A Higher algebra PDF
Preview A Higher algebra
This is a reproduction of a library book that was digitized by Google as part of an ongoing effort to preserve the information in books and make it universally accessible. https://books.google.com TX 512.1.6478h Wentworth,G. A. Higher algebra / Stanford University Libraries 3 6105 04932 6403 Caran , 78. 99.8.4 4 0 4 dOARD EL SCHOOL OF EDUCATION LIBRARY TEXTBOOK COLLECTION STANFORD JUNIOR STANFORD GANIZED100 UNIVERSITY LIBRARIES , * 32 3 1 39 (Seulsurized - j I 632325 ceress, EnteredaccordingtoActofCongress,intheyear1891,by G. A. WENTWORTH, intheOfficeoftheLibrarianofCongress,atWashington. ALL RIGHTS RESERVED. 3 TYPOGRAPHY BY J. 8. CUSHING & Co., Boston, U.S.A. PRESSWORK BY GINN & Co., BOSTON, U.S.A. PREFACE. THISwork isintendedto give inonebookathorough prepara tory coursefor Collegesand Scientific Schools, and in addition asufficiently full treatment of the subjects usually read by students in general in such institutions. In short, it provides a course parallel to the course covered by the author's School and College Algebras together. The elementary part is as full as the School Algebra; the advanced part, however, is briefer than the College Algebra. The book is substantially equivalent to the author's Complete Algebra, but is greatly superior to that work in the arrangementoftopics and in themethodsofpresenting them. Preparatory Schools and Academies, if their pupils have had a thorough drillin Arithmeticbefore they begin thestudyofAlgebra, will find this book specially suited to their needs. The brighter boys of the class can read the advanced chapters while the duller boysreviewthe elementary chapters. Colleges and Scientific Schools, if their pupils, owing to lack of previous drill, have to review carefully the preparatory work oftheschoolsbeforeenteringupon thecollegeworkproper, will find inthisaaconvenientand sufficiently full book for theirrequirements. Answers to the problems are bound separately, in paper covers, andwillbefurnishedfree forpupils when teachersapply to the pub lishersforthem. Any corrections or suggestions relating to the work will be thankfully received. G. A. WENTWORTH. PHILLIPS EXETER ACADEMY, EXETER, N.H., May, 1891. CONTENTS. CHAPTER PAGE I. DEFINITIONS 1 II. ADDITION AND SUBTRACTION 12 III. MULTIPLICATION 26 IV. DIVISION 39 V. SIMPLE EQUATIONS . 48 VI. MULTIPLICATION AND DIVISION 61 VII. FACTORS. 70 VIII. Common FACTORS AND MULTIPLES 93 IX. FRACTIONS 109 . X. FRACTIONAL EQUATIONS 134 XI. SIMULTANEOUS EQUATIONSOFTHEFIRST DEGREE 154 XII. PROBLEMS INVOLVING TwoUNKNOWNNUMBERS . 169 XIII. SIMPLE INDETERMINATE EQUATIONS 186 XIV. INEQUALITIES 192 XV. INVOLUTION AND EVOLUTION 194 XVI. THEORY OF EXPONENTS 207 XVII. RADICAL EXPRESSIONS. 214 XVIII. IMAGINARY EXPRESSIONS . 229 XIX. QUADRATIC EQUATIONS 234 XX. SIMULTANEOUS QUADRATIC EQUATIONS 260 XXI. PROPERTIES OF QUADRATICS . 271 XXII. Ratio, PROPORTION, AND VARIATION 277 vi CONTENTS. CHAPTER PAGE XXIII. PROGRESSIONS 295 XXIV. INDETERMINATE COEFFICIENTS 312 . XXV. BINOMIAL THEOREM 319 XXVI. COMMON LOGARITHMS 331 XXVII. INTEREST AND ANNUITIES 346 XXVIII. CHOICE 356 . XXIX. CHANCE . 377 XXX. CONTINUED FRACTIONS. 381 XXXI. SCALES OF NOTATION 392 XXXII. THEORY OF NUMBERS . 397 XXXIII. VARIABLES AND LIMITS 403 XXXIV. SERIES 412 XXXV. GENERAL PROPERTIES OF EQUATIONS 441 XXXVI. NUMERICAL EQUATIONS 473 XXXVII. DETERMINANTS 499 XXXVIII. COMPLEX NUMBERS: 515 HIGHER ALGEBRA. CHAPTER I. DEFINITIONS. 1. Units. In counting separate objects the standards by which wecount are called units; and in measuring contin uous magnitudes the standards by which we measure are called units. Thus, in countingthe boys in a school, the unitis aboy; in sell ; ing eggs by thedozen, the unitis adozen eggs; in sellingbricks by a the thousand, the unitisa thousand bricks; in measuringshort dis tances, the unit is an inch, a foot, or a yard; in measuring long distances, the unitis arod or amile. 2. Numbers. Repetitions of the unit are expressed by numbers. If a man, in sawing logs into boards, wishes to keep a count of the logs, he makes a straight mark for every log sawed, and his record at differenttimes will be as follows: // /// //// Ne NW MV // MU /// NU MII NUNNU These representative groups are named one, two, three, four, five, six, seven, eight, nine, ten, etc., and are known collectively under the general name of numbers. It is obvious that these representative groups will have the samemeaning, whateverthe nature ofthe unit counted.
The list of books you might like
