Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
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Αποτελέσματα 1 - 5 από τα 24.
Σελίδα 15
... ellipse , origin at centre , + ყვ a2 b2 = 1 . Equation to tangent at ( x ' , y ' ) , a2yy ' + b2xx ' = a2b2 , or y = mx + √ a2 m2 + b2 . Equation to normal at ( x ' , y ' ) , y — y ' = a2y ( x − x2 ) , b2x √ b2 m2 + a2 or y = mx ...
... ellipse , origin at centre , + ყვ a2 b2 = 1 . Equation to tangent at ( x ' , y ' ) , a2yy ' + b2xx ' = a2b2 , or y = mx + √ a2 m2 + b2 . Equation to normal at ( x ' , y ' ) , y — y ' = a2y ( x − x2 ) , b2x √ b2 m2 + a2 or y = mx ...
Σελίδα 16
... ellipse , focus , the pole , r = a ( 1 - e2 ) 1+ e cos 0 centre , the pole , r2 ( a2 sin2 0 + b2 cos2 0 ) = Polar equation to hyperbola , focus , the pole , r = centre , the pole , r2 ( a2 sin2 0 b2 cos2 0 ) - a2b2 . - a ( e2 . 1 ) 1+ e ...
... ellipse , focus , the pole , r = a ( 1 - e2 ) 1+ e cos 0 centre , the pole , r2 ( a2 sin2 0 + b2 cos2 0 ) = Polar equation to hyperbola , focus , the pole , r = centre , the pole , r2 ( a2 sin2 0 b2 cos2 0 ) - a2b2 . - a ( e2 . 1 ) 1+ e ...
Σελίδα 19
... Ellipse , p = ( a2 — e2x2 ) 3 ̧ ab Hyperbola , p = Cycloid , p = 2√2ay . ( e2x2 x2 — a2 ) 3 ab FORMULE IN INTEGRAL CALCULUS . axm + 1 m + 1 Sax TM dx = Seda = e . S sin x S sec2 sin x dx = dx ; log x ; X Sa2dx ax a * dx = ; log , a cos ...
... Ellipse , p = ( a2 — e2x2 ) 3 ̧ ab Hyperbola , p = Cycloid , p = 2√2ay . ( e2x2 x2 — a2 ) 3 ab FORMULE IN INTEGRAL CALCULUS . axm + 1 m + 1 Sax TM dx = Seda = e . S sin x S sec2 sin x dx = dx ; log x ; X Sa2dx ax a * dx = ; log , a cos ...
Σελίδα 20
... Ellipse , s 2а 2xa { 1 e2 1.3e4 22 2o . 43 — etc. } 22.42 Areas of Curves . A = ff ( x ) dx . с § ( « 2— ‹ ̈ ̈ ) . 2 ra Circle , A = r2 ; Sector , A = ; Ellipse , A = Tаb ; 2 Cycloid , A = 3πr2 . 2 Parabola , △ = of circumscribing ...
... Ellipse , s 2а 2xa { 1 e2 1.3e4 22 2o . 43 — etc. } 22.42 Areas of Curves . A = ff ( x ) dx . с § ( « 2— ‹ ̈ ̈ ) . 2 ra Circle , A = r2 ; Sector , A = ; Ellipse , A = Tаb ; 2 Cycloid , A = 3πr2 . 2 Parabola , △ = of circumscribing ...
Σελίδα 110
... ellipse from an external point , and prove that they subtend equal angles at either focus . 10. If the tangent PT at a point P of a hyperbola meet the transverse axis in T , and if PN be the ordinate , prove that , CN.CT = AC2 , C being ...
... ellipse from an external point , and prove that they subtend equal angles at either focus . 10. If the tangent PT at a point P of a hyperbola meet the transverse axis in T , and if PN be the ordinate , prove that , CN.CT = AC2 , C being ...
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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 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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 78 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.