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 12
... distances in an ellipse inclined to each other at the angle a , find the greatest and least values of the area of the triangle PSQ . 9. Find expressions for the perpendicular on the tangent and for the radius of curvature in polar ...
... distances in an ellipse inclined to each other at the angle a , find the greatest and least values of the area of the triangle PSQ . 9. Find expressions for the perpendicular on the tangent and for the radius of curvature in polar ...
Σελίδα 13
... the other sides in D and E , DE and BC are equal to ( b ) and ( a ) respectively ; if ( h ) be the line drawn from A bisecting BC , prove that the distance of the centre of gravity of FURTHER EXAMINATION . STATICS . 13.
... the other sides in D and E , DE and BC are equal to ( b ) and ( a ) respectively ; if ( h ) be the line drawn from A bisecting BC , prove that the distance of the centre of gravity of FURTHER EXAMINATION . STATICS . 13.
Σελίδα 14
Woolwich roy. military acad. prove that the distance of the centre of gravity of the trapezoid BCED from A is 2 3 h . a2 + ab + b2 a ( a + b ) 5. Describe any arrangement of three equal moveable pulleys by which a mechanical advantage is ...
Woolwich roy. military acad. prove that the distance of the centre of gravity of the trapezoid BCED from A is 2 3 h . a2 + ab + b2 a ( a + b ) 5. Describe any arrangement of three equal moveable pulleys by which a mechanical advantage is ...
Σελίδα 15
... distance a , and b be the range when fired at an elevation of 45 ° , prove that is equal to α 26 approximately . 5. Find the acceleration of a particle sliding down a smooth inclined plane . What is the vertical component of this ...
... distance a , and b be the range when fired at an elevation of 45 ° , prove that is equal to α 26 approximately . 5. Find the acceleration of a particle sliding down a smooth inclined plane . What is the vertical component of this ...
Σελίδα 16
... distance from the vertex . 13. If the particle in the last question start from rest from an extremity of the base of the cycloid , and if T be the time in which it reaches the vertex , prove that at any time t , the height of the ...
... distance from the vertex . 13. If the particle in the last question start from rest from an extremity of the base of the cycloid , and if T be the time in which it reaches the vertex , prove that at any time t , the height of the ...
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 moving 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...