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Algebra angle increases angles included angular points AP coincides approximately arithmetical progression Binomial Theorem calculated centre circle inscribed circular measure circumference circumscribed circle coefficient cosec cosine cotangent deduce denote determine distance divided equal error escribed circles Euclid example expression factors feet figure formed by joining formula four right angles fraction given angle given log greater height Hence hypotenuse indefinitely integer limit logarithmic sine multiple nine points circle number of degrees number of grades obtain opposite sides places of decimals plane positive angle positive integer positive or negative preceding Article produced prove quadrant quadrilateral quantity radii radius regular polygon respectively result right-angled triangle root secant sexagesimal shew shewn Similarly Solve the equation straight line subtend suppose Table tabular logarithmic tangent Taylor's Theorem theorem tower triangle ABC Trigonometrical Functions Trigonometrical Ratios Trigonometrical Tables zero
Page 9 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Page 1 - Accordingly a right angle is divided into 90 equal parts called degrees; and any angle may be estimated by ascertaining the number of degrees which it contains. If the angle does not contain an exact number of degrees we can express it in degrees and a fraction of a degree. A degree is divided into 60 equal parts called minutes, and a minute into 60 equal parts called seconds; and thus a fraction of a degree may if we please be converted into minutes and seconds.
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 56 - B. cos (A + B) - cos A cos B - sin A sin B. cos (A - B) = cos A cos B + sin A sin B.
Page 37 - PM is equal to AP; thus as the angle increases from 0 to 90° the sine increases from 0 to 1. While AP moves through the second quadrant PM is positive, and continually decreases until AP coincides with AB...
Page 221 - 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 94 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 94 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 93 - 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.