The Elements of Analytic GeometryGinn, 1904 - 424 pages |
Table des matières
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Autres éditions - Tout afficher
The Elements of Analytic Geometry Percey Franklyn Smith,Arthur Sullivan Gale Affichage du livre entier - 1904 |
The Elements of Analytic Geometry Percey Franklyn Smith,Arthur Sullivan Gale Affichage du livre entier - 1904 |
The Elements of Analytic Geometry Percey Franklyn Smith,Arthur Sullivan Gale Affichage du livre entier - 1904 |
Expressions et termes fréquents
a²b² a²y² abscissa Analytic Geometry asymptotes Ax² b²x² bisecting C₁ chord circle x² coefficients conic conjugate hyperbolas coördinate planes Corollary cos² curve Cy² degenerate determined direction cosines directrix distance ellipse equal figure Find the equation Find the locus fixed point given equation given line Hence homothetic transformation hyperbola intercepts inverse line joining line passing loci middle point negative obtain origin P₁ parabola parametric equations perpendicular point of intersection point P1 polar coördinates polar reciprocal positive problem projection Proof quadratic quadric radical axis radius ratio real numbers required equation roots Rule satisfy second degree Second step Show slope Solution Solving straight line strophoid Substituting symmetrical with respect system of lines tangent Theorem III Theorem VII Third step transformation triangle whose vertices values variables vertex X-axis x₁ XY-plane Y-axis y₁
Fréquemment cités
Page 417 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 97 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Page 64 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 63 - Find the equation of the locus of a point which moves so that its distances from (8, 0) and (2, 0) are always in a constant ratio equal to 2.
Page 27 - The projection of a point upon a line is the foot of the perpendicular from the point to the line. 329. DEF. The projection of one line upon another is the segment between the projections of the extremities of the first line upon the second. A' / ri U/ A A B' A
Page 64 - A point moves so that the difference of the squares of its distances from two fixed points is constant. Show that...
Page 333 - ... cos y cos y' = 0. That is, two lines are parallel and in the same direction when and only when their direction angles are equal, and perpendicular when and only when the sum of the products of their direction cosines is zero.
Page 85 - N6 is to say that if two nonvertical lines are perpendicular, then the slope of one is the negative reciprocal of the slope of the other.
Page 55 - Find the equations of the perpendicular bisectors of the sides of the triangle in problem 2, and show that they meet in a point.
Page 74 - A conic section is the locus of a point whose distances from a fixed point and a fixed line are in a constant ratio. 4. Show that every conic is represented by an equation of the second degree in x and y. Hint. Take Y Y' to coincide with the fixed line, and draw XX