A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on Conic SectionsHodges and Smith, 1852 - 316 pagine |
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... George Salmon Visualizzazione completa - 1852 |
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... George Salmon Visualizzazione completa - 1852 |
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... George Salmon Visualizzazione completa - 1852 |
Parole e frasi comuni
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
Brani popolari
Pagina 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.
Pagina 122 - The locus of a point whose distances from two fixed points are in a constant ratio (not one of equality) is a circle.
Pagina 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...
Pagina 206 - This curve is generated by the motion of a point on the circumference of a circle which rolls along a right fcline.
Pagina 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...
Pagina 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...
Pagina 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.
Pagina 247 - Ex. 4. The three sides of a triangle pass through fixed points, and two...
Pagina 204 - This lemniscata is the locus of the foot of the perpendicular from the centre on the tangent to an equilateral hyperbola.
Pagina 225 - ... non inconcinne adhiberi posse. Quoniam enim semper sibi similem et eandem spiram gignit, utcunque volvatur...