A mathematical course for the University of London. (2nd)
Longmans, Green, 1865 - Mathematics - 192 pages
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Common terms and phrases
a b c added algebraic amount angle arithmetical becomes called cent column common common measure contained decimal Define denominator determine difference digits distance divide dividend divisible divisor ellipse equal equation EXAMPLES Explain expression Extract factors feet figures Find Find the sum four fraction geometrical given gives greater greatest Hence hour least less letters logarithm means miles multiply negative obtained origin period positive pound preceding progression proportion prove quantities question quotient ratio Reduce remainder represented respectively result rule rule of signs Show sides signs sine Solve square root straight line Substituting subtract taken tangent third triangle units unity unknown quantity Whence whole number yards
Page xxxv - Determine the expression for the cosine of an angle of a triangle in terms of the sides, and deduce the expression for the sine.
Page xxvii - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page xxxviii - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Page xii - A privateer running at the rate of 10 miles an hour discovers a ship 1 8 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken?
Page vi - Explain fully what is meant by a fraction, and show that the value of a fraction is not altered by multiplying the numerator and denominator by the same number.
Page 67 - Any term may be transposed from one side of an equation to the other by changing its sign.
Page 78 - A ship sails with a supply of biscuit for 60 days, at a daily allowance of a pound a head ; after being at sea 20 days she encounters a storm in which 5 men are washed overboard, and damage sustained that will cause a delay of 24 days, and it is found that each man's daily allowance must be reduced to fivesevenths of a pound.
Page xxix - A and B are two fixed points 4 inches apart, and a point P moves so that the sum of its distances from A and B is 5 inches. Take as axes of co-ordinates the line AB and the line bisecting AB perpendicularly, and find the equation of the locus of P.
Page xliv - If the numerator and denominator of a fraction be multiplied by the same number, the value of the fraction is not altered.
Page 44 - Multiply as in whole numbers, and point off in the product as many decimal places as there are in both factors.