Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
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Σελίδα 127
... direction at right angles to the line joining one end to the base of a tower standing on the plane . The angles of elevation of the tower from the two ends of the measured line are 30 ° and 18 ° respectively . Find the height of the ...
... direction at right angles to the line joining one end to the base of a tower standing on the plane . The angles of elevation of the tower from the two ends of the measured line are 30 ° and 18 ° respectively . Find the height of the ...
Σελίδα 145
... direction north - west for four miles , and observes A to bear due east and B north east of his new position . Find the distance from A to B.- П 12. If π be the ratio of the circumference of a circle to its diameter , point out any ...
... direction north - west for four miles , and observes A to bear due east and B north east of his new position . Find the distance from A to B.- П 12. If π be the ratio of the circumference of a circle to its diameter , point out any ...
Σελίδα 185
... in the line AB , find two other points C , D , such that a line OP given in direction shall bisect the angle CPD , and the segments CO , OD , shall bear a given ratio to each other . C. ARITHMETIC . 1. What would be the cost of PAPERS .
... in the line AB , find two other points C , D , such that a line OP given in direction shall bisect the angle CPD , and the segments CO , OD , shall bear a given ratio to each other . C. ARITHMETIC . 1. What would be the cost of PAPERS .
Σελίδα 253
... direction at right angles to the line joining their bases he observes the elevations of the two to be 45 ° and 30 ° . Find their height and the distance between them . 25. A , B , C are three points at known distances from one another ...
... direction at right angles to the line joining their bases he observes the elevations of the two to be 45 ° and 30 ° . Find their height and the distance between them . 25. A , B , C are three points at known distances from one another ...
Σελίδα 255
... direction relatively to AP must it sail to be seen from P in the line PB after 40 minutes ? 44. The plane of the side of a hill running E. and W. is inclined to the horizon at an angle a . It is required to con- struct a straight road ...
... direction relatively to AP must it sail to be seen from P in the line PB after 40 minutes ? 44. The plane of the side of a hill running E. and W. is inclined to the horizon at an angle a . It is required to con- struct a straight road ...
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Arithmetic axis ball base bisected body cent centre of gravity circle coefficient of friction compound interest cone cost crown 8vo cube cubic foot curve Define determine diameter Divide dwts ellipse English equal equilibrium expression feet Find the area Find the centre Find the distance Find the equation Find the number Find the sum Find the value fluid forces acting formula fraction geometrical Grammar horizontal plane hyperbola inches inclined plane inscribed Integrate isosceles latus rectum least common multiple length logarithms miles Multiply parabola parallel particle perpendicular pressure Prove pulleys radius ratio rectangle rectangular Reduce right angles sides simple interest sin² sine spherical triangle square root straight line string subtended Subtract surface tangent theorem tons tower triangle ABC velocity vertical vulgar fraction weight yards
Δημοφιλή αποσπάσματα
Σελίδα 123 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 10 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Σελίδα 184 - If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other.
Σελίδα 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 184 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third (20.
Σελίδα 184 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 163 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 184 - In right angled triangles the square on the side subtending the right angle is equal to the (sum of the) squares on the sides containing the right angle.
Σελίδα 154 - If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F, D : As AE is to EB, so is CF to FD.