## New Cambridge Guide; Or, A Description of the University, Town, and County of Cambridge |

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Page 94 - That man is little to be envied, whose patriotism would not gain force upon the plain of Marathon, or whose piety would not grow • warmer among the ruins of lona.

Page 109 - The rectangle contained by the diagonals of a quadrilateral ,figure inscribed in a circle, is equal to both the rectangles contained by i'ts opposite sides.

Page 71 - A course of Lectures, containing a description and systematic arrangement of the several branches of Divinity, accompanied with an account both of the principal authors, and of the progress which has been made at different periods, in Theological learning.

Page 139 - 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 the Year 1801 to the Year 1810 inclusive; with a Preface. By a Graduate of the University.

Page 69 - ... and bisecting, a very distant object, be given, and in it the position of the eye and image, and also the apparent magnitudes of the object and image ; to determine the magnitude and position of the refracting surface. 20. A body is projected in a given direction, at a known distance from an horizontal plane, with a given velocity, acted on by a force perpendicular to the plane, which is inversely proportional to the square of its distance from the plane ; construct the orbit it will describe....

Page 176 - Find the inclination of the bar to the horizon, upon supposition that the semi-circle is devoid of weight. 2. Prove, from a property of the circle, that if four quantities are proportionals, the sum of the greatest and least is greater than the sum of the other two. 3. Given the area of any plane surface, it is required to find the content of a solid, formed ' by drawing lines from a given point without the plane, to every part of its surface.

Page 174 - AF is perpendicular to each of the straight lines GH, DE. But if a straight line stand at right angles to each of two straight lines in the point of their intersection, it is also at right angles to the plane passing through them : (xi.

Page 3 - IV. 34. Having given the vertical angle of a triangle, and the radii of the inscribed and circumscribed circles, to construct the triangle. 35. Given the base and vertical angle of a triangle, and also the radius of the inscribed circle, required to construct it. 36. Given the three angles of a triangle, and the radius of the inscribed circle, to construct the triangle. 37. If the base and vertical angle of a plane triangle be given, prove that the locus of the centers of the inscribed circle is...

Page 138 - Solve the equation 1 = — i 1 x 2 and of the two expressions 3. With what velocity must a body be projected from a tower, in a direction parallel to the horizon, so that it shall strike the ground at a distance from the foot of the tower, equal half the

Page 65 - A body, of weight 2P, is kept in equilibrium on an inclined plane by a horizontal force P, together with a force P acting parallel to the plane ; find the ratio of the base of the...