## 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 2University at Cambridge, 1801 - Mathematics |

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altitude angle answer axes axis base called centre circle circumference Computation consequently Construction contained corresponding cosine course curve declination DEMONSTRATION departure describe dial diameter difference of latitude difference of longitude direction distance divided double draw drawn ecliptic ellipse equal EXAMPLES feet figure formed four given greater half height Hence horizon hour inches intersection length less manner mark mean measure meridian method middle miles multiply namely NOTE object oblique observed opposite parallel passing perpendicular plane pole primitive PROBLEM projection proportion PROPOSITION quadrant radius rectangle reduce right-angled rule sailing segment side similar sine solidity sphere spherical triangle square star station sun's surface taken tang tangent THEOREM triangle true whole

### 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 93 - 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 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 93 - 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 93 - The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.

Page 140 - 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 225 - 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.