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added algebraical arithmetical arranged base begin binomial brackets called cents changed CHAPTER coefficients column combinations compound consider consists contains continued fraction convergent corresponding cube DEFINITION denominator denote determinant difference digits Divide division divisor equal equation Example expansion expression feet find the number Find the value four fraction function give given greater Hence highest common factor integer involving less letters logarithm lowest common means method miles Multiply negative NOTE obtain places positive powers preceding present prove quadratic quantities quotient ratio Reduce remainder removed Resolve into factors respectively result rule rule of signs Show side simple Simplify solution Solve square root Substituting subtraction Suppose surds symbols taken things third transformed unknown walk whence write written yards zero
Side 331 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Side 168 - Thus the 4th root (2x2) = the square root of the square root ; the sixth root (3x2) = the cube root of the square root, or the square root of the cube root.
Side 178 - A basket of oranges is emptied by one person taking half of them and one more, a second person taking half of the remainder and one more, and a third person taking half of the remainder and six more. How many did the basket contain at first ? 17.
Side 179 - Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half water.
Side 280 - The pressure of wind on a plane surface varies jointly as the area of the surface, and the square of the wind's velocity. The pressure on a square foot is 1...
Side 213 - Art. 167 we saw that if the number of unknown quantities is greater than the number of independent equations, there will be an unlimited number of solutions, and the equations will be indeterminate. By introducing conditions, however, we can limit the number of solutions. When positive integral values of the unknown quantities are required, the equations are called simple indeterminate equations. The introduction of this restriction enables us to express the solutions in a very simple form. Ex. 1....