The Principles of Analytical Geometry: Designed for the Use of Students |
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Page 53
... locus of the equation f ( x , y ) = 0 . 45. Of the two quantities a and b , which represent AM and MP , the former is called the abscissa , the latter , the ordinate of the given point P : they are both comprehended under the general ...
... locus of the equation f ( x , y ) = 0 . 45. Of the two quantities a and b , which represent AM and MP , the former is called the abscissa , the latter , the ordinate of the given point P : they are both comprehended under the general ...
Page 54
... locus of a given equa- tion is described ,, we may deduce , from some known property of the curve , the relation subsisting between the co - ordinates of any one of its points . The equation which expresses this re- lation , supposing ...
... locus of a given equa- tion is described ,, we may deduce , from some known property of the curve , the relation subsisting between the co - ordinates of any one of its points . The equation which expresses this re- lation , supposing ...
Page 55
... locus of the equation of the first degree . The general form of this equation is Ay + Br + C = 0 , B C B C or y = Ꮖ hence , if a = - = A Α A ' A ' A ' the equation becomes y = ax + b . Now let x = 0 , then y = b , y = 0 , b X = a XA In ...
... locus of the equation of the first degree . The general form of this equation is Ay + Br + C = 0 , B C B C or y = Ꮖ hence , if a = - = A Α A ' A ' A ' the equation becomes y = ax + b . Now let x = 0 , then y = b , y = 0 , b X = a XA In ...
Page 56
... locus required . COR . 1 . y = ax + b . Conversely , the equation to any straight line is COR . 2. The constant quantity a , denotes the ratio of the ordinate to the abscissa , and may be expressed in terms of the angles which the ...
... locus required . COR . 1 . y = ax + b . Conversely , the equation to any straight line is COR . 2. The constant quantity a , denotes the ratio of the ordinate to the abscissa , and may be expressed in terms of the angles which the ...
Page 78
... loci of the above equations , since the points in which they intersect , will evidently be the points of contact . Now the locus of ( 1 ) is the given circle ; that of ( 2 ) is a straight line , which must therefore be the chord joining ...
... loci of the above equations , since the points in which they intersect , will evidently be the points of contact . Now the locus of ( 1 ) is the given circle ; that of ( 2 ) is a straight line , which must therefore be the chord joining ...
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The Principles of Analytical Geometry: Designed for the Use of Students Henry Parr Hamilton No preview available - 2016 |
Common terms and phrases
a²² abscissa Algebra ANALYTICAL GEOMETRY assumed asymptotes axes are rectangular bisect centre CHAP chords co-ordinate planes coefficients conjugate diameters constructed cos² denote directrix distance draw ellipse and hyperbola equal equation becomes equation required equation sought find the equation formulas given line given point Hence hyperboloid imaginary inclination indeterminate equation infinite latus rectum Let y=0 locus major axis manner meet the curve negative ordinate origin parabola parallelepiped perpendicular dropped plane of xy point of intersection points of contact polar equation positive principal diameters principal vertex PROB PROP quadratic equation radius rectangular axes right angles roots second order shewn sides sin x sin² square straight line substitution supposed surface system of conjugate tangent triangle unknown quantity values whence
Popular passages
Page 7 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 1 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Page 244 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 116 - Fig. 83,84. conjugate diameters is equal to the sum of the squares of the...
Page 66 - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
Page 115 - ... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Page 14 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 68 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Page 79 - If two chords intersect in a circle, the difference of their squares is equal to the difference of the squares of the difference of the segments.
Page 253 - It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle.