# Vectors and Rotors: With Applications

E. Arnold, 1903 - Electronic book - 204 pages

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Page 21 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 29 - If the exterior angle of a triangle be bisected by a straight line which also cuts the base produced, the segments between the bisecting line and the extremities of the base have the same ratio which the other sides of the triangle have to one another...
Page 8 - If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.
Page 112 - ... is equal to the rectangle contained by the segments of the other.
Page 56 - ... are 8 in. Find the surface and volume of the greatest possible cylinder, of the same axis, that can be cut from the prism. Ex. 1634. The base of a right pyramid is a regular hexagon whose sides are 20 in., and the lateral faces are inclined to the base at an angle of 60°. Find the volume. Ex. 1635. Lines joining the mid.points of opposite edges of a tetrahedron meet in a point and bisect each other. Ex. 1636. The altitude of a cone of revolution is 27 in., and its curved surface is 7 times the...
Page 29 - The parallelograms about the diameter of any parallelogram are similar to the whole, and to one another. Let...
Page 116 - Show that the work done by a force in producing a given displacement may be measured (1) by the product of the displacement and the component of the force in the direction of the displacement...
Page 181 - A, the algebraic sum of the moments of all the forces to the left of the section is zero, since there are no forces to the left.
Page 3 - In vector geometry, a vector quantity is represented diagrammatically by a line called a vector. The length of the line represents, to scale, the magnitude of the quantity, and its direction represents the direction in which the quantity acts.
Page 29 - L' and L" cut at right angles. (8) Prove that the three bisectors of the angles of a triangle meet in a point. (9) Show that the equation of a straight line in polar co-ordinates is of the form r = p cosec (в — ф). What is the meaning of "p...