A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on Conic SectionsHodges and Smith, 1852 - 316 σελίδες |
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ angle asymptotes axis b₁ centre circle co-ordinates coefficients coincide coincident points condition conic sections conjugate point consecutive points constant corresponding Crelle's Journal cubic cusp cycloid denotes determine double point double tangents drawn dx dy dy dz elimination ellipse elliptic functions envelope epitrochoid equa equal roots equation evolute figure fixed points foci fourth degree function geometrical given curve given point Hence hyperbola imaginary last Article line at infinity line joining line meets locus meets the curve method multiple point nth degree obtained origin oval parabola pass perpendicular Plücker points at infinity points of contact points of inflexion polar conic polar curve pole radius vector ratio right line substituting theorem third degree tion touch the curve transformation triangle U₁ values variable
Δημοφιλή αποσπάσματα
Σελίδα 5 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Σελίδα 122 - The locus of a point whose distances from two fixed points are in a constant ratio (not one of equality) is a circle.
Σελίδα 269 - Archimedes depend on the same formulse as in the case of the parabola.* The following is a method by which rectification may in general be reduced to quadratures, and by which, in particular, Van Huraet rectified the semicubical parabola, the first curve rectified. (Lardner's Algebraic Geometry, p. 464.) Produce each ordinate until the whole length be in a constant ratio to the corresponding normal divided by the old ordinate, and the locus of the extremity of the produced ordinate is a curve whose...
Σελίδα 206 - This curve is generated by the motion of a point on the circumference of a circle which rolls along a right fcline.
Σελίδα 225 - Cum autem ob proprietatem tam singularem tamque admirabilem mire mihi placeat Spira haec mirabilis, sic ut ejus contemplatione satiari vix queam; cogitavi, illam ad varias res symbolice repraesentandas non inconcinne adhiberi posse. Quoniam enim semper sibi similem...
Σελίδα 223 - ... 0, &c. The same right line then meets the curve in an infinity of points, and the curve is transcendental. Let us first take the spiral of Archimedes, which is the path described by a point receding uniformly from the origin, while the radius vector on which it travels...
Σελίδα 118 - ... refraction of a circle. Let a circle be described through A, the radiant point, and R, the point of incidence, to touch OR ; then the point B is given, since OA . OB = OR1.
Σελίδα 247 - Ex. 4. The three sides of a triangle pass through fixed points, and two...
Σελίδα 204 - This lemniscata is the locus of the foot of the perpendicular from the centre on the tangent to an equilateral hyperbola.
Σελίδα 225 - ... non inconcinne adhiberi posse. Quoniam enim semper sibi similem et eandem spiram gignit, utcunque volvatur...