An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of ProjectionsMacmillan, 1866 - 182 σελίδες |
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An Elementary Treatise on Trilinear Co-Ordinates, the Method of Reciprocal ... Norman MacLeod Ferrers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ aa+bB+cy angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ c₁ centre Chap co-ordinates coefficients common tangents condition of tangency conic section determine directrix escribed circles find the equation fixed point fixed straight line focus four points given conic given point given straight line harmonic pencil Hence imaginary internal bisectors investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem passing perpendicular point f point of intersection points of contact pole prove radical axis reciprocated with respect rectangular hyperbola represented right angles second degree shewn sin POS tangents drawn theorem three points three straight lines touches the line triangle of reference ua² V'ca v'f+u'g+wh values Vb² vß² W'ab whence wy² λα
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.