Coordinate Geometry

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Sivu 39 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Sivu 207 - A PLANE is a surface, such, that if any two of its points be joined by a straight line, such.
Sivu 184 - The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle.
Sivu 170 - The right cycloid is the curve traced by a point on the circumference of a circle which rolls without sliding upon a fixed straight line in the same plane.
Sivu 163 - The cissoid was used to solve the problem of the duplication of the cube, that is, of finding the edge of a cube whose volume is twice that of a given cube, one of the famous problems of antiquity.
Sivu 75 - From the definition of an ellipse, as the locus of a point the sum of whose distances from two fixed points is constant, •shew that the ellipses are similar when the eccentricities are the same.
Sivu 27 - Consider the circle whose center is at the origin and whose radius is a: (1) * + y1 = a'.
Sivu 22 - Find the equation of the line which passes through the point (0, 5) and makes an angle of 60° with the positive direction of x-axis.
Sivu 202 - Find the coordinates of the mid-point of the line segment joining the points (5, — 2, 7) and (2, 2, — 5); also the coordinates of the points where this line segment is trisected.
Sivu 26 - Prove analytically that the medians of a triangle meet in a point. 70. Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.

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