44 Of Geometrical Proportions
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    Chapter 45 Observations on the Rules of Proportion and their Utility
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    Chapter 46 Of Compound Relations
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    Chapter 47 Of Geometrical Progressions
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    Chapter 48 Of Infinite Decimal Fractions
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    Chapter 49 Of the Calculation of Interest
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    Chapter 50 Of the Solution of Problems in general
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    Chapter 51 Of the Resolution of Simple Equations, or Equations of the First Degree
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    Chapter 52 Of the Solution of Questions relating to the preceding Chapter
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    Chapter 53 Of the Resolution of two or more Equations of the First Degree
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    Chapter 54 Of the Resolution of Pure Quadratic Equations
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    Chapter 55 Of the Resolution of Mixed Equations of the Second Degree
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    Chapter 56 Of the Extraction of the Roots of Polygonal Numbers
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    Chapter 57 Of the Extraction of the Square Roots of Binomials
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    Chapter 58 Of the Nature of Equations of the Second Degree
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    Chapter 59 Of Pure Equations of the Third Degree
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    Chapter 60 Of the Resolution of Complete Equations of the Third Degree
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    Chapter 61 Of the Rule of Cardan, or of Scipio Ferreo
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    Chapter 62 Of the Resolution of Equations of the Fourth Degree
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    Chapter 63 Of the Rule of Bombelli for reducing the Resolution of Equations of the Fourth Degree to that of Equations of the Third Degree
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    Chapter 64 Of a new Method of resolving Equations of the Fourth Degree
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    Chapter 65 Of the Resolution of Equations by Approximation
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    Chapter 66 Of the Resolution of Equations of the First Degree which contain more than one unknown Quantity
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    Chapter 67 Of the Rule which is called Regula Cæci, for determining by means of two Equations, three or more Unknown Quantities
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    Chapter 68 Of Compound Indeterminate Equations, in which one of the Unknown Quantities does not exceed the First Degree
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    Chapter 69 On the Method of rendering Surd Quantities of the form √ ( a + bx + cx 2 ) Rational
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    Chapter 70 Of the Cases in which the Formula a + bx + c x 2 can never become a Square
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    Chapter 71 Of the Cases in Integer Numbers, in which the Formula ax 2 + b becomes a Square
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    Chapter 72 Of a particular Method, by which the Formula, an 2 + 1, becomes a Square in Integers
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    Chapter 73 Of the Method of rendering the Irrational Formula, √( a + bx + cx 2 + dx 3 ), Rational
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    Chapter 74 Of the Method of rendering Rational the incommensurable Formula, √ ( a + bx + cx 2 + dx 3 + ex 4 )
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    Chapter 75 Of the Method of rendering rational the irrational Formula, $$ \mathop{\surd }\limits^{3} \left( {a + bx + c{x^{2}} + d{x^{3}}} \right) $$
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    Chapter 76 Of the Resolution of the Formula, ax 2 + bxy + cy 2 into its Factors
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    Chapter 77 Of the Transformation of the Formula ax 2 + cy 2 into Squares, and higher Powers
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    Chapter 78 Of some Expressions of the Form ax 4 + by 4 , which are not reducible to Squares
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    Chapter 79 Solution of some Questions that belong to this part of Algebra
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    Chapter 80 Solutions of some Questions in which Cubes are required
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    Chapter 81 On Continued Fractions
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    Chapter 82 Solution of some curious and new Arithmetical Problems
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    Chapter 83 Of the Resolution, in Integer Numbers, of Equations of the first Degree, containing two unknown Quantities
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    Chapter 84 General Method for resolving, in Integer Numbers, Equations with two unknown Quantities, of which one does not exceed the first Degree
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    Chapter 85 A direct and general Method for finding the values of x, that will render Quantities of the form √(a+bx+cx 2 ) Rational, and for resolving, in Rational Numbers, the indeterminate Equations of the second Degree, which have two unknown Quantities, when they admit of Solutions of this kind
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    Chapter 86 Of Double and Triple Equalities
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    Chapter 87 A direct and general Method for finding all the values of y expressed in Integer Numbers, by which we may render Quantities of the form √ ( a y 2 + b ), rational; a and b being given Integer Numbers; and also for finding all the possible Solutions, in Integer Numbers, of indeterminate Quadratic Equations of two unknown Quantities
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    Chapter 88 Remarks on Equations of the form p 2 = a q 2 +1, and on the common method of resolving them in Whole Numbers
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    Chapter 89 Of the Manner of finding Algebraic Functions of all Degrees, which , when multiplied together , may always produce Similar Functions