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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Αποτελέσματα 1 - 5 από τα 29.
Σελίδα 1
... Shew how to find the least common multiple of two quantities and extend the method to find that of several quan- tities . Ex . Find the least common multiple of x3 — x , 33 23 +1 . - 1 , 5. Find the sum of any number of terms of a ...
... Shew how to find the least common multiple of two quantities and extend the method to find that of several quan- tities . Ex . Find the least common multiple of x3 — x , 33 23 +1 . - 1 , 5. Find the sum of any number of terms of a ...
Σελίδα 2
... Shew that tan ( A + B ) Prove that tan ( 450 + A ) = - 1 √1 + x tan Atan B 1 tan A tan B ' - tan ( 45o - A ) = 2 ... Shew that there can be but one pair of rectangular conjugate diameters . 13. Shew how to reduce the reciprocal equation ...
... Shew that tan ( A + B ) Prove that tan ( 450 + A ) = - 1 √1 + x tan Atan B 1 tan A tan B ' - tan ( 45o - A ) = 2 ... Shew that there can be but one pair of rectangular conjugate diameters . 13. Shew how to reduce the reciprocal equation ...
Σελίδα 3
... Shew how to construct a table of natural sines . Given cosine 34 ° .29 ′ = 4338335 , cosine 34 ° . 30 ′ 4335938 . Find the cosine of 34 ° .29.48 " . WEDNESDAY , January 4 . QUESTIONS IN NATURAL PHILOSOPHY . N.B. - The Differential ...
... Shew how to construct a table of natural sines . Given cosine 34 ° .29 ′ = 4338335 , cosine 34 ° . 30 ′ 4335938 . Find the cosine of 34 ° .29.48 " . WEDNESDAY , January 4 . QUESTIONS IN NATURAL PHILOSOPHY . N.B. - The Differential ...
Σελίδα 4
... Shew that the image of an object in a plane mirror is equal to the object , and equally inclined to the mirror . 11. Find the limit of the refracting angle of a prism of given refractive power so that the passage of a ray of light ...
... Shew that the image of an object in a plane mirror is equal to the object , and equally inclined to the mirror . 11. Find the limit of the refracting angle of a prism of given refractive power so that the passage of a ray of light ...
Σελίδα 5
... Shew that in latitude 66 ° . 32 ′ the longest is 24 hours . 16. What are the three usual modes of measuring time ? What time does the astronomical clock shew ? What time does a dial shew ? Find the mean time of a given star's transit ...
... Shew that in latitude 66 ° . 32 ′ the longest is 24 hours . 16. What are the three usual modes of measuring time ? What time does the astronomical clock shew ? What time does a dial shew ? Find the mean time of a given star's transit ...
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.