# 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

Printed at the University Press, by WilliamHilliard, 1801 - Mathematics
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### Contents

 DEFINITIONS 11 Problems 25 1 62 Instruments and Field Book 207 Practice of Surveying Page 215 Planning and Computing 246 Division of Land 260 Levelling 266
 CONIC SECTIONS 349 Ellipse 356 Hyperbola 379 Parabola 404 DIALING 419 SPHERICAL GEOMETRY 457 Stereographic Projection 464 Projections of the Sphere 484

 Plane Sailing 275 Oblique Plane Sailing 286 Traverse Sailing 301 Parallel Sailing 307 Middle Latitude Sailing 313
 SPHERICAL TRIGONOMETRY 501 Rectangular Spherical Trigonometry 507 Rectilateral Spherical Trigonometry 528 SPHERICAL ASTRONOMY 555

### Popular passages

Page 21 - 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 17 - 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 83 - 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 326 - 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 28 - 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 83 - 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 83 - The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.
Page 130 - 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 205 - 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 38 - Multiply the sum of the two parallel sides by the perpendicular distance between them, and half the product will be the area.