Woolwich Mathematical Papers for Admission Into the Royal Military Academy for the Years, 1880-1888E. J. Brooksmith Macmillan, 1889 |
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Σελίδα 2
... inscribed in a circle must also be equiangular . IO . If a straight line be drawn parallel to one of the sides of a triangle , it shall cut the other sides , or those sides produced , proportionally . Shew that two straight lines drawn ...
... inscribed in a circle must also be equiangular . IO . If a straight line be drawn parallel to one of the sides of a triangle , it shall cut the other sides , or those sides produced , proportionally . Shew that two straight lines drawn ...
Σελίδα 7
... inscribed in the triangle ABC , prove ( 1 ) r = 2 area a + b + c ( 2 ) r = b.sin A.sin 2 B COS 2 2 8. In a right - angled triangle ABC , C being the right angle , find AB , if B = 30 ° and BC = 100 feet . A'B'C ' is also a right ...
... inscribed in the triangle ABC , prove ( 1 ) r = 2 area a + b + c ( 2 ) r = b.sin A.sin 2 B COS 2 2 8. In a right - angled triangle ABC , C being the right angle , find AB , if B = 30 ° and BC = 100 feet . A'B'C ' is also a right ...
Σελίδα 8
... at right angles to each other . 7. Prove that the subnormal in the parabola is constant ; and shew how to draw a normal to the curve at any given point . 8. A quadrilateral is inscribed in a circle , one 8 WOOLWICH ENTRANCE EXAMINATION .
... at right angles to each other . 7. Prove that the subnormal in the parabola is constant ; and shew how to draw a normal to the curve at any given point . 8. A quadrilateral is inscribed in a circle , one 8 WOOLWICH ENTRANCE EXAMINATION .
Σελίδα 9
E. J. Brooksmith. 8. A quadrilateral is inscribed in a circle , one of its diagonals coin- ciding with the diameter of the circle ; find in terms of its sides ( 1 ) the radius of the circle , ( 2 ) the other diagonal , ( 3 ) the area of ...
E. J. Brooksmith. 8. A quadrilateral is inscribed in a circle , one of its diagonals coin- ciding with the diameter of the circle ; find in terms of its sides ( 1 ) the radius of the circle , ( 2 ) the other diagonal , ( 3 ) the area of ...
Σελίδα 11
... inscribed in a circle ; if E , F , G , H be the centres of the circles which circumscribe the triangles ABC , BCD , CDA , DAB , prove that the quadrilateral EFGH is also inscribable in a circle . [ π = 3.14159 . ] VII . PURE MATHEMATICS ...
... inscribed in a circle ; if E , F , G , H be the centres of the circles which circumscribe the triangles ABC , BCD , CDA , DAB , prove that the quadrilateral EFGH is also inscribable in a circle . [ π = 3.14159 . ] VII . PURE MATHEMATICS ...
Άλλες εκδόσεις - Προβολή όλων
Woolwich Mathematical Papers for Admission Into the Royal Military Academy ... E J Brooksmith Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Woolwich Mathematical Papers for Admission Into the Royal Military Academy ... E. J. Brooksmith Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Woolwich Mathematical Papers for Admission Into the Royal Military Academy ... E. J. Brooksmith Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD acceleration accuracy in results ALGEBRA ARITHMETIC asymptotes attached to accuracy axis base Binomial Theorem bisected body cent centre of gravity chord circular measure circumference Common Logarithms cubic curve decimal described diameter distance Divide ellipse equal angles equilateral equilibrium expression feet Find the equation find the number Find the value forces acting fraction Full marks geometrical given point given straight line horizontal hyperbola inches inclined plane inscribed integral intersection latus rectum Least Common Multiple logarithms miles an hour N.B.-Great importance opposite parabola parallel parallelogram parallelogram of forces particle perpendicular position projectile prove pulley PURE MATH PURE MATHEMATICS radius ratio rectangle contained rectilineal figure right angles Royal Military Academy Shew Show sides sine Solve the equations STATICS string subtend tangent triangle ABC TRIGONOMETRY velocity vertex vertical weight x²+y² yards
Δημοφιλή αποσπάσματα
Σελίδα 7 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 8 - 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 7 - 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 8 - 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 7 - 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 8 - 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 8 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Σελίδα 8 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Σελίδα 7 - 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 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.