As far as the authors know, this is the first beginners' book that graphically illustrates the fundamental rules, laws and facts of algebra, and brings into bold relief those portions of it that are indispensable to the study of geometry, physics, and chemistry pursued in secondary schools. The first ten chapters furnish an easy introduction to algebra, with simple problems having natural solutions. The second ten chapters demand more of the student, while fixing principles in the mind by means of examples that move from easy, to those of increasing difficulty.
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acres added algebraic amount angle arithmetic buys called cents Check City coefficient common contains cost cube denominator difference digits dimensions diminished direction distance Divide dollars equal equation Example exceeds EXERCISE exponent expression Extract factors feet figures Find the number Find the value five four fraction geometric give given greater half Hence horses hour ILLUSTRATION inches increased indicated integral interest invested length less letter logarithms marked means mercury miles miles an hour minutes months Multiply negative paying positive pounds problem proportional quadratic quantity quotient ratio received rectangle remainder represent result selling side sold SOLUTION Solve square root stand Step Substitute subtract symbols third train Transposing travels twice units width Write written yards zero
Page 3 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Page 143 - That is, the square of the sum of two numbers is equal to the square of the first number, plus twice the product of the two numbers, plus the square of the second number.
Page 60 - To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: (Sab — 12ac) -i- 4a = 36 — 3c.
Page 72 - I cannot demonstrate, that two quantities which are equal to the same quantity, are equal to each other; neither can I demonstrate that the tree which I perceive exists.
Page 172 - In any proportion, the product of the means equals the product of the extremes.
Page 74 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 63 - Thus, |-, -f, f, f, -|-, etc., are improper fractions. The numerator and the denominator are called the terms of a fraction.
Page 167 - The ratio of one quantity to another quantity of the same kind is the quotient of the first quantity divided by the second quantity. Thus, the ratio of 2 feet to 3 feet 2 is the quotient of 2 feet divided by 3 feet, ie -• о Magnitudes of the same kind only can be compared.