# The Projection and Calculation of the Sphere for Young Sea Officers Being a Complete Initiation Into Nautical Astronomy

Longmans, Green, 1861 - Nautical astronomy - 112 pages
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Page 18 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Page 18 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 19 - IF two straight lines cut one another, the vertical, or opposite, angles shall be equal.
Page 22 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 56 - As any one side, Is to the sine of its opposite angle ; So is any other side, To the sine of its opposite angle.
Page 20 - The greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Page 21 - The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference.
Page 78 - The sine of half the sum of two angles of a spherical triangle is 'to the sine of half their difference as the tangent of half the included side is to the tangent of half the difference of the other two sides.
Page 75 - As the cosine of half the sum of the two sides is to the cosine of half their difference, so is the cotangent of half the contained angle to the tangent of half the sum of the other two angles.
Page 6 - Fig. 23 (A to B, B to C, C to D and D to E).