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 6.
Σελίδα 7
... draw a straight line , such , that the portions of it intercepted by each circle shall be respectively proportional to their radii . 4. If two parallel lines be drawn at an inclination to the axis of a through two points whose co ...
... draw a straight line , such , that the portions of it intercepted by each circle shall be respectively proportional to their radii . 4. If two parallel lines be drawn at an inclination to the axis of a through two points whose co ...
Σελίδα 8
Cambridge univ, exam. papers. 5. A straight line is drawn from a point whose co - ordinates are a b , so as to touch the circle ( x2 + y2 = r2 ) , and to cut off a portion ( c ) from the axis of y ; obtain an equation for deter- mining c ...
Cambridge univ, exam. papers. 5. A straight line is drawn from a point whose co - ordinates are a b , so as to touch the circle ( x2 + y2 = r2 ) , and to cut off a portion ( c ) from the axis of y ; obtain an equation for deter- mining c ...
Σελίδα 15
... drawn to the paraboloid ( 2 ) W ' z — ( 1 x2 + l ' y2 ) = 0 ; shew that the planes of contact all touch the surface 4z ( lx2 + l ' y2 ) — ( l2x2 + l'2 y2 ) = 0 : also shew that the surface ( 1 ) contains the directrices of all the ...
... drawn to the paraboloid ( 2 ) W ' z — ( 1 x2 + l ' y2 ) = 0 ; shew that the planes of contact all touch the surface 4z ( lx2 + l ' y2 ) — ( l2x2 + l'2 y2 ) = 0 : also shew that the surface ( 1 ) contains the directrices of all the ...
Σελίδα 21
... drawn to an ellipse from any point . If the point move along a straight line , shew that the chord of contact will always pass through a fixed point . 5. Shew how to determine the existence of points in which different branches of a ...
... drawn to an ellipse from any point . If the point move along a straight line , shew that the chord of contact will always pass through a fixed point . 5. Shew how to determine the existence of points in which different branches of a ...
Σελίδα 26
... draw a curve of given length , such that its projection on a given plane may subtend at a given point in the plane a sector of maximum area . TUESDAY , January 10 . QUESTIONS IN PURE MATHEMATICS AND CAMBRIDGE PROBLEMS , 1843 .
... draw a curve of given length , such that its projection on a given plane may subtend at a given point in the plane a sector of maximum area . TUESDAY , January 10 . QUESTIONS IN PURE MATHEMATICS AND CAMBRIDGE PROBLEMS , 1843 .
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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.