Vector Analysis: A Text-book for the Use of Students of Mathematics and Physics ; Founded Upon the Lectures of J. Willard GibbsC. Scribner's sons, 1901 - 436 sivua |
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a b c a₁ a₂ angle angular velocity antecedents axes axis b₁ b₂ c₁ c₂ center of gravity collinear components consequently constant coördinates coplanar cosine curl curve definition denote derivative differentiators direction divergence dyadic dyads expressed in terms force formulæ function of position geometric given Hence hodograph line integral linear multiplied negative obtained operator origin parallel parallelogram perpendicular plane position in space potential radius vector ratio reciprocal system resultant rigid body rotation scalar coefficients scalar function scalar product scalar triple product sides sphere surface integral tetrahedron theorem three non-coplanar vectors three vectors tion triangle unit vectors unknown vector V₁ v₂ vanishes vector drawn vector equation vector function vector product versor zero д х ду дх
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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 59 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
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.
Sivu 39 - In finding the center of gravity of two systems of masses each system may be replaced by a single mass equal in magnitude to the sum of the masses in the system and situated at the center of gravity of the system.