Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 pages |
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Page 12
... Curve surface of cylinder = 2xrh ; r = rad . of base , h = height ; Whole surface of cylinder = 2πr ( h + r ) . Curve surface of cone = url ; 1 = slant 12 FORMULE .
... Curve surface of cylinder = 2xrh ; r = rad . of base , h = height ; Whole surface of cylinder = 2πr ( h + r ) . Curve surface of cone = url ; 1 = slant 12 FORMULE .
Page 13
... Curve surface of cone = url ; 1 = slant height . Curve surface of frustum of cone = π ( r1 + r2 ) l r1 , 72 , radii of ends ; 7 : Surface of sphere = 4πr2 . = slant height . Curve surface of segment of sphere = 2xrh ; h = height of ...
... Curve surface of cone = url ; 1 = slant height . Curve surface of frustum of cone = π ( r1 + r2 ) l r1 , 72 , radii of ends ; 7 : Surface of sphere = 4πr2 . = slant height . Curve surface of segment of sphere = 2xrh ; h = height of ...
Page 20
... Curves . : = √√ { 1+ dy ( d ) } dx . Parabola , s = √ ax + x2 + a log ; √x + √ α + x ; va с Cycloid , s = √ / 8ax ; Catenary , s = § ( e — e` * ) . 2 Ellipse , s 2α- : 2xa { 1 . e2 1.3e4 22 22.42 etc. } Areas of Curves . A = -Sf ...
... Curves . : = √√ { 1+ dy ( d ) } dx . Parabola , s = √ ax + x2 + a log ; √x + √ α + x ; va с Cycloid , s = √ / 8ax ; Catenary , s = § ( e — e` * ) . 2 Ellipse , s 2α- : 2xa { 1 . e2 1.3e4 22 22.42 etc. } Areas of Curves . A = -Sf ...
Page 110
... y2 = 4ax . Prove that the straight line , x + y = 1 , touches the parabola , x2 = x — y . 14. Trace the curve- x2 + xy + y2 = a2 , and find the lengths of its axes . LXVII . 1. If ABC be a triangle right angled 110 WOOLWICH.
... y2 = 4ax . Prove that the straight line , x + y = 1 , touches the parabola , x2 = x — y . 14. Trace the curve- x2 + xy + y2 = a2 , and find the lengths of its axes . LXVII . 1. If ABC be a triangle right angled 110 WOOLWICH.
Page 113
... curve a3y = x4-2c3x + 3c1 cannot be cut more than twice by any right line passing through the origin , and find the equation to the tangent through the origin . 4. When is one quantity said to be a function of another ? If x2 + y2 + z2 ...
... curve a3y = x4-2c3x + 3c1 cannot be cut more than twice by any right line passing through the origin , and find the equation to the tangent through the origin . 4. When is one quantity said to be a function of another ? If x2 + y2 + z2 ...
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Arithmetic axis ball base bisected body cent centre of gravity circle coefficient of friction compound interest cone cost crown 8vo cube cubic foot curve Define determine diameter Divide dwts ellipse English equal equilibrium expression feet Find the area Find the centre Find the distance Find the equation Find the number Find the sum Find the value fluid forces acting formula fraction geometrical Grammar horizontal plane hyperbola inches inclined plane inscribed Integrate isosceles latus rectum least common multiple length logarithms miles Multiply parabola parallel particle perpendicular pressure Prove pulleys radius ratio rectangle rectangular Reduce right angles sides simple interest sin² sine spherical triangle square root straight line string subtended Subtract surface tangent theorem tons tower triangle ABC velocity vertical vulgar fraction weight yards
Popular passages
Page 123 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 10 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 184 - If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other.
Page 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 184 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third (20.
Page 184 - 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.
Page 163 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 184 - In right angled triangles the square on the side subtending the right angle is equal to the (sum of the) squares on the sides containing the right angle.
Page 154 - If two straight lines be cut by parallel planes, they shall be cut in the same ratio. Let the straight lines AB, CD be cut by the parallel planes GH, KL, MN, in the points A, E, B; C, F, D : As AE is to EB, so is CF to FD.