## A Collection of Cambridge Mathematical Examination Papers: Papers in pure mathematics: SupplementW. P. Grant, 1833 |

### From inside the book

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**find**the position in which W will rest . 6. One sphere is supported by three others which touch ,**find**the pressures ...**equation**between P and W , when the weights of the pulleys are equal , and each hangs by a separate string ... Page 11

... find the accelerating force on a body descending in the tube ; and prove that if it descends from a point very near the vertex , it will make its successive revolutions in equal times . 20.

... find the accelerating force on a body descending in the tube ; and prove that if it descends from a point very near the vertex , it will make its successive revolutions in equal times . 20.

**Find the equation**to the curve described by ... Page 13

... found from this proportion 1 e : C : 2c- C. 15. A body is projected in a given direction , and with a given velocity , and is acted on by the constant force of gravity in parallel lines :

... found from this proportion 1 e : C : 2c- C. 15. A body is projected in a given direction , and with a given velocity , and is acted on by the constant force of gravity in parallel lines :

**find the equation**to its path ; shew that it is ... Page 17

... Find the weight of the timber , and the place of the which the timber would balance without the weights . prop on 15.

... Find the weight of the timber , and the place of the which the timber would balance without the weights . prop on 15.

**Find the equation**of equilibrium on the inclined plane , when friction , proportional to the pressure , is taken into ... Page 19

... Find the centre of gravity of a wedge , of which the sides are cut into the form of a parabola , the flat surfaces being exactly similar and equal . 13.

... Find the centre of gravity of a wedge , of which the sides are cut into the form of a parabola , the flat surfaces being exactly similar and equal . 13.

**Find the equation**... equations of motion : de d2s f = dt dt vdv = fds 15. Under ...### Other editions - View all

### Common terms and phrases

aberration altitude angular velocity base body be projected centre of force centre of gravity chord circle circumference cone conic section curvature curve cycloid cylinder density described determine diameter direction distance drawn Earth ecliptic elastic ellipse equal equilibrium Find the centre Find the equation find the position find the pressure find the velocity fixed fluid focal length focus force tending force varying forces acting given point given velocity horizontal plane hyperbola immersed incident inclined plane inversely JOHN'S COLLEGE latitude latus rectum law of force lens longitude meridian Moon's motion moving Newton observed orbit oscillation parabola parallax parallel particle pencil perpendicular placed prism Prop prove pulley quantity radius ratio rays reflector refraction rest right angles right ascension shew sides SIDNEY SUSSEX COLLEGE sine specific gravity sphere spherical reflector spherical triangle square star straight line string Sun's supposing tangent TRINITY COLLEGE vertex vessel

### Popular passages

Page 243 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...

Page 240 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 12 - If two forces, acting at a point, be represented in magnitude and direction by the...

Page 202 - Nutation of lunar orbit. The action of the bulging matter at the earth's equator on the moon occasions a variation in the inclination of the lunar orbit to the plane of the ecliptic. Suppose the plane N/?

Page 230 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.

Page 215 - WHAT sum of money must be laid out in the 3 per cent consols, at 63f per cent, to produce an income of £ 400 a year ? 2. The sine of any angle of a plane triangle has to the opposite side a constant ratio. — What is this ratio ? 3. Find by the method of continued fractions a series of fractions converging to V'lp.

Page 282 - Let ABC be a triangle, of which the side AC is greater than the side AB; the angle ABC shall be greater than the angle BCA.

Page 247 - IF a straight line be at right angles to a plane, every plane which passes through it shall be at right angles to that plane.

Page 125 - Upon comparing the observations with each other, it was discovered that in both the fore-mentioned stars, the apparent difference of declination from the maxima was always nearly proportional to the versed sine of the sun's distance from the equinoctial points. This was an inducement to think that the cause, whatever it was, had some relation to the sun's situation with respect to those points.

Page 160 - If two similar mediums are separated from each other by a space terminated on each side by parallel planes ; and a body in its transit through this space, is attracted or impelled perpendicularly towards either medium, and is not agitated or hindered by any other force; and the attraction is every where the same at equal distances from either plane, taken towards the same side of the plane; prove that the velocity of the body before incidence is to its velocity after emergence as the sine of emergence...