# Mathematics: Compiled from the Best Authors and Intended to be the Text-book of the Course of Private Lectures on These Sciences in the University at Cambridge, Volume 2

University at Cambridge, 1801 - Mathematics

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### Contents

 DEFINITIONS c 8 MENSURATION or SUPERFICIES 29 Definitions 91 Problems relating to the content of a Cube Parallelopipe 97
 Miscellaneous Questions I 39 139 GAUGING I 53 151 HEIGHTS AND DISTANCES 169 SURVEYING 207

### Popular passages

Page 19 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Page 15 - To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference...
Page 91 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 346 - The conjugate to any diameter is the line drawn through the centre, and parallel to the tangent of the curve at the vertex of the diameter. So...
Page 26 - But if the hypothenuse be made radius -, then each leg "will represent the sine of its opposite angle ; namely, the leg AB the sine of the arc AE or angle c, and the leg BC the sine of the arc CD or angle A.
Page 91 - The axis of a solid is a line drawn from the middle of one end to the middle of the opposite end ; as between the opposite ends of a prism.
Page 91 - The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.
Page 138 - Between these, in a right line, stands an ancient statue, the head whereof is 97 feet from the summit of the higher, and 86 feet from the top of the lower column, and the distance between the...
Page 223 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 36 - Multiply the sum of the two parallel sides by the perpendicular distance between them, and half the product will be the area.