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acceleration angular velocity applied arbitrary axis called Cartesian circuit closed surface coefficients components considered const constant vector contour curl F curve defined definition denote density differential directional derivative distribution divergence theorem dt dt dx dy dz electrical ellipsoid equal evidently expression F-dr field fluid flux formula function F Gauss's Theorem gives grad Green's Theorem heat hence hodograph i j k Laplace's equation line-integral lines of force magnetic mass mathematical multiplied normal notation obtain operator origin osculating plane parallel particle path perpendicular plane positive quantity Quaternions radius vector represented respectively result rigid body rotation scalar function scalar point-function scalar product Show solenoidal solid angle sphere surface integral symbols taken tangent Taylor's Theorem term three vectors tion unit charge unit vector vanishes Vector Analysis vector function vector point-function vector product volume write written zero
Page 22 - A person travelling eastward at the rate of 4 miles per hour, finds that the wind seems to blow directly from the north; on doubling his speed it appears to come from the north-east; find the direction of the wind and its velocity.
Page viii - Poinsot has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligible propositions supersede equations".
Page 24 - ... intersection of corresponding sides lie on a line, then the lines joining the corresponding vertices pass through a common point and conversely. 5. Given a quadrilateral in space. Find the middle point of the line which joins the middle points of the diagonals. Find the middle point of the line which joins the middle points of two opposite sides. Show that these two points are the same and coincide with the center of gravity of a system of equal masses placed at the vertices of the quadrilateral....
Page 44 - The squares of the sides of any quadrilateral exceed the squares of the diagonals by four times the square of the line which joins the middle points of the diagonals.
Page 44 - P meet in a point and are directed along the diagonals of the three faces of a cube meeting at the point. Determine the magnitude of their resultant.
Page 113 - A through a closed surface S is equal to the volume integral of the divergence of the vector field over the region enclosed by S.
Page 46 - The triangle formed by joining the middle point of one of the nonparallel sides of a trapezoid to the extremities of the opposite side, is equivalent to one-half the trapezoid.
Page iii - Vector analysis; an introduction to vector-methods and their various applications to physics and mathematics. Ed.2. 1911. Wiley. "Bibliography,