## An introduction to the theory ... of plane and spherical trigonometry ... including the theory of navigation |

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### Common terms and phrases

acute added altitude Answer apparent azimuth base called centre chords circle compasses complement consequently CONSTRUCTION contained correction cosec cosine cotangent declination describe difference distance divided division double draw ecliptic equal equation EXAMPLE extent fall feet find the angle formed given gives greater Greenwich half height Hence horizon hour hypothenuse latitude less logarithm longitude mean measured meridian middle miles moon's natural noon North object oblique observed obtuse opposite parallax parallel perpendicular plane triangle Plate pole PRACTICAL PROBLEM proportions PROPOSITION quadrant radius remainder represent right angles right ascension rising RULE scale secant side side ac sine species sphere spherical triangle star subtract sun's supplement suppose taken tangent third triangle ABC true yards zenith

### Popular passages

Page 109 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 141 - Consequently, a line drawn from the vertex of an isosceles triangle to the middle of the base, bisects the vertical angle, and is perpendicular to the base.

Page 33 - An angle at the circumference of a circle is measured by half the arc that subtends it. Let BAC be an angle at the circumference : it has for its measure half the arc "BC, which subtends it.

Page 29 - The sine, or right sine, of an arc, is the line drawn from one extremity of the arc, perpendicular to the diameter passing through the other extremity. Thus, BF is the sine of the arc AB, or of the arc BDE.

Page 256 - The HORIZON is a great circle which separates the visible half of the heavens from the invisible ; the earth being considered as a point in the centre of the sphere of the fixed stars.

Page 116 - C = sin. A sin. B sin. C; dividing both sides of this equation by cos. A cos. B cos. C, we have sin. A sin. B sin. C _ sin.

Page 360 - Now it is plain, that if any great circle of the sphere (as 1, 2, 3.) be divided into any number of equal parts, and through the points of division...

Page 23 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...

Page 328 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.