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An Elementary Treatise on Trilinear Co-Ordinates: The Method of Reciprocal ...
N. M. 1829-1903 Ferrers
No preview available - 2016
angular points appears asymptotes auxiliary becomes called centre Chap CHAPTER chord circle co-ordinates coefficients coincide common tangents condition conic considered constant corresponding curve denoted described determinant directrix distance equal equation EXAMPLES expressed find the equation fixed point focus follows four points given point given straight lines gives harmonic Hence identical imaginary letters line at infinity locus lying meet move multiplying obtain opposite sides pair parabola parallel passing pencil perpendicular point f point of intersection points of contact polar pole positive produced projection proposition prove ratios reciprocal relation represented respect right angles satisfy second degree seen sides similar Similarly suppose tangents tangents drawn term theorem third three points tion touch triangle of reference values whence writing written
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.