Cambridge problems proposed by the moderators to the candidates for mathematical honors at the general examination, 1843, Τόμος 21843 - 30 σελίδες |
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Σελίδα 5
... result . 2. Adapt the general formulæ for finding the centre of gravity of a body to the case of a solid revolution . A solid sector of a sphere hangs from a point in its circular rim with its axis horizontal , find its vertical angle ...
... result . 2. Adapt the general formulæ for finding the centre of gravity of a body to the case of a solid revolution . A solid sector of a sphere hangs from a point in its circular rim with its axis horizontal , find its vertical angle ...
Σελίδα 11
... of the normal at any point which is a harmonic mean between the greatest and least radii of curvature at that point . Interpret this result . FRIDAY , January 6 . QUESTIONS IN PURE MATHEMATICS . CAMBRIDGE PROBLEMS , 1843 . 11.
... of the normal at any point which is a harmonic mean between the greatest and least radii of curvature at that point . Interpret this result . FRIDAY , January 6 . QUESTIONS IN PURE MATHEMATICS . CAMBRIDGE PROBLEMS , 1843 . 11.
Σελίδα 21
... result according to the nature of n . 4. Find the equation to the line joining the points of con- tact of two tangents drawn to an ellipse from any point . If the point move along a straight line , shew that the chord of contact will ...
... result according to the nature of n . 4. Find the equation to the line joining the points of con- tact of two tangents drawn to an ellipse from any point . If the point move along a straight line , shew that the chord of contact will ...
Σελίδα 22
... result obtained ? 11. Integrate the equations dy xy J x + x2 = y2 , y ( dy ) 2 + ( 2x− a ) dy — y = 0 . - dx Find the value of So dxε 2 . 12. Having given one of the principal axes through any point of a body , find the other two ...
... result obtained ? 11. Integrate the equations dy xy J x + x2 = y2 , y ( dy ) 2 + ( 2x− a ) dy — y = 0 . - dx Find the value of So dxε 2 . 12. Having given one of the principal axes through any point of a body , find the other two ...
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Cambridge Problems Proposed by the Moderators to the Candidates for ... Exam Papers Cambridge Univ Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
asymptotes axes axis centre of gravity circle conjugate diameters cosine curve cylinder determine developable surface diagonal double curvature dx a² ecliptic elastic string ellipse ellipsoid equal equilibrium Find dy Find the centre find the condition Find the equation Find the position Find the ratio fixed point fluid forces act fraction function given plane given point harmonic mean inclined plane January least common multiple MATHEMATICS AND NATURAL meridian minimum Moon's motion NATURAL PHILOSOPHY north polar distance number of terms orbit oscillations osculating plane parabola parallel parallelograms particle point of contact pole pressure projection prove the formula pulley PURE MATHEMATICS QUESTIONS IN PURE r₁ radii radius of curvature radius vector rays refracted rest right angle right-angled triangle roots segment shew smooth horizontal plane sphere spherical triangles surface tangents temperature touch vertex vertical plane x y z
Δημοφιλή αποσπάσματα
Σελίδα 3 - The third, viz. that the squares of the periodic times are proportional to the cubes of the mean distances...
Σελίδα 10 - But when a solid angle is formed by three plane angles, the sum of any two of them is greater than the third (Prop.
Σελίδα 10 - Triangles and parallelograms of the same altitude are to one another as their bases.
Σελίδα 6 - ... string passing over a pulley at the top of the inclined plane hangs vertically, supporting a weight (P).
Σελίδα 1 - To express the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides. Let ABC be a spherical triangle, O the centre of the sphere.
Σελίδα 8 - A Screw of Archimedes is capable of turning freely round its axis, which is fixed in a vertical position ; a heavy particle is placed at the top of the tube and runs down through it; determine the whole angular velocity communicated to the screw.