Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
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Σελίδα 117
... horizontal plane are each equal to tan - 1 2. Prove that the angle ACO is equal to π - tan - 1 24 . Hence , by the aid of a tabie of logarithms , find the distance OC . LXX . 1. If a be a root of the equation f ( x ) = 0 prove that f ...
... horizontal plane are each equal to tan - 1 2. Prove that the angle ACO is equal to π - tan - 1 24 . Hence , by the aid of a tabie of logarithms , find the distance OC . LXX . 1. If a be a root of the equation f ( x ) = 0 prove that f ...
Σελίδα 127
... horizontal plane in a 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 ...
... horizontal plane in a 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 ...
Σελίδα 133
... horizontal plane is 200 feet high , and there is a small loophole in the tower at a certain height above the ground ; an observer is at a horizontal distance from the tower of 300 feet , but stands on a mound so that his eye is 12 feet ...
... horizontal plane is 200 feet high , and there is a small loophole in the tower at a certain height above the ground ; an observer is at a horizontal distance from the tower of 300 feet , but stands on a mound so that his eye is 12 feet ...
Σελίδα 249
... horizontal plane as its base , and is 30 ° from a point 30 ft . directly above the former point . Find the height and distance of the steeple . 3. An object C being inaccessible from B , a line BA , 408 yards in length , is measured ...
... horizontal plane as its base , and is 30 ° from a point 30 ft . directly above the former point . Find the height and distance of the steeple . 3. An object C being inaccessible from B , a line BA , 408 yards in length , is measured ...
Σελίδα 250
... horizontal plane at a distance of 350 yards from the point where the balloon left the earth ; after a time he observes the angle of elevation of the balloon to be 55 ° 17 ' , and after an interval of three minutes he observes the angle ...
... horizontal plane at a distance of 350 yards from the point where the balloon left the earth ; after a time he observes the angle of elevation of the balloon to be 55 ° 17 ' , and after an interval of three minutes he observes the angle ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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 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.