Mathematica

CHAPTER 𝐼𝐼.  Negative Quantities. Addition of Like Terms. 𝟏𝟗. In his arithmetical work the student has been accustomed to deal with numerical quantities connected by the signs + and — ; and in finding the value of an expression such as 𝟏 𝟑/𝟒 + 𝟕 𝟐/𝟑 — 𝟑 𝟏/𝟖 + 𝟔 ― 𝟒 𝟏/𝟓 he understands that the quantities to which the sign-f- is prefixed are additive, and those to which the sign — is prefixed are subtractive, while the first quantity, 𝟏 𝟑/𝟒, to which no sign is prefixed, is counted among the additive terms. The same notions prevail in Algebra; thus in using the expression 𝟕𝑎 + 𝟑𝑏 — 𝟒𝑐 — 𝟐𝑑 we understand the symbols 𝟕𝑎 and 𝟑𝑏 to be additive, while 𝟒𝑐 and 𝟐𝑑 are subtractive. 𝟐𝟎. But in Arithmetic the sum of the additive terms is always greater than the sum of the subtractive terms; and if the reverse were the case, the result would have no arithmetical meaning. In Algebra, however, not only may the sum of the subtractive terms exceed that of the ad...

  ALGEBRA  CHAPTER 𝐼.  Definitions. Substitutions.  𝟏. Algebra treats of quantities as in Arithmetic, but with greater generality; for while the quantities used in arithmetical processes are denoted by ƒigures , which have a single definite value, algebraic quantities are denoted by symbols , which may have any value we choose to assign to them.  The symbols of quantity employed are usually the letters of our own alphabet; and, though there is no restriction as to the numerical values a symbol may represent, it is understood that in the same piece of work it keeps the same value throughout. Thus, when we say "let 𝑎 equal 𝟏," we do not mean that 𝑎 must have the value 𝟏 always, but only in the particular example we are considering. Moreover, we may operate with symbols without assigning to them any particular numerical value; indeed it is with such operations that Algebra is chiefly concerned. We begin with the definitions of Algebra, premising that the sym...

ELEMENTARY ALGEBRA  BY   H. S. HALL, M.A., and S. R. KNIGHT, B.A.  REVISED AND ENLARGED   FOR THE USE OF AMERICAN SCHOOLS  BY  F. L. SEVENOAK, A.M.  Assistant Principal of the Academic Department,  Stevens Institute of Technology  𝔑𝔢𝔴 𝔜𝔬𝔯𝔨 THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd.  1896  All rights reserved.