Vector Analysis: A Text-book for the Use of Students of Mathematics and Physics, Founded Upon the Lectures of J. Willard Gibbs ...

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C. Scribner's Sons, 1901 - 436 من الصفحات
 

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الصفحة 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.
الصفحة 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...
الصفحة 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.
الصفحة 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.
الصفحة 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.
الصفحة 98 - Let a (Fig. 25) be a vector drawn along the axis of rotation in that direction in which a right-handed screw would advance if turned in the direction in which the body is rotating.
الصفحة 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'.
الصفحة 109 - The scalar product of two vectors is equal to the product of their lengths multiplied by the cosine of the angle between them.
الصفحة 92 - The moment of a force f about the point 0 is equal to the product of the force by the perpendicular distance from 0 to the line of action of the force.
الصفحة 249 - 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.

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