### тИ КщМЕ ОИ ВЯчСТЕР -сЩМТАНГ ЙЯИТИЙчР

дЕМ ЕМТОПъСАЛЕ ЙЯИТИЙщР СТИР СУМчХЕИР ТОПОХЕСъЕР.

### пЕЯИЕВЭЛЕМА

 CHAPTER 1 ALGEBRAIC POSITIVE AND NEGATIVE NUMBERS 13 CHAPTER II 19 SUBTRACTION OF ALGEBRAIC NUMBERS 27 DivisioN OF ALGEBRAIC NUMBERS 41 Positive INTEGRAL Powers 47 ADDITION AND SUBTRACTION 54 Division 68
 CHAPTER XXIV 336 SIMULTANEOUS Higher EQUATIONS 349 Ratio 356 VARIATION 365 DOCTRINE OF EXPONENTS 366 CHAPTER XXVII 379 GEOMETRICAL PROGRESSION 391 CHAPTER XXVIII 402

 CHAPTER IV 80 LINEAR EQUATIONS IN ONE UNKNOWN NUMBER 86 CHAPTER VI 100 TYPEFORMS IN DIVISION 107 CHAPTER VII 113 FRACTIONS 152 Reduction of Fractions to a Lowest Common Denominator 158 Multiplication of Fractions 166 Complex Fractions 172 CHAPTER X 180 CHAPTER XI 188 CHAPTER XII 196 CHAPTER XIII 203 SYSTEMS OF LINEAR EQUATIONS 209 SYSTEMS OF FRACTIONAL EQUATIONS 218 CHAPTER XIV 225 PROBLEMS WHICH LEAD TO SIMULTANEOUS LINEAR EQUATIONS 233 CHAPTER XVI 239 SQUARE Roots of MultiNOMIALS 247 INEQUALITIES 258 Problems 264 The Fundamental Operations with Irrational Numbers 271 Addition and Subtraction of Surds 278 Surd Factors 284 Evolution of Surd Expressions 290 Complex Factors 301 QUADRATIC EQUATIONS 304 CHAPTER XXIII 330
 CHAPTER XXIX 408 Systems of Logarithms 418 To find a Number from its Logarithm 426 Exponential Equations 434 PERMUTATIONS AND COMBINATIONS 440 COMBINATIONS 448 CHAPTER XXXII 456 CHAPTER XXXIII 464 The General Term of a Series 472 CHAPTER XXXIV 481 UNDETERMINED COEFFICIENTS 488 PARTIAL FRACTIONS 495 CHAPTER XXXVI 501 Properties of Convergents 507 To reduce a Periodic Continued Fraction to an Irrational 513 Method of Finite Differences 524 CHAPTER XXXVIII 534 DETERMINANTS 540 Solution of Linear Simultaneous Equations 551 Synthetic Division 557 Symmetrical Functions 563 To transform an Equation into Another whose Roots 569 Newtons Method 575 Greatest and Least Terms in fx 587 Horners Method of Approximation 593 Roots of Numbers 599 Reciprocal Equations 606 пМЕУЛАТИЙэ ДИЙАИЧЛАТА

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
сЕКъДА 73 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
сЕКъДА 359 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
сЕКъДА 64 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
сЕКъДА 363 - One quantity is said to vary directly as a second and inversely as a third, when it varies as the second and the reciprocal of the third jointly.
сЕКъДА 456 - ж2), etc-, are functions of x ; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
сЕКъДА 364 - The volume of a gas varies inversely as the pressure when the temperature is constant. When the pressure is 15, the volume is 20; what is the volume when the pressure is 20 ? Let v stand for the volume and p for the pressure. Then from pv = k we obtain k = 300. Therefore pv = 300. Consequently, when p = 20, 20 v = 300 ; whence v = 15. EXERCISES III. If zee y, what is the expression for x in terms of y, 1.
сЕКъДА 379 - Progression (AP), is a series in which each term, after the first, is formed by adding a constant number to the preceding term.
сЕКъДА 204 - A system of linear equations has a definite number of solutions. (i.) When the number of equations is the same as the number of unknown numbers. (ii.) When the equations are independent and consistent.
сЕКъДА 100 - The square of the sum of two numbers is equal to the square \ (¿ of the first, plus twice the product of the first and second, plus the J square of the second.