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abscissa angle asymptote axes becomes bisects called chord circle conjugate diameters constant continually coordinates Corollary corresponding curve direction cosines directrix distance Draw ellipse equal EXAMPLES extremities fixed point focal focus fraction Geom given Hence hyperbola inclination intercept intersection joining length locate locus move negative normal opposite ordinate origin parabola parallel parameter perpendicular plane point of tangency polar pole positive produced projection PROPOSITION prove quadric referred represented revolve satisfy the equation secant set of values sides Similarly slope spiral square stand straight line straight line passing Substituting these values Substituting this value taken tangent tangents drawn third tion transverse axis Trig variables vertex x and y
Page 363 - ... an arc whose length is equal to the radius of the circle. Thus in Fig.
Page 360 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 360 - A straight line is perpendicular to a plane, if it is perpendicular to every straight line drawn through its foot in the plane ; and the plane is perpendicular to the line.
Page 359 - Two right triangles are equal if the hypotenuse and an acute angle of the one are equal respectively to the hypotenuse and an acute angle of the other.
Page 359 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Page 57 - ... lines, and the perpendiculars from the three vertices of the triangle upon this line will be equal, by Chap. I, II, 13. A perpendicular to AB erected midway between any two of these three is perpendicular to the corresponding side of the triangle at its middle point (Chap.
Page 361 - COR. 1. If two planes are perpendicular to each other, a perpendicular to one of them at any point of their intersection will lie in the other plane.
Page 360 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.