## Normals Sentence Examples

- Properties of the limagon may be deduced from its mechanical construction; thus the length of a focal chord is constant and the
**normals**at the extremities of a focal chord intersect on a fixed circle. - Apollonius' genius takes its highest flight in Book v., where he treats of
**normals**as minimum and maximum straight lines drawn from given points to the curve (independently of tangent properties), discusses how many**normals**can be drawn from particular points, finds their feet by construction, and gives propositions determining the centre of curvature at any point and leading at once to the Cartesian equation of the evolute of any conic. - Now, if one of these latter children of the second brother marries a cousin - a child of the first brother, - their offspring, if large enough, will consist of some pure
**normals**N, impure**normals**N(A), and of albinoes A. - Leonhard Euler, in his paper on curvature in the Berlin Memoirs for 1760, had considered, not the
**normals**of the surface, but the**normals**of the plane sections through a particular normal, so that the question of the intersection of successive**normals**of the surface had never presented itself to him. - .and A, B, C, of the two funiculars draw
**normals**to the plane of the diagram, to meet w and w respectively. - Since the quadratic moments with respect to w and of are equal, it follows that w is a plane 01 stationary quadratic moment at P, and therefore a principal plane of inertia at P. In other words, the principal axes 01 inertia at P are the
**normals**to the three confocals of the systen (3,~) which pass through P. Moreover if x, y, z be the co-ordinates of P, (33) is an equation to find the corresponding values of 0; and if Of, 02, 03 be the roots we find Oi+O2+81r1a2$-7, (35) - Thus, in a plane path, let P,Q be two consecutive positions, corresponding to the C times t, t + t; and let the
**normals**at - v+~v P, Q meet in C, making an angle ~ Let v (=s) be the velocity at P, V v+v that at Q. - In mathematics, the "caustic surfaces" of a given surface are the envelopes of the
**normals**to the surface, or the loci of its centres of principal curvature. - Secondary caustics are orthotomic curves having the reflected or refracted rays as
**normals**, and consequently the proper caustic curve, being the envelope of the**normals**, is their evolute. - Many well-known derivative curves present themselves in this manner; thus the variable curve may be the normal (or line at right angles to the tangent) at any point of the given curve; the intersection of the consecutive
**normals**is the centre of curvature; and we have the evolute as at once the locus of the centre of curvature and the envelope of the normal. - It may be added that the given curve is one of a series of curves, each cutting the several
**normals**at right angles.