Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 pages |
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Page 2
... diameter 1 Surface of sphere to diameter 1 Area of circle to radius 1 π = 7853986 ; log π = 1.8950899 ; - 4 Unit of Circular Measure Do. = do . = = 3.1415926 ; log 0.4971499 log 1 - = 1.5028501 . π * 5235988 ; log = 1.7189986 57 ...
... diameter 1 Surface of sphere to diameter 1 Area of circle to radius 1 π = 7853986 ; log π = 1.8950899 ; - 4 Unit of Circular Measure Do. = do . = = 3.1415926 ; log 0.4971499 log 1 - = 1.5028501 . π * 5235988 ; log = 1.7189986 57 ...
Page 57
... diameter . By how much did he exceed or fall short of his allowance , actual contents being taken for the cylinder , and fractions of a cubic foot being omitted in the result ? 14. The chord of an arc is 8 feet and the height of the arc ...
... diameter . By how much did he exceed or fall short of his allowance , actual contents being taken for the cylinder , and fractions of a cubic foot being omitted in the result ? 14. The chord of an arc is 8 feet and the height of the arc ...
Page 59
... diameter is 15 yards , is covered with carpet two feet wide ; what will it cost at 3s . 6d . per yard ( allowing 11-6425 square yards for waste ) . Given π = = 3.1416 . 16. Show how to reduce an irregular polygon of five sides to a ...
... diameter is 15 yards , is covered with carpet two feet wide ; what will it cost at 3s . 6d . per yard ( allowing 11-6425 square yards for waste ) . Given π = = 3.1416 . 16. Show how to reduce an irregular polygon of five sides to a ...
Page 60
... 3 ; what will the fencing cost at 3s . 6d . per yard ? 11. What is the weight of a hollow sphere of metal , whose inside diameter is 18 inches , and the thickness 2 inches ? Given T ounces . 22 יד and a cubic foot 60 SANDHURST AND.
... 3 ; what will the fencing cost at 3s . 6d . per yard ? 11. What is the weight of a hollow sphere of metal , whose inside diameter is 18 inches , and the thickness 2 inches ? Given T ounces . 22 יד and a cubic foot 60 SANDHURST AND.
Page 65
... diameter is that of 3 · 1416 to unity , find the volume and the surface of a cylinder , the radius of which is 4 feet and the height 100 feet . Supposing that a wedge is cut out of this cylinder by two planes through its axis inclined ...
... diameter is that of 3 · 1416 to unity , find the volume and the surface of a cylinder , the radius of which is 4 feet and the height 100 feet . Supposing that a wedge is cut out of this cylinder by two planes through its axis inclined ...
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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.