## A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ; Adapted to the Use of Students ; Extracted Mostly from Similar Works of Ludlam, Playfair, Vince, and Bonnycastle |

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### Common terms and phrases

acute adjacent affection analogy angle ACB Answer arc or angle base becomes calculation called centre chord circle comp complement computed consequently contained cosine cotangent difference direction distance Draw drawn equal equation expressed feet find the rest formed formulæ geometry given greater half the sum half their difference height Hence hypothenuse included angle increases known less less than 90 logarithms manner mathematics means measured middle minutes natural negative object observed opposite angle perpendicular plane positive problem produced PROP proportion propositions quadrant quantity radius Required right-angled spherical triangle right-angled triangle rules secant segments side AC signs sine a sine solution sphere spherical triangle station supplement tables taken tangent theorems three angles three sides tion triangle ABC trigonometry versed sine yards

### Popular passages

Page 12 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.

Page ix - 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 23 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.

Page 13 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.

Page 87 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...

Page 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.