دانلود کتاب Elements of Algebra

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Front Matter....Pages i-lx
Of Mathematics in general ....Pages 1-2
Explanation of the Signs + Plus and — Minus....Pages 3-6
Of the Multiplication of Simple Quantities....Pages 6-10
Of the Nature of whole Numbers, or Integers, with respect to their Factors....Pages 10-12
Of the Division of Simple Quantities....Pages 13-15
Of the Properties of Integers, with respect to their Divisors....Pages 16-19
Of Fractions in general ....Pages 20-23
Of the Properties of Fractions....Pages 24-27
Of the Addition and Subtraction of Fractions....Pages 27-30
Of the Multiplication and Division of Fractions....Pages 30-35
Of Square Numbers....Pages 36-38
Of Square roots, and of Irrational Numbers resulting from them ....Pages 38-42
Of Impossible, or Imaginary Quantities, which arise from the same source ....Pages 42-44
Of Cubic Numbers....Pages 45-46
Of Cube Roots, and of Irrational Numbers resulting from them ....Pages 46-48
Of Powers in general ....Pages 48-52
Of the Calculation of Powers....Pages 52-54
Of Roots, with relation to Powers in general ....Pages 54-55
Of the Method of representing Irrational Numbers by Fractional Exponents....Pages 56-60
Of the different Methods of Calculation, and of their mutual Connexion....Pages 60-63
Of Logarithms in general ....Pages 63-66
Of the Logarithmic Tables now in use ....Pages 66-69
Of the Method of expressing Logarithms....Pages 69-75
Of the Addition of Compound Quantities....Pages 76-78
Of the Subtraction of Compound Quantities....Pages 78-79
Of the Multiplication of Compound Quantities....Pages 79-84
Of the Division of Compound Quantities....Pages 84-88
Of the Resolution of Fractions into Infinite Series....Pages 89-97
Of the Squares of Compound Quantities....Pages 97-100
Of the Extraction of Roots applied to Compound Quantities....Pages 100-104
Of the Calculation of Irrational Quantities....Pages 104-107
Of Cubes, and of the Extraction of Cube Roots....Pages 107-109
Of the higher Powers of Compound Quantities....Pages 110-115
Of the Transposition of the Letters, on which the demonstration of the preceding Rule is founded ....Pages 115-120
Of the Expression of Irrational Powers by Infinite Series....Pages 120-122
Of the Resolution of Negative Powers....Pages 123-126
Of Arithmetical Ratio, or of the Difference between two Numbers....Pages 126-128
Of Arithmetical Proportion....Pages 129-131
Of Arithmetical Progressions....Pages 131-134
Of the Summation of Arithmetical Progressions....Pages 135-139
Of Figurate, or Polygonal Numbers....Pages 139-145
Of Geometrical Ratio....Pages 146-148
Of the Greatest Common Divisor of two given Numbers....Pages 148-151
Of Geometrical Proportions....Pages 152-155
Observations on the Rules of Proportion and their Utility....Pages 155-159
Of Compound Relations....Pages 159-164
Of Geometrical Progressions....Pages 164-170
Of Infinite Decimal Fractions....Pages 171-176
Of the Calculation of Interest....Pages 177-185
Of the Solution of Problems in general ....Pages 186-189
Of the Resolution of Simple Equations, or Equations of the First Degree....Pages 189-194
Of the Solution of Questions relating to the preceding Chapter....Pages 194-206
Of the Resolution of two or more Equations of the First Degree....Pages 206-216
Of the Resolution of Pure Quadratic Equations....Pages 216-222
Of the Resolution of Mixed Equations of the Second Degree....Pages 222-229
Of the Extraction of the Roots of Polygonal Numbers....Pages 230-234
Of the Extraction of the Square Roots of Binomials....Pages 234-243
Of the Nature of Equations of the Second Degree....Pages 244-248
Of Pure Equations of the Third Degree....Pages 248-252
Of the Resolution of Complete Equations of the Third Degree....Pages 253-262
Of the Rule of Cardan, or of Scipio Ferreo....Pages 262-271
Of the Resolution of Equations of the Fourth Degree....Pages 272-278
Of the Rule of Bombelli for reducing the Resolution of Equations of the Fourth Degree to that of Equations of the Third Degree....Pages 278-282
Of a new Method of resolving Equations of the Fourth Degree....Pages 282-288
Of the Resolution of Equations by Approximation....Pages 289-298
Of the Resolution of Equations of the First Degree which contain more than one unknown Quantity....Pages 299-312
Of the Rule which is called Regula Cæci, for determining by means of two Equations, three or more Unknown Quantities....Pages 312-317
Of Compound Indeterminate Equations, in which one of the Unknown Quantities does not exceed the First Degree....Pages 317-321
On the Method of rendering Surd Quantities of the form √ ( a + bx + cx 2 ) Rational....Pages 322-335
Of the Cases in which the Formula a + bx + c x 2 can never become a Square....Pages 335-342
Of the Cases in Integer Numbers, in which the Formula ax 2 + b becomes a Square....Pages 342-350
Of a particular Method, by which the Formula, an 2 + 1, becomes a Square in Integers....Pages 351-360
Of the Method of rendering the Irrational Formula, √( a + bx + cx 2 + dx 3 ), Rational....Pages 361-368
Of the Method of rendering Rational the incommensurable Formula, √ ( a + bx + cx 2 + dx 3 + ex 4 )....Pages 368-379
Of the Resolution of the Formula, ax 2 + bxy + cy 2 into its Factors....Pages 379-386
Of the Transformation of the Formula ax 2 + cy 2 into Squares, and higher Powers....Pages 387-396
Of some Expressions of the Form ax 4 + by 4 , which are not reducible to Squares....Pages 396-405
Solution of some Questions that belong to this part of Algebra....Pages 405-413
Solutions of some Questions in which Cubes are required ....Pages 413-449
On Continued Fractions....Pages 449-462
Solution of some curious and new Arithmetical Problems....Pages 465-495
Of the Resolution, in Integer Numbers, of Equations of the first Degree, containing two unknown Quantities....Pages 495-529
General Method for resolving, in Integer Numbers, Equations with two unknown Quantities, of which one does not exceed the first Degree....Pages 530-534
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 ....Pages 534-537
Of Double and Triple Equalities....Pages 537-547
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....Pages 547-549
Remarks on Equations of the form p 2 = a q 2 +1, and on the common method of resolving them in Whole Numbers....Pages 550-577
Of the Manner of finding Algebraic Functions of all Degrees, which , when multiplied together , may always produce Similar Functions....Pages 578-583
Back Matter....Pages 583-593
....Pages 595-595