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a x b angle angular velocity antecedents applied axes axis bivector closed curve collinear components conjugate consequents constant coplanar curl definition denoted differential displacement distributive law divergence dyadic dyads ellipse ellipsoid equation expressed in terms factor finite force formulae function of position given Hence hodograph idemfactor infinitesimal Laplacian line integral linear vector function magnetic multiplied negative normal obtained operator origin osculating plane parallel perpendicular planar plane point xv yv position in space potential quadric radius vector ratio reciprocal system reduced region rotation scalar function scalar product scalar triple product side sphere surface integral taken tangent terminus Theorem three non-coplanar vectors three vectors tion triangle unit vector vanishes variables vector analysis vector drawn vector product versor volume integral
Sivu 53 - ... and surfaces of the second and third orders are also there founded upon the composition of vectors. EXAMPLES TO CHAPTER I. 1. The lines which join, towards the same parts, the extremities of two equal and parallel lines are themselves equal and parallel. (Euclid, I. xxxiii.) 2. Find the vector of the middle point of the line which joins the middle points of the diagonals of any quadrilateral, plane or gauche, the vectors of the corners being given ; and so prove that this point is the mean point...
Sivu 256 - The surface integral of a vector over a closed surface is equal to the volume integral of the divergence of the vector throughout the enclosed volume.
Sivu 109 - B is defined as the product of the magnitudes of A and B and the sine of the angle between them. The direction of the vector...
Sivu 60 - The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its four Dem.— Let ABCD be the a.
Sivu iii - University, a series of volumes has been prepared by a number of the Professors and Instructors, to be issued in connection with the Bicentennial Anniversary, as a partial indication of the character of the studies in which the University teachers are engaged.
Sivu iii - Sons, of New York. With the approval of the President and Fellows of Yale University, the series has been prepared by a number of the Professors and Instructors, to be issued in connection with the Bicentennial Anniversary, as a partial indication of the studies in which the University teachers are engaged. The list of volumes includes some of a special and technical nature, others of a more general character.
Sivu 106 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. Let the Js be AH, BP, and CK. Through A, B, C suppose B'C', A'C', A'B', drawn II to BC, AC, AB, respectively. Then AH is _L to B'C'. (Why ?) Now ABCB' and A CBC' are EJ (why ?) , and AB' = BC, and AC' = BC. (Why ?) That is, A is the middle point of B'C'.
Sivu 109 - The scalar product of two vectors is equal to the product of their lengths multiplied by the cosine of the angle between them.