The Elements of Analytical Geometry: Comprehending the Doctrine of the Conic Sections, and the General Theory of Curves and Surfaces of the Second OrderJohn Souter, School Library, 73, St. Paul's Church Yard; and J. and J.J. Deighton, Cambridge., 1830 - Conic sections - 312 pages |
Contents
| 1 | |
| 7 | |
| 8 | |
| 13 | |
| 14 | |
| 26 | |
| 32 | |
| 40 | |
| 145 | |
| 150 | |
| 165 | |
| 171 | |
| 177 | |
| 181 | |
| 191 | |
| 200 | |
| 46 | |
| 52 | |
| 57 | |
| 63 | |
| 64 | |
| 69 | |
| 79 | |
| 98 | |
| 99 | |
| 102 | |
| 104 | |
| 108 | |
| 110 | |
| 117 | |
| 129 | |
| 130 | |
| 137 | |
| 139 | |
| 201 | |
| 209 | |
| 212 | |
| 215 | |
| 218 | |
| 224 | |
| 227 | |
| 233 | |
| 241 | |
| 247 | |
| 259 | |
| 260 | |
| 267 | |
| 285 | |
| 296 | |
| 299 | |
| 304 | |
Other editions - View all
Common terms and phrases
A² B² A² y² algebraical analytical analytical representation asymptotes axis of abscissas axis of y becomes bisects called centre circle circumference coefficient conjugate diameters constant construction coordinates cos.² cosine curve denote determine directrix distance ellipse equa equal expression focus formulas fourth proportional Geom geometrical given point given straight line hence hyperbola inclination indeterminate equation latus rectum length line passing locus major diameter negative obviously ordinate origin parabola parallelogram perpendicular plane point of contact positive primitive axes primitive equation principal diameters PROBLEM proposed line radii radius vector rectangle rectangular axes represent resulting value right angle secant semi-conjugates semi-diameter sides sin.² square substitution subtangent supplemental chords suppose surface system of conjugate taken for axes tangent tion transformed transverse axis triangle vertex x²² y²²
Popular passages
Page xxii - ELEMENTS OF GEOMETRY; containing a new and universal Treatise on the Doctrine of Proportions, together with Notes, in which are pointed out and corrected several important errors that have hitherto remained unnoticed in the writings of Geometers. Also, an Examination of the various Theories of Parallel Lines that have been proposed by Legendre, Bertrand, Ivory, Leslie, and others.
Page 185 - Given the base and the sum of the sides of a triangle, to find the locus of the point of intersection of lines from the angles bisecting the opposite sides.
Page 114 - ... is equal to the rectangle of the sum and difference of the same abscissa and semi-transverse axis. Thus OM-MR = A'M-MB...
Page 49 - They may cut each other, having two points common, when the distance between the centers is less than the sum and greater than the difference of the radii.
Page 95 - III. ON THE HYPERBOLA. Its equation and Properties. (69.) An hyperbola is a curve from any point, P. in which, if two straight lines be drawn to two fixed points, F, F', their difference shall always be the same. The given points, F, F', are called the foci of the hyperbola, and the lines, FP, F'P, drawn therefrom to any point, P, in the curve, are called the radii vectores, or focal distances of that point.
Page 186 - Given the base, an angle adjacent to the base, and the difference of the sides of a triangle, to construct it.
Page 269 - THEOREM II. (224.) The square of the area of any plane figure is equal to the sum of the squares of its projections on three rectangular planes. * Let S represent any plane surface, and S', S", S'", its three projections on the planes...
Page 134 - ... characterize the other branch of the curve. PROBLEM IV. (114.) To find the polar equation of the hyperbola, when the centre is the pole. By substituting r
Page 130 - ... the curve, by means of an equation between its distance from the assumed point and the angle formed by this distance and the fixed line. The assumed point is called the pole; its distance from any point in the curve the radius vector ; and the radius vector, together with its angle of inclination to the fixed line, are called the polar coordinates of the point. Thus assuming the point A on the fixed line, AX, as pole, then the polar coordinates of any point, P will be the radius vector AP, and...