Elements of Analytic Geometry |
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Common terms and phrases
a¹² a² y a²b² a²y a²y¹² a²y² abscissa asymptote b¹² b²x¹² b²x² bisects a system circle conjugate axis conjugate diameters conjugate hyperbola Corollary 1.-The Corollary.-The cos² curve directrix Draw eccentricity ellipse equa equal equation of PT extremities Find the equation fixed point focal radii focus Geom Hence substituting inclination intersection Let LM Let PT limaçon line MN LMNO locus traced normal parabola parallel chords parameter perpendicular plane point of tangency point whose coordinates polar equation prove PT and P'T Q. E. D. PROPOSITION quadric represented satisfy the equation secant semi-axes semi-conjugate semi-transverse axis set of values Similarly sin² slope straight line passing Substituting these values Substituting this value subtangent supplementary angles system of chords tangent tangent PT tangents drawn transverse axis Trig VA² vertex x¹² y¹²
Popular passages
Page 363 - ... an arc whose length is equal to the radius of the circle. Thus in Fig.
Page 361 - If two angles, not in the same plane, have their sides respectively parallel and lying in the same direction, they are equal and their planes are parallel. Let BA C,B'A...
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.
Page 361 - If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane.