Vectors and Rotors: With ApplicationsE. Arnold, 1903 - 204 σελίδες |
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Αποτελέσματα 1 - 5 από τα 25.
Σελίδα v
... Parallelogram of Forces . On giving the directed quantity , the Vector , a geometrical definition , instead of treating it as merely representing a Force and deriving its properties from those found to hold for Forces , it becomes a.
... Parallelogram of Forces . On giving the directed quantity , the Vector , a geometrical definition , instead of treating it as merely representing a Force and deriving its properties from those found to hold for Forces , it becomes a.
Σελίδα xi
... equation 135. Complete Quadrilateral . 137. Mechanisms for drawing a straight line 138. The Peaucellier Cell 102 103 104 104 105 105 105 106 106 107 • 108 109 § 139. The Hart Contra - parallelogram 140. The Circle CONTENTS xi.
... equation 135. Complete Quadrilateral . 137. Mechanisms for drawing a straight line 138. The Peaucellier Cell 102 103 104 104 105 105 105 106 106 107 • 108 109 § 139. The Hart Contra - parallelogram 140. The Circle CONTENTS xi.
Σελίδα xii
... parallelogram 140. The Circle equation 141. Some Properties of the circle 142. Area of triangle in coordinates 143. Angle between two straight lines 144. Angle between two lines in coordinates 145. ( a , b1 + a2b2 + a3b3 ) 2 + ( a2b3 ...
... parallelogram 140. The Circle equation 141. Some Properties of the circle 142. Area of triangle in coordinates 143. Angle between two straight lines 144. Angle between two lines in coordinates 145. ( a , b1 + a2b2 + a3b3 ) 2 + ( a2b3 ...
Σελίδα 24
... of vectors . ( i ) If the diagonals of a quadrilateral bisect one another , the figure is a parallelogram . Let AB and CD be the bisecting diagonals and the point of bisection . Let then OA = a and OC = y , 24 VECTORS AND ROTORS.
... of vectors . ( i ) If the diagonals of a quadrilateral bisect one another , the figure is a parallelogram . Let AB and CD be the bisecting diagonals and the point of bisection . Let then OA = a and OC = y , 24 VECTORS AND ROTORS.
Σελίδα 25
... parallelogram bisect one another . Let a and ẞ denote two adjacent sides , then the diagonal concurrent with these is a + ß . But the mid - point of the other diagonal is ( see § 44 ) and the result follows at once . a + B 2 ( iii ) The ...
... parallelogram bisect one another . Let a and ẞ denote two adjacent sides , then the diagonal concurrent with these is a + ß . But the mid - point of the other diagonal is ( see § 44 ) and the result follows at once . a + B 2 ( iii ) The ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A₁ ABCD Algebra angle axis B₁ bars base beam bending bending moment bisect C₁ called centre collinear Commutative Law components compression coordinates coplanar couple definite denote determined diagonals direction and sense distance divide draw drawn equal equation equilibrium figure find the mass-centre forces acting frame friction given points given rotor Hence the mass-centre horizontal length line joining line parallel link-polygon load m₁ magnitude mass mid-point momental area move multiplying negative number of vectors origin orts parallel rotors parallelogram parallelopiped perpendicular plane pole polygon position vector projection quadrilateral reaction rectangle represent resultant rigid body scalar product shearing force shew shewn sides straight line stress diagram string suppose symmetry system of rotors tension tetrahedron theorem three vectors triangle vanishes vector product vector-polygon vertex vertices weight
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 112 - ... is equal to the rectangle contained by the segments of the other.
Σελίδα 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...
Σελίδα 29 - The parallelograms about the diameter of any parallelogram are similar to the whole, and to one another. Let...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...