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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Yale University Press, 1901 - 436 pàgines
 

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Pàgina 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...
Pàgina 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...
Pàgina 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...
Pàgina 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.
Pàgina 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'.
Pàgina 109 - The scalar product of two vectors is equal to the product of their lengths multiplied by the cosine of the angle between them.
Pàgina 55 - staging." scalar product. The scalar product of two vectors is the scalar quantity obtained by multiplying the product of the magnitudes of the two vectors by the cosine of the angle between them. The scalar product of two vectors A and B may be indicated by means of a dot, AB.
Pàgina 353 - ... 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...
Pàgina 255 - 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.
Pàgina 66 - Calculating the values of sin x, cos x, & and log x using series. The fundamental formulae for the sine and cosine of the sum or difference of two angles, that is sin (A + B) = sin A cos B + cos A sin B. -, and the others. Formulae derived from the above, such as those for the sum and difference of two sines or cosines, and those which connect an angle and the double angle. The sine rule, or — — - = - in triangles. Also the rule sin B b c* = a?

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