Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 pages |
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Page 72
... I to pay for another cubical block of the same marble , of which the side is equal in length to the diagonal of the first block ? 9. Determine to the nearest hundredth of an inch the radius ( 1 ) of a sphere whose volume is 72 SANDHURST ...
... I to pay for another cubical block of the same marble , of which the side is equal in length to the diagonal of the first block ? 9. Determine to the nearest hundredth of an inch the radius ( 1 ) of a sphere whose volume is 72 SANDHURST ...
Page 79
... Determine its three angles . 13. A , B , C , are three points in a straight line on a level piece of ground . A vertical pole is erected at C ; the angle of elevation of its top , as observed from A , is 5 ° 30 ' ; and , as observed ...
... Determine its three angles . 13. A , B , C , are three points in a straight line on a level piece of ground . A vertical pole is erected at C ; the angle of elevation of its top , as observed from A , is 5 ° 30 ' ; and , as observed ...
Page 95
... determining- ( 1 ) The remaining angles of the triangle . ( 2 ) The area of the triangle . 14. In the triangle in which each angle at the base is double the third angle , given the base 200 ft . find the area . 15. The angle of ...
... determining- ( 1 ) The remaining angles of the triangle . ( 2 ) The area of the triangle . 14. In the triangle in which each angle at the base is double the third angle , given the base 200 ft . find the area . 15. The angle of ...
Page 102
... determined ? 10. Compute by logarithms the fraction . five places of decimals . 3 0073288 05482637 to 11. What is the compound interest to the nearest penny on £ 83 14s . 7d . in 7 years at the rate of 3 per cent . per annum , interest ...
... determined ? 10. Compute by logarithms the fraction . five places of decimals . 3 0073288 05482637 to 11. What is the compound interest to the nearest penny on £ 83 14s . 7d . in 7 years at the rate of 3 per cent . per annum , interest ...
Page 108
... Determine the values of m which make the expres- sion 3mx2 + ( 6m - 12 ) x + 8 a complete square . 10. If a с e b = d f prove that each of these fractions a + c + e = a2 + c2 + e2 b2 + d2 + f2 3 ace = bdf b + d + f 11. Show how to ...
... Determine the values of m which make the expres- sion 3mx2 + ( 6m - 12 ) x + 8 a complete square . 10. If a с e b = d f prove that each of these fractions a + c + e = a2 + c2 + e2 b2 + d2 + f2 3 ace = bdf b + d + f 11. Show how to ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.