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 3
... roots equal to unity . ... If the terms be alternately positive and negative , and p not greater than 2n , the roots cannot all be real . 14. In isosceles spherical triangles , the angles at the base are equal . 15. Prove the formula ...
... roots equal to unity . ... If the terms be alternately positive and negative , and p not greater than 2n , the roots cannot all be real . 14. In isosceles spherical triangles , the angles at the base are equal . 15. Prove the formula ...
Σελίδα 8
... roots are in geometric progression , shew that k " is one of the roots , n being odd . Shew that , in a similar manner , one root of an equation of odd degree , whose roots are either in arithmetic or harmonic progression , may be found ...
... roots are in geometric progression , shew that k " is one of the roots , n being odd . Shew that , in a similar manner , one root of an equation of odd degree , whose roots are either in arithmetic or harmonic progression , may be found ...
Σελίδα 12
... roots " 1 = 0 is equal to zero , unless m be a multiple of n , in which case the sum is equal to n . 6. Define an ellipse , and from your definition deduce the polar equation referred to the focus as pole . Shew that , when the curve is ...
... roots " 1 = 0 is equal to zero , unless m be a multiple of n , in which case the sum is equal to n . 6. Define an ellipse , and from your definition deduce the polar equation referred to the focus as pole . Shew that , when the curve is ...
Σελίδα 13
... roots x - 1 = 0 is equal to zero , unless m be a multiple of n , in which case the sum is equal to n . 6. Define an ellipse , and from your definition deduce the polar equation referred to the focus as pole . Shew that , when the curve ...
... roots x - 1 = 0 is equal to zero , unless m be a multiple of n , in which case the sum is equal to n . 6. Define an ellipse , and from your definition deduce the polar equation referred to the focus as pole . Shew that , when the curve ...
Σελίδα 14
... roots of z2 10 . - 4. The stereographic projection of a cube on a plane per- pendicular to its diagonal ( the pole being in the diagonal pro- duced ) is an equilateral hexagon , whose angles are alternately greater and less . If the ...
... roots of z2 10 . - 4. The stereographic projection of a cube on a plane per- pendicular to its diagonal ( the pole being in the diagonal pro- duced ) is an equilateral hexagon , whose angles are alternately greater and less . If the ...
Άλλες εκδόσεις - Προβολή όλων
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.