Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics, and Hydrostatics. With Tables ... and ReferencesLongmans, Green & Company, 1877 - 413 σελίδες |
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Σελίδα 287
... a be the semi - major axis , prove that 2a . S.√2 ―r . ds along any arc is proportional to the sec- r tional area subtended by that arc at the other focus . MIXED MATHEMATICS FORMULE IN STATICS . R = resultant of INTEGRAL CALCULUS . 287.
... a be the semi - major axis , prove that 2a . S.√2 ―r . ds along any arc is proportional to the sec- r tional area subtended by that arc at the other focus . MIXED MATHEMATICS FORMULE IN STATICS . R = resultant of INTEGRAL CALCULUS . 287.
Σελίδα 288
... resultant of P and Q acting at an angle 0 , R2 = P2 + Q2 + 2 PQ cos 0 ; if P = Q , R = 2P cos } 0 . 0 = 0 , R = P + Q ; 0 = π , R = P— Q • If P , Q , R are in equilibrium at a point o , PQR = sin QOR : sin POR : sin POQ . R = resultant ...
... resultant of P and Q acting at an angle 0 , R2 = P2 + Q2 + 2 PQ cos 0 ; if P = Q , R = 2P cos } 0 . 0 = 0 , R = P + Q ; 0 = π , R = P— Q • If P , Q , R are in equilibrium at a point o , PQR = sin QOR : sin POR : sin POQ . R = resultant ...
Σελίδα 293
... resultant of two forces is 100 lbs . , and the angles which it makes with the directions of the forces are 20 ° and 30 ° ; find the component forces . 7. A heavy body is drawn up an inclined plane by means of a string , which being ...
... resultant of two forces is 100 lbs . , and the angles which it makes with the directions of the forces are 20 ° and 30 ° ; find the component forces . 7. A heavy body is drawn up an inclined plane by means of a string , which being ...
Σελίδα 294
... resultant . 2. Three forces of 3 , 4 , 5 lbs . act on a particle in the cen- tre of a square in directions towards three of the angles of the square : find the magnitude and direction of the force which will keep the particle at rest ...
... resultant . 2. Three forces of 3 , 4 , 5 lbs . act on a particle in the cen- tre of a square in directions towards three of the angles of the square : find the magnitude and direction of the force which will keep the particle at rest ...
Σελίδα 296
... resultant is greatest when 0 = 0 ; least when 0 = 7 ; and intermediate for intermediate values of A. 2. Find the resultant of two equal forces acting on a point . 3. Three forces , 99 , 100 , 101 lbs . respectively act upon a point in ...
... resultant is greatest when 0 = 0 ; least when 0 = 7 ; and intermediate for intermediate values of A. 2. Find the resultant of two equal forces acting on a point . 3. Three forces , 99 , 100 , 101 lbs . respectively act upon a point in ...
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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.