Mathematics for Collegiate Students of Agriculture and General Science |
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Page 190
... ellipse , the parabola , and the hyperbola , are curves which can be cut out of a right circular conical surface by planes passing through it in various directions . For this reason , they are called also conic sections . Being plane ...
... ellipse , the parabola , and the hyperbola , are curves which can be cut out of a right circular conical surface by planes passing through it in various directions . For this reason , they are called also conic sections . Being plane ...
Page 198
... it , 4 ft . from the top ? 8. A parabolic reflector is 8 inches across and 8 inches deep . How far is the focus from the vertex ? Ans . 2 in . 157. Ellipse . so that the sum of its distances 198 [ IX , § 156 MATHEMATICS.
... it , 4 ft . from the top ? 8. A parabolic reflector is 8 inches across and 8 inches deep . How far is the focus from the vertex ? Ans . 2 in . 157. Ellipse . so that the sum of its distances 198 [ IX , § 156 MATHEMATICS.
Page 199
... ellipse . The points A and A ' are called the vertices . The segment A'A is called the major axis of the ellipse . Another position of P is a point B on the y - axis above O and OB is denoted by b . By ( 12 ) , we have F'B + FB = 20 ...
... ellipse . The points A and A ' are called the vertices . The segment A'A is called the major axis of the ellipse . Another position of P is a point B on the y - axis above O and OB is denoted by b . By ( 12 ) , we have F'B + FB = 20 ...
Page 200
... ellipse . The rectangle formed by drawing lines perpendicular to the major and minor axes at their extremities is called the rectangle on the axes . Let a denote the acute angle OFB . Then cos a is called the eccentricity of the ellipse ...
... ellipse . The rectangle formed by drawing lines perpendicular to the major and minor axes at their extremities is called the rectangle on the axes . Let a denote the acute angle OFB . Then cos a is called the eccentricity of the ellipse ...
Page 201
... ellipse . Hence we may state the fol- lowing theorem . The equation of the ellipse whose semi - major axis is a , whose semi - minor axis is b , whose center is at the origin , and whose foci are on the x - axis , is ( 19 ) y2 + - 1 ...
... ellipse . Hence we may state the fol- lowing theorem . The equation of the ellipse whose semi - major axis is a , whose semi - minor axis is b , whose center is at the origin , and whose foci are on the x - axis , is ( 19 ) y2 + - 1 ...
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Mathematics for Collegiate Students of Agriculture and General Science Alfred Monroe Kenyon,William Vernon Lovitt No preview available - 2016 |
Common terms and phrases
abscissas algebraic amount annuity arithmetic mean average ax² axes axis binomial binomial coefficients binomial theorem called cent circle coefficient common logarithm completing the square computed coördinates correlation cos² cosine COTANGENT curve decimal denoted determine distance ears ellipse equal error EXAMPLE EXERCISES exponent feet Find the equation forces formula frequency geometric given equation graph Hence hyperbola inches intersection law of sines law of tangents length locus Log10 Value Log10 logarithm magnitude mantissa measured multiplying negative parabola parallel perpendicular plane Plot positive quadratic quadratic equation RADIANS radius ratio real number represents respect resultant side sin² sine slope solution solve square root standard deviation straight line Substituting tabular difference tangent temperature term tion trigonometric functions Value Log10 Value varies vertex vertical weight whence x-axis y-axis zero
Popular passages
Page 59 - Find the equation of the locus of a point which moves so that the sum of the squares of its distances from the x and the j/-axis equals 4.
Page 122 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Page 277 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.
Page 124 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 199 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 167 - moment of a force" with respect to a point is the product of the force and the perpendicular distance from the given point to the line of action of the force.
Page 223 - The weight of an object above the surface of the earth varies inversely as the square of its distance from the center of the earth.
Page 207 - Find and classify the equation of the locus of a point which moves so that...
Page 204 - 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 74 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.