## Unified Mathematics |

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abscissa algebraic angle annuity approximately arch arithmetical mean arithmetical series axes axis coefficients complementary angle complex numbers Compute conic conic sections coordinates corresponding cos2 cosine cubic curve decimal place determine diagram diameter directrix distance divided ellipse equal feet per second Find the equation formula function geometrical geometrical series given line gives graphically height hence horizontal hyperbola hyperboloid inches integers interpolation intervals length line joining log cot logarithms method multiplied negative Note obtained ordinate parabola parallel parametric equations perpendicular plane plane geometry Plot the graph points of intersection polar positive quadratic quotient radians radical axis ratio represents right triangle sides significant figures Similarly sin2 sine solution Solve straight line substituting surface tangent tangent of slope theorem tion trigonometric trigonometric functions units values variable vector velocity vertex vertical whence Write the equation x-axis xu yi y-axis zero

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Page 309 - 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 347 - The square of the period of a planet is proportional to the cube of its mean distance from the Sun.

Page 327 - PF'/PH'= e, by the definition of the curve. Furthermore :J (b) \PF—PF'\=2a. In fact, the hyperbola is often defined as the locus of a point which moves so that the difference of its distances from two fixed points is constant.

Page 347 - These are: (1) The orbits of the planets are ellipses, with the sun at a common focus. (2) As a planet moves in its orbit, the line joining the planet and sun sweeps over equal areas in equal intervals of time. Also called "law of equal areas.

Page 45 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.

Page 45 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.

Page 343 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. 144. Theorem. The bisector of an exterior angle of a triangle divides the opposite side produced into segments proportional to the other two sides.

Page 42 - The logarithm of the quotient of two numbers is the logarithm of the dividend minus the logarithm of the divisor. DEM. — Let a be the base of the system, and m and n any two numbers whose logarithms are, respectively, x, and y. Then by definition wenave<tI=m, and a' = n. Dividing, we have a* — * = — . Whence x — y is the logarithm of — . QED 123.

Page 125 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.

Page 17 - The triangles formed are similar to the whole triangle, and to each other. II. The perpendicular is a mean proportional between the segments of the hypotenuse. III.