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

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A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ... John Hymers No preview available - 2016 |

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angle BAC angular points base bisected calculation circular measure circumscribed circle common logarithms consequently corresponding cosb cosc cosec cosē cota cotangent decimal point denoted determined diff difference digits distance equal equation expressed formulae given angle given triangle greater than 90 Hence hypothenuse inscribed integer intersection inverse Trigonometrical functions less than 90 log-cos log-sin logarithms magnitude middle points multiple nēr obtained perpendicular plane triangle pole positive angles positive or negative produced quadrant quantities radius regular polyhedron right angle right-angled triangle secant second member shew Similarly sin a sin sine and cosine sinē solid angle solution sphere spherical triangle Spherical Trigonometry subsidiary angle subtends subtracting suppose tables tangent three sides triangle ABC Trigonometrical Ratios values whole number zero

### Popular passages

Page 9 - ... 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 101 - The logarithm of a product is equal to the sum of the logarithms of its factors.

Page 2 - Degrees, minutes, and seconds are marked by the symbols *, ', "; thus, to represent 14 degrees, 9 minutes, 37,4 seconds, wewriteUe.9'.37",4. 4. Another division of the right angle has sometimes been employed, with a view of assimilating the measures of angles to the decimal notation. In this system the right angle is divided into 100 equal parts called grades, the grade into 100 minutes, the minute into 100 seconds, and so on; and since a minute and second, expressed by decimal parts of a grade,...

Page 133 - 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 2 - The axis of a circle of a sphere is the diameter of the sphere which is perpendicular to the plane of the circle. The ends of the axis are called the poles of the circle.

Page 56 - 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 55 - ... 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 2 - For the purpose of measuring angles, the circumference is divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; each minute into 60 equal parts called seconds.

Page 31 - 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 23 - 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.