Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
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Σελίδα 77
... vertical angle , the greatest is that in which the two sides are equal . 3. Divide a given straight line so that the rectangle contained by its segments shall be equal to a given square , not greater than the square on half the line . 4 ...
... vertical angle , the greatest is that in which the two sides are equal . 3. Divide a given straight line so that the rectangle contained by its segments shall be equal to a given square , not greater than the square on half the line . 4 ...
Σελίδα 79
... vertical pole is erected at C ; the angle of elevation of its top , as observed from A , is 5 ° 30 ' ; and , as observed from B , is 10 ° 45 ' ; the distance from A to B being 100 yards . Find the distance BC , and the height of the ...
... vertical pole is erected at C ; the angle of elevation of its top , as observed from A , is 5 ° 30 ' ; and , as observed from B , is 10 ° 45 ' ; the distance from A to B being 100 yards . Find the distance BC , and the height of the ...
Σελίδα 122
... vertical angle of a triangle be con- stant , and the base given in magnitude and position , the bisecting line passes always through a fixed point . 3. Multiply 5 + 3x3 - x2 + 1 by x2 - 8x + 4 , and divide x6 - 2x3 + 1 by x2 - 2x + 1 ...
... vertical angle of a triangle be con- stant , and the base given in magnitude and position , the bisecting line passes always through a fixed point . 3. Multiply 5 + 3x3 - x2 + 1 by x2 - 8x + 4 , and divide x6 - 2x3 + 1 by x2 - 2x + 1 ...
Σελίδα 133
... vertically and uniformly for 20 minutes , he observes the angle of depression of the same object to be 55 ° 40 ' find the rate of ascent of the balloon in miles per hour . : 11. A tower which stands on a horizontal plane is 200 feet ...
... vertically and uniformly for 20 minutes , he observes the angle of depression of the same object to be 55 ° 40 ' find the rate of ascent of the balloon in miles per hour . : 11. A tower which stands on a horizontal plane is 200 feet ...
Σελίδα 167
... vertical depth descended in the quarter of a mile . 9. Prove the following : — x2 x3 ( 1 ) e2 = 1 + 1 + 1.2 + 1.2.3 ( 2 ) log . ( 1 + x ) = x- + ; x2 , x3 + 2 3 and explain the principle and the formation of the tables of proportional ...
... vertical depth descended in the quarter of a mile . 9. Prove the following : — x2 x3 ( 1 ) e2 = 1 + 1 + 1.2 + 1.2.3 ( 2 ) log . ( 1 + x ) = x- + ; x2 , x3 + 2 3 and explain the principle and the formation of the tables of proportional ...
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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 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.