A Treatise on Analytic Geometry: Especially as Applied to the Properties of Conics; Including the Modern Methods of Abridged Notation |
Contents
| 83 | |
| 89 | |
| 95 | |
| 98 | |
| 113 | |
| 120 | |
| 126 | |
| 129 | |
| 135 | |
| 149 | |
| 155 | |
| 168 | |
| 176 | |
| 181 | |
| 189 | |
| 196 | |
| 205 | |
| 209 | |
| 218 | |
| 222 | |
| 225 | |
| 227 | |
| 242 | |
| 250 | |
| 251 | |
| 254 | |
| 264 | |
| 265 | |
| 273 | |
| 280 | |
| 288 | |
| 289 | |
| 296 | |
| 339 | |
| 340 | |
| 343 | |
| 349 | |
| 354 | |
| 362 | |
| 367 | |
| 371 | |
| 374 | |
| 381 | |
| 386 | |
| 388 | |
| 392 | |
| 398 | |
| 404 | |
| 408 | |
| 415 | |
| 422 | |
| 426 | |
| 436 | |
| 437 | |
| 438 | |
| 444 | |
| 447 | |
| 453 | |
| 456 | |
| 468 | |
| 483 | |
| 515 | |
| 537 | |
| 543 | |
| 570 | |
Other editions - View all
Common terms and phrases
a²b² a²y² abscissa algebraic analytic Analytic Geometry b²x² bisectors bisects Cartesian chord of contact circle co-efficients co-ordinates condition conic conjugate hyperbola constant construct Corollary corresponding curve denotes determine diagram distance drawn ellipse equa equal equation Art equation of Art expression find the locus fixed point focal radii foci focus Form the equation formulæ geometric meaning given equation given line given point Given the base Hence hyperbola imaginary infinite intercepts internal angle intersection latus rectum length loci middle point negative obtain ordinate origin Parabola perpendicular point of contact polar equation pole positive radical axis radius ratio rectangle rectangular axes referred Remark represent required equation right angles right line passing second degree sides signs subtangent suppose symbols tangent Theorem tion transformation transverse axis triangle Trig values variable vertex vertices
Popular passages
Page 254 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 238 - ... proved that, if a point and a straight line be such that the straight line joining the centre of a circle to the point is at right angles to the line, and the rectangle contained by the distances of the point and the line from the centre is equal to the square on the radius of the circle, the point is the pole of the line, and the line the polar of the point with respect to the circle. In the diagram O is the centre of the circle : H is a point in OP such that the rectangle OP, OH is equal to...
Page 192 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.
Page 109 - I (Ax +By+C) + m (A'x + B'y + C') = 0, the new equation will represent a right line passing through the intersection of the lines Ax + By -\- C= 0 and A'x + B'y + C
Page 542 - Three planes meet in a point, and through the line of intersection of each pair a plane is drawn perpendicular to the third ; prove that, in general, these planes pass through the same line.
Page 80 - ... the tangent of the angle which the line makes with the axis of abscissae), was lately employed by M. Crova* for the discussion of experiments relating to the degree of constancy possessed by so-called
Page 221 - The straight lines joining the vertices of a triangle to the middle points of the opposite sides meet in a point* which is for each line the point of trisection further from the vertex.
Page 169 - The two fixed points, F' and F, are called the foci of the curve ; and the variable distances with a constant difference, F'P and FP, are termed its focal radii. The portion A' A of the right line drawn through the foci, is called the transverse axis.
Page 478 - Conic, is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line.
Page 250 - The perpendiculars erected at the middle points of the sides of a triangle meet in a point equidistant from the three vertices.