Woolwich mathematical papers [aftwerw.] Mathematical papers for admission into the Royal military academy (and the Royal military college, and papers in elementary engineering for naval cadetships). |
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Σελίδα 13
... smooth wall is supported by a string passing over a smooth peg driven into the wall ; the ends of the string are fastened to two points in the upper rim of the frame which are equidistant from the centre of the rim , and the angle at ...
... smooth wall is supported by a string passing over a smooth peg driven into the wall ; the ends of the string are fastened to two points in the upper rim of the frame which are equidistant from the centre of the rim , and the angle at ...
Σελίδα 15
... smooth inclined plane . What is the vertical component of this acceleration ? If two particles P and Q start simultaneously from A , one sliding down the plane AB at the angle a to the horizon , and the other falling freely , prove that ...
... smooth inclined plane . What is the vertical component of this acceleration ? If two particles P and Q start simultaneously from A , one sliding down the plane AB at the angle a to the horizon , and the other falling freely , prove that ...
Σελίδα 16
... smooth horizontal plane ; if e be the coefficient of elasticity prove that after the impact A's velocity will be to B's velocity as 1 + e : 1 - e . 9. If , after the impact described in the foregoing question , A moves on and impinges ...
... smooth horizontal plane ; if e be the coefficient of elasticity prove that after the impact A's velocity will be to B's velocity as 1 + e : 1 - e . 9. If , after the impact described in the foregoing question , A moves on and impinges ...
Σελίδα 13
... smooth hemispherical bowl of which the axis is vertical and the radius √3 inches long . Shew that one fourth of the rod will project over the rim of the bowl . 3. Shew that if a body be suspended by a single point , its centre of ...
... smooth hemispherical bowl of which the axis is vertical and the radius √3 inches long . Shew that one fourth of the rod will project over the rim of the bowl . 3. Shew that if a body be suspended by a single point , its centre of ...
Σελίδα 14
... smooth plane inclined to the horizon at an angle cos - 1 . The rope may be supposed to be always parallel to the surface of the plane . Find also the force applied to the end of the lever , and the distance through which its point of ...
... smooth plane inclined to the horizon at an angle cos - 1 . The rope may be supposed to be always parallel to the surface of the plane . Find also the force applied to the end of the lever , and the distance through which its point of ...
Συχνά εμφανιζόμενοι όροι και φράσεις
accuracy in numerical accuracy in results ALGEBRA ARITHMETIC asymptotes attached to accuracy axis ball Binomial Theorem bisected body cent centre of gravity chord circular measure circumference Common Logarithms cosine cubic curve decimal Define described diameter differential coefficient Divide ellipse equal angles equilateral equilibrium expression Find the length find the number Find the value forces acting fraction Full marks geometrical given point given straight line Harmonic means horizontal hyperbola inches inclined plane inscribed intersect latus rectum Least Common Multiple logarithms miles an hour N.B.-Great importance number of forces opposite parabola parallel parallelogram parallelogram of forces particle perpendicular positive projectile prove pulleys PURE MATHEMATICS radius ratio rectangle contained rectilineal figure respectively rhombus right angles segment Shew sides sine Solve the equations string subtended tangent triangle ABC TRIGONOMETRY uniform vertical weight yards
Δημοφιλή αποσπάσματα
Σελίδα 2 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 1 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 2 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 1 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 1 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 7 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Σελίδα 1 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 2 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. Let the straight line AB be divided into any two parts in the point C. Then the squares on AB, BC shall be equal to twice the rectangle AB, BC} together with the square on AC.
Σελίδα 2 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 2 - If the angle of a triangle be bisected by a straight line which also cuts the base ; the segments of the base shall have the...