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angle increases angle PAB angles in terms AP coincides AP moves Arithmetical Progression centre circle circular measure cos2 cosec cosine cotangent decimal decreases numerically deduced denote the radius determine distance divided draw PM perpendicular equation Euclid example feet figure of Art find log find the angle find the height Find the number formula four right angles given angle Given log Hence horizontal plane hypotenuse inscribed known L tan length Let x denote metrical Ratios multiple of four number of degrees number of grades observe the angle opposite side preceding Article present Chapter quadrant PM regular polygon right-angled triangle secant sexagesimal shew sin2 sine solution of triangles solve a triangle straight line drawn subtends an angle Suppose tangent tower triangle having given Trigono Trigonometrical Ratios vers versed sine yards zero
Página 166 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Página 31 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 92 - ... and 24° 19' respectively : how much higher is the cliff than the lighthouse ? Ans. 1942 feet. 77. A person standing on the bank of a river observes -.J ' the elevation of the top of a tree on the opposite bank to be 51...
Página 2 - French method, a right angle is divided into 100 equal parts called grades ; a grade into 300 equal parts called minutes ; a minute into 100 equal parts called seconds. The symbol for each is g V " ; as, for example, 12" 15V 754V means 12 grades, 15 minutes, 75 seconds.
Página 172 - To prove that if 6 be the circular measure of a positive angle less than a right angle, sin 6 lies between 6 and 6 -iff1.
Página 21 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Página 167 - To shew that the angle subtended at the centre of a circle by an arc equal to the radius of the circle if the same for all circles.
Página 32 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art. 9) M—cf, then, raising both sides to the mth power, we have Mm = (a*)"1 = a™ . Therefore, log (Mm) = xm = (log M) X m.
Página 31 - Suppose a' = n, then x is called the logarithm of n to the base a; thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number. The logarithm of n to the base a is written Iog0 n ; thus loga n — x expresses the same relation as a1 = n.