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). |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 84.
Σελίδα 2
... Prove that the base of any segment of a circle makes equal angles with the diameter drawn through one extremity of the base , and with the perpendicular let fall from that extremity upon the tangent at the other extremity . 7. In equal ...
... Prove that the base of any segment of a circle makes equal angles with the diameter drawn through one extremity of the base , and with the perpendicular let fall from that extremity upon the tangent at the other extremity . 7. In equal ...
Σελίδα 4
... 1 ) x + a ( a − 1 ) . and 2 . Find the value of - - x3 − x2 + 3x + 5 , when x = 1 + 2√√ − 1 ; and prove that ( √ 3 + 1 ) 2 − 2 ( √2 − 1 ) 2 = √59-24√√6 . 2 − 3. Simplify and 21 I - a2 -2 a2 2 4 WOOLWICH : -JULY , 1880 .
... 1 ) x + a ( a − 1 ) . and 2 . Find the value of - - x3 − x2 + 3x + 5 , when x = 1 + 2√√ − 1 ; and prove that ( √ 3 + 1 ) 2 − 2 ( √2 − 1 ) 2 = √59-24√√6 . 2 − 3. Simplify and 21 I - a2 -2 a2 2 4 WOOLWICH : -JULY , 1880 .
Σελίδα 6
... Prove ( sin A ) 2 + ( cos A ) 2 = 1 , and express the numerical values of sin 135 ° and tan 150 ° with their proper ... prove sec 1050 = −√√2 ( 1 + √√√3 ) . 4 . Prove : ( 1 ) sin 343 sin 6 WOOLWICH : -JULY , 1880 .
... Prove ( sin A ) 2 + ( cos A ) 2 = 1 , and express the numerical values of sin 135 ° and tan 150 ° with their proper ... prove sec 1050 = −√√2 ( 1 + √√√3 ) . 4 . Prove : ( 1 ) sin 343 sin 6 WOOLWICH : -JULY , 1880 .
Σελίδα 7
Woolwich roy. military acad. 4 . Prove : ( 1 ) sin 343 sin A − 4 ( sin A ) 3 . - ( 2 ) sin 54 ° = √5 + 1 . 4 sin ( A - C ) sin ( B - A ) ( 3 ) + cos A cos C cos B cos A sin ( C- B ) cos C cos B = 0 . 5. Prove that in every circle the ...
Woolwich roy. military acad. 4 . Prove : ( 1 ) sin 343 sin A − 4 ( sin A ) 3 . - ( 2 ) sin 54 ° = √5 + 1 . 4 sin ( A - C ) sin ( B - A ) ( 3 ) + cos A cos C cos B cos A sin ( C- B ) cos C cos B = 0 . 5. Prove that in every circle the ...
Σελίδα 8
... prove that they are 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 WOOLWICH ...
... prove that they are 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 WOOLWICH ...
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...