## A Treatise on Trigonometry, and on Trigonometrical Tables and Logarithms: Together with a Selection of Problems and Their Solutions |

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Treatise on Trigonometry and Trigonometrical Tables and Logarithms; Together ... John Hymers No preview available - 2012 |

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acute angular base becomes calculation called characteristic circle circular measure circumscribed common computation consequently containing corresponding cosē cosec decimal denoted described determined diff difference digits direction distance dividing division equal equation evidently expressed former formula four give given greater Hence horizontal increase intersect join known latter less log-cos log-sin logarithms magnitude means middle multiple nearly negative object observe obtain opposite perpendicular places plane pole positive produced proportional proved quantities radius relation replacing respectively right angle right-angled triangle shew sides Similarly sin A sin sinē sines and cosines solution sphere spherical triangle substituting subtracting suppose tables tangent telescope triangle Trigonometrical Ratios values zero

### Popular passages

Page 3 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.

Page 95 - The logarithm of a product is equal to the sum of the logarithms of its factors.

Page 127 - suffice to afford such an approximation to it as shall be of use in the ' present stage of the reader's knowledge, and help him to many just ' conceptions, on which account we shall exemplify its application in ' numbers. Now, it appears by observation, that two points, each ten...

Page 50 - 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 49 - ... these elements must be given, one of which must be a side, in order to solve a plane triangle. The solution of plane triangles depends upon the following FUNDAMENTAL PROPOSITIONS. 109. In a right-angled triangle, the side opposite to an acute angle is equal to the product of the hypothenuse into the sine of the angle ; and the side adjacent to an acute angle is equal to the product of the hypothenuse into the cosine of the angle. Let...

Page 25 - В; by means of which we can express the sine and cosine of the sum or difference of two angles in terms of the sines and cosines of the angles themselves.

Page 17 - OP — sin A cos B + cos A sin B. OM_OQ-QM_OQ NR '" OP~ OP ~ OP OP _ OQ_ ON_NR NP "ON'OP~WP'"OP =^cos A cos .B- sin .4 sin B. 77. To express the sine and cosine of the difference of two angles in terms of the sines and cosines of the angles themselves.