## A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical Applications |

### Other editions - View all

A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle No preview available - 2014 |

A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle No preview available - 2018 |

### Common terms and phrases

A B C acute added adjacent altitude ambiguous angle apparent base become CALCULATION centre chords circle complement cosec cosine declination describe diameter diff difference distance draw equal equation Example expressions extent will reach feet former formulæ given given side gives greater greater than 90 half height Hence horizon hypothenuse kind latitude latter less than 90 logarithms longitude manner means measured meridian moon's Note object oblique oblique-angled observed obtain opposite opposite angle passing perpendicular points pole PROBLEM projected quadrant radius remaining right ascension right-angled spherical triangle rising RULE scale semitangent side sines sphere spherical triangle spherical triangle ABC star substituted sun's supplement tables taken tangents THEOREM trigonometry true unlike whence

### Popular passages

Page xxxi - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.

Page 6 - ... for the second term, and the greater for the first ; and in either case multiply the second and third terms together, and divide the product by the first for the answer, which will always be of the same denomination as the third term.

Page 329 - 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 363 - The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side.

Page vii - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.

Page 13 - 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 17 - 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 2 - SECANT of an arc, is a straight line drawn from the centre, through one end of the arc, and extended to the tangent which is drawn from the other end.

Page 181 - The AMPLITUDE of any object in the heavens is an arc of the horizon, contained between the centre of the object when rising, or setting, and the east or west points of the horizon. Or, it is...

Page 75 - Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them.