## An introduction to the theory ... of plane and spherical trigonometry ... including the theory of navigation1839 |

### Common terms and phrases

acute altitude angle CAB arc BF base centre complement construction cosec cosine cotangent degrees diff difference of latitude distance division draw ecliptic equator Euclid extent will reach find the angle formulæ given angle given side greater Greenwich half the sum Hence horizon hypoth less line of numbers line of sines logarithm logarithmic sine mean arc measure meridian moon's natural number Nautical Almanac observed obtuse opposite angles parallax parallel perpendicular plane sailing Plate pole primitive PROPOSITION quadrant rad2 radius rhumb line right angles right ascension right-angled plane triangle right-angled spherical triangle right-angled triangle RULE scale of chords scale of equal SCHOLIUM secant semi-tangents side AC side opposite sin² sphere spherical angle spherical triangle ABC spherical trigonometry straight line subtract supplement Tang tangent of half three angles three sides Trigonometry versed sine

### 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 258 - 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 362 - 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 330 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.