Solutions to the mathematical examination papers set for admission to the Royal military academy, Woolwich, and for the Royal military college [&c.] by D. Tierney and H. Sharratt1877 |
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Página 23
... curve , T the point where the tangent at P meets the axis produced , PQ perpendicular to the directrix , prove ( 1 ) PT bisects the angle SPQ , ( 2 ) the quadrilateral SPQT is a rhombus . Drew , Geom . Conics , Props . v . , VIII . 9 ...
... curve , T the point where the tangent at P meets the axis produced , PQ perpendicular to the directrix , prove ( 1 ) PT bisects the angle SPQ , ( 2 ) the quadrilateral SPQT is a rhombus . Drew , Geom . Conics , Props . v . , VIII . 9 ...
Página 24
... curve represented by 5x + 5y + 2xy - 12 = 0 . Now , to determine the directions of the principal axes , we have tan 20 = ∞ 0 = 45 ° . Now , transforming the equation to axes through same origin as last , but making an angle of 45 ...
... curve represented by 5x + 5y + 2xy - 12 = 0 . Now , to determine the directions of the principal axes , we have tan 20 = ∞ 0 = 45 ° . Now , transforming the equation to axes through same origin as last , but making an angle of 45 ...
Página 25
... curve from the centre is a mean proportional between the distances of the same point from the foci . Salmon , Conic Sections , Art . 174 . If in any hyperbola CD be conjugate to CP , we have SP.HP = CD , but in the rectangular hyperbola ...
... curve from the centre is a mean proportional between the distances of the same point from the foci . Salmon , Conic Sections , Art . 174 . If in any hyperbola CD be conjugate to CP , we have SP.HP = CD , but in the rectangular hyperbola ...
Página 45
... curve or curvilinear area . Determine either the volume or the surface of a ring made by the revolution of a regular hexagon ; the radius of the circle that would circumscribe the hexagon is a , and b is the distance of the centre of ...
... curve or curvilinear area . Determine either the volume or the surface of a ring made by the revolution of a regular hexagon ; the radius of the circle that would circumscribe the hexagon is a , and b is the distance of the centre of ...
Página 48
... curve y = f ( x ) . Todhunter , Diff . Calc . , Art . 257 . The equations to the tangents drawn from the origin to the parabola ay = x2 + bx + c are y = b + 2c 3 . a Since ay = x2 + bx + c2 , dy_2x + b = dx a Now , because the tangent ...
... curve y = f ( x ) . Todhunter , Diff . Calc . , Art . 257 . The equations to the tangents drawn from the origin to the parabola ay = x2 + bx + c are y = b + 2c 3 . a Since ay = x2 + bx + c2 , dy_2x + b = dx a Now , because the tangent ...
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Solutions To The Mathematical Examination Papers Set For Admission To The ... D Tierney,Handell Sharratt Sin vista previa disponible - 2023 |
Solutions to the Mathematical Examination Papers Set for Admission to the ... D. Tierney,Handell Sharratt Sin vista previa disponible - 2016 |
Solutions To The Mathematical Examination Papers Set For Admission To The ... D. Tierney,Handell Sharratt Sin vista previa disponible - 2023 |
Términos y frases comunes
AB² ABCD acceleration AD² ARITHMETIC axis BC² cent centre of gravity circle coefficient of friction Conic Sections cose cubic curve decimal described diameter Differential Calculus directrix Divide dy dx equal and parallel Euclid expression feet Find the equation forces fraction given straight line hyperbola inches inclined integration intersect Join latus rectum least common multiple logarithmic mechanical advantage METCALFE AND SON moment of inertia Multiply opposite angles parabola parallelogram Parkinson's Mechanics particle perpendicular plane point of bisection Prop prove quadrilateral radius ratio rectangle contained Result right angles roots seconds segments semicircle shew sides Similarly sin² sine square string subtending Subtract tangent Todhunter Todhunter's Trigonometry triangle ABC Trig vertex vertical virtual velocities weight whence whole number yards
Pasajes populares
Página 55 - If two triangles have two sides of the one equal to two sides of the...
Página 71 - 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.
Página 11 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Página 12 - 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.
Página 13 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Página 15 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 13 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Página 62 - 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 acute angle and the perpendicular let fall upon it from the opposite angle.
Página 13 - PROP. X. THEOR. IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Página 70 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.