## Cambridge Problems: Being a Collection of the Printed Questions Proposed to the Candidates for the Degree of Bachelor of Arts at the General Examinations, from 1801 to 1820, Inclusive |

### Common terms and phrases

abscissa altitude angle axis base bisected body fall body is projected body revolve center of force center of gravity chord circle circumference Compare conic section curve cycloid cylinder density descending described determine diameter distance drawn earth elastic ellipse equal FIFTH AND SIXTH Find the fluents Find the sum Find the value fluid fluxion focus force varies inversely FOURTH CLASSES frustum geometric geometric progression given point greatest horizontal plane inclined plane latus rectum logarithmic spiral logarithms meridian moon's motion moving Newton's orbit ordinate orifice oscillation parabola paraboloid parallel perpendicular Prove quantity radius ratio rays rectangle refraction Required a proof right ascension round shew sides SIXTH CLASSES solid space specific gravity sphere spherical reflector spiral square root straight line Sum the following Sum the series sun's surface tangent triangle Tuesday Afternoon velocity acquired versed sine vertex vertical vessel weight

### Popular passages

Page 122 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.

Page 108 - A and ~B move in opposite directions with velocities, the sum of which is given. Shew that the sum of the products of each body into the square of its velocity is a minimum, when the velocities are reciprocally proportional to the quantities of matter in the bodies. 7. If from one extremity of the diameter of a circle, chords are drawn intersecting the radius which is perpendicular to the diameter or that radius produced, and from the points of intersection...

Page 84 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.

Page 132 - If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides.

Page 168 - ... in the ratio of the sine of incidence to the sine of refraction (Art. 881.) when the light passes from water into air.

Page 102 - ... similar mediums be separated from each other by a space terminated on both sides by parallel planes, and a body in its passage through that space be attracted or impelled perpendicularly towards either of those mediums, and not agitated or hindered by any other force; and the attraction be...

Page 210 - A projectile is to be thrown across a plain 120 feet wide, to strike a mark 30 feet high, the velocity of projection being that acquired down 80 feet j find at what angle it must be projected.

Page 85 - THIRD AND FOURTH CLASSES. 1 . Shew from the principles of the fifth Book of Euclid, that a ratio of greater inequality is diminished, and of less inequality increased by adding a quantity to both its terms. 2. The time of day at a given place determined from observations of the Sun's altitude is9h. 10'. 43''; and a chronometer set to Greenwich time shews 6h

Page 199 - Show that the time in which a heavy body descends down the straight line drawn from any point in the surface of a sphere to the lowest point = the time of descent down the vertical axis of the sphere. 8. A straight line is immersed vertically in a, fluid. Divide it into three portions that shall be equally pressed. 9. A straight line passes through the principal focus of a spherical reflector at right angles to the axis. Determine the conic section that forms the image. Where must the straight line...

Page 202 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included...