# An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections

Macmillan, 1866 - Conic sections - 182 pages

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### Contents

 CHAPTER 1 Anharmonic Ratio of a given Pencil 23 CHAPTER 11 33 ence 49 ELIMIMATION BETWEEN LINEAR EQUATIONS 59 ARTS 65 CHAPTER IV 73 Equation of the pair of Tangents drawn to the Conic from 79
 23 118 26 119 EXAMPLES 127 CHAPTER VII 130 Equation of circumscribed Conic 137 12 140 Tangential rectangular Coordinates 141 19 153

 Condition for a Rectangular Hyperbola 85 51 90 22 94 3 100 19 112 Any straight line drawn through a given point A is divided har 114
 CHAPTER IX 160 Two points and two tangents 166 ARTS PAGE 170 2 174 is 1124 179

### Popular passages

Page iii - FERRERS.— AN ELEMENTARY TREATISE on TRILINEAR CO-ORDINATES, the Method of Reciprocal Polars, and the Theory of Projections. By the Rev. NM FERRERS, MA, Fellow and Tutor of Gonville and Caius College, Cambridge.
Page 128 - ... intersection of perpendiculars of a triangle inscribed in an equilateral hyperbola lies on the curve. (246) The tangents from any point to two confocal conies are equally inclined to each other. (247) The locus of the pole of a fixed line with regard to a series of confocal conies is a straight line. (248) On a fixed tangent to a conic are taken a fixed point A and two moveable points P, Q, such that AP, AQ subtend equal angles at a fixed point 0. From P, Q are drawn two other tangents to the...
Page 141 - A parabola touches one side of a triangle in its middle point, and the other two sides produced; prove that the perpendiculars drawn from the angular points of the triangle upon any tangent to the parabola are in harmonical progression.
Page 119 - ... 8 right angles. 10. Represent the arithmetic, geometric, and harmonic means, between two given lines geometrically. 11. The centre of the circle circumscribed about any triangle, the point of intersection of the perpendiculars let fall from the angular points of the same triangle to the opposite sides, and the point of intersection of the lines joining the angular points with the middle of the opposite sides, all lie in the same right line. 12. If four circles touch each either internally or...
Page 10 - The plane curve described by a point which moves in such a manner that the sum of its distances from two fixed points (the foci) remains the same in all its positions.
Page 12 - To find the co-ordinates of the point of intersection of two given straight lines. Let the equations of the lines be ax + by +c = 0 (i), and a'x + b'y + c
Page 127 - OI/On, and On is constant and na fixed point. 2. Another proof is given as a problem in The Ancient and Modern Geometry of Conies, page 122 (1881), thus, " 279. If PQ be a chord of a conic which subtends a right angle at a given point...
Page 168 - Any straight line drawn from the vertex of a triangle to the base is bisected by the straight line which joins the middle points of the other sides of the triangle.
Page 123 - Let them be denoted by F and F' (fig. 72), and let the axis of x be taken through them, and the origin halfway between them. Then if P is any point on the ellipse and 2 a represents the constant sum of its distances from the foci, we have F'P+FP=2a.
Page 128 - ... subtends a right angle at a fixed point. Prove that the locus of the point of intersection of the variable tangents is a straight line.