Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
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Αποτελέσματα 1 - 5 από τα 46.
Σελίδα 45
... ratios : : 5. How many yards of cloth , at 9s . per yard , must be given in exchange for 3 cwt . 3 qrs . 12 lbs . of sugar at 7d . per pound ? 6. If the expenses of a family of 10 persons for 3 weeks be £ 22 1s . , what will be the ...
... ratios : : 5. How many yards of cloth , at 9s . per yard , must be given in exchange for 3 cwt . 3 qrs . 12 lbs . of sugar at 7d . per pound ? 6. If the expenses of a family of 10 persons for 3 weeks be £ 22 1s . , what will be the ...
Σελίδα 58
... ratio of 1 : 2 , show that one of them satisfies the equation 6pa2 + ( 5p2 - 6q ) x + p ( p2 - 2q ) = 0 , and find the other root of this equation . X y 10. If == , prove that each of these fractions α b = _x + y + z ̧ a + b + c = x2 + ...
... ratio of 1 : 2 , show that one of them satisfies the equation 6pa2 + ( 5p2 - 6q ) x + p ( p2 - 2q ) = 0 , and find the other root of this equation . X y 10. If == , prove that each of these fractions α b = _x + y + z ̧ a + b + c = x2 + ...
Σελίδα 65
... ratio of the perimeter of a circle to its 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 ...
... ratio of the perimeter of a circle to its 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 ...
Σελίδα 74
... ratio to PB . Prove that P lies on a circle , and find the centre of that circle . 5. Define a degree , a grade ... ratios in terms of the sine . If the cosecant be twice the sine , find the angle . 7. Prove that cos ( A + B ) = cos A ...
... ratio to PB . Prove that P lies on a circle , and find the centre of that circle . 5. Define a degree , a grade ... ratios in terms of the sine . If the cosecant be twice the sine , find the angle . 7. Prove that cos ( A + B ) = cos A ...
Σελίδα 76
... ratio , and prove that similar triangles are to one another in the duplicate ratio of their homologous sides . On the side AB of a triangle ABC , AD is taken equal to one third of AB ; and on AC , AE is taken equal to one third of AC ...
... ratio , and prove that similar triangles are to one another in the duplicate ratio of their homologous sides . On the side AB of a triangle ABC , AD is taken equal to one third of AB ; and on AC , AE is taken equal to one third of AC ...
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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.