## Elements of Plane and Spherical Trigonometry: With Practical Applications |

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A B C acute angle Algebra angle equal applications Arithmetics base blog called characteristic complement complete contains corresponding cos² cosec Cosine Cotang decimal denoted determined difference distance divided ELEMENTARY elements equation EXAMPLES Exercises expressed feet figure formulæ fraction Geom Geometry given gives greater Greenleaf's half the sum height Hence horizontal hypothenuse included angle known less log sin logarithmic sine manner Mathematics means measured method middle minutes negative object oblique-angled spherical triangle observed obtain opposite perpendicular plane positive practical Principal Prop quadrants Required respectively right-angled right-angled triangle rods School secant Series side side b equal sin a sin Solution solve the triangle species spherical triangle Substituting subtract sun's taken Tang tangent tangent of half triangle ABC triangle equal trigonometric functions values whence yards

### Popular passages

Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 7 - This process, like its converse (Art. 23), is based upon the supposition that the differences of logarithms are proportional to the differences of their corresponding numbers.

Page 4 - 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=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.

Page 72 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...

Page 43 - 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 39 - ... be at the head of the column, take the degrees at the top of the table, and the minutes on the left ; but if the name be at the foot of the column, take the degrees at the bottom, and the minutes on the right.

Page 46 - The cosine of half of any angle of a plane triangle is equal to the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides.