## 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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a b c acceleration angle applied axes axis becomes body bounding called closed coefficients components condition consequents Consider constant curl curve definition denoted derivative determined differential direction displacement divergence drawn dyadic dyads equal equation Example exists expressed factor finite fixed follows force formula given gives Hence integral known length limit linear magnitude manner masses means method multiplied necessary negative normal obtained operator origin parallel particle pass perpendicular plane positive potential proved quantity radius vector ratio reciprocal reduced regarded region relation represents respectively result rotation scalar function seen side space sphere surface surface integral taken tangent theorem third tion triangle triple unit vector vanishes variable vector function vector product velocity volume zero

### Popular passages

Page 79 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 113 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...

Page 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...

Page 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.

Page 33 - If a line be drawn parallel to the base of a triangle, it will divide, the.

Page 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'.

Page 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.

Page 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...

Page 347 - ... out the economy of using one half-prism attached to the collimator with one face perpendicular to the axis, and another similar half-prism attached in a similar way to the telescope. A beam of light can thus be used larger, in proportion to the size of the face of the prism, than when a single prism with an angle equal to the sum of the angles of the half-prisms is used. Thollon has given a mathematical investigation to...

Page 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.