## A Practical Text-book on Plane and Spherical Trigonometry |

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according acute angle adjacent application Area B₁ base calculated called characteristic circle column cos x cos² cosc cotangent decimal definitions denote derived determined difference distance Dividing draw elements equal equations evident example expressed figure find the values formulę formulę of Art functions Geometry Given giving greater than 90 Hence illustrate increases less than 90 log cos log cosec log sin loga logarithm mantissa method multiply negative Note observation obtain opposite perpendicular positive positive angle prove Putting quadrant quantity radius ratio remaining respectively right angle right triangle rule side similar Similarly sin B sin sin x sin² sinc sine sines and cosines sinx siny solution spherical triangle Substituting subtract taken tanc tangent theorem trigonometrical unity Whence

### Popular passages

Page 118 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.

Page 117 - 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 73 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 157 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 78 - This table is added simply for convenience, as the same mantissas are to be found in the other part of the table. To find the logarithm of any number consisting of four figures. Find, in the column headed N, the first three figures of the given number. Then the mantissa of the required logarithm will be found in the horizontal line corresponding, in the vertical column which has the fourth figure of the given number at the top. If only the last four figures of the mantissa are found, the first two...

Page 70 - If a number is not an exact power of 10, its common logarithm can only be expressed approximately ; the integral part of the logarithm is called the characteristic, and the decimal part the mantissa.

Page 183 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.

Page 68 - Any positive number being selected as a base, the logarithm of any other positive number is the exponent of the power to which the base must be raised to produce the given number. Thus, if a

Page 72 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors.

Page 156 - If two sides of a spherical triangle are unequal, the angles opposite them are unequal, and the greater angle lies opposite the greater side ; and conversely.