Plane Trigonometry for the Use of Colleges and Schools: With Numerous Examples |
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A+B+C Algebra angle increases angles are nearly angles included angular AP coincides approximately arithmetical progression calculated centre circular measure circumscribed circumscribed circle cos² cos³ cosec cosine cotangent deduce denote distance equal equation error example expression factors feet formula four right angles given angle given log greater height Hence inscribed circle integer less limit logarithmic sine number of degrees observed obtain places of decimals plane positive angle positive integer preceding article prove quadrant quantity radius regular polygon right angle right-angled triangle sec² secant shew shewn sides Similarly sin A sin sin² sin³ sine and cosine subtend suppose Table tabular logarithmic tan² tan³ tangent theorem tower triangle ABC Trigonometrical Functions Trigonometrical Ratios unity zero µh cot
Popular passages
Page 9 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Page 18 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 93 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 219 - From eight times the chord of half the arc, subtract the chord of the whole arc, and divide the remainder by 3, and the quotient will be the length of the arc, nearly.
Page 93 - The logarithm, of any power, integral or fractional, of a number is equal to the product of the logarithm of the number by the index of the power. For let m = a*'} therefore m' = (a*)' = a", therefore loga (mr) =xr = r log, m.
Page 94 - ... is some number between — 2 and — 3 ; that is, — 3 plus a fraction ; and so on. 5. In the common system, as the logarithms of all numbers which are not ^exact powers of 10 are incommensurable with those numbers, their values can only be obtained approximately, and are expressed by decimals. 6. The integral part of any logarithm is called the CHARACTERISTIC, and the decimal part is sometimes called the MANTISSA.
Page 175 - On the bank of a river there is a column 200 feet high, supporting a statue 30 feet high ; the statue to an observer on the opposite bank subtends the same angle as a man 6 feet high standing at the base of the column : find the breadth of the river.
Page 173 - From a station, B, at the base of a mountain, its summit A is seen at an elevation of 60° ; after walking one mile towards the summit, up a plane making an angle of 30° with the horizon, to another station, C, the angle BCA is observed to be 135° : find the height of the mountain in yards.
Page 1 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Page 92 - The Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number. Thus if m = a", x is called the logarithm of m to the base a.