## The elements of plane trigonometry |

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A.cos appears approximate base becomes calculated called centre changed CHAPTER circle common computed constant contained correct corresponding cosec cosines decimal described determined Diff difference digits draw equal equation errors expand expression factors figures formulæ functions give given goniometric greater Hence increases increment integer Join known L sin last Article less logarithms magnitude manner mantissa measured method multiplied nearly negative neglecting number of seconds observed obtain opposite perpendicular places plane pole polygon positive powers proved quantity radius regular represented respectively result right angles roots shew shewn sides Similarly sines solid solution solved sphere spherical triangle subtended successively tables tangents THEOREM versin Wherefore whole writing

### Popular passages

Page 141 - Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number.

Page 10 - Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than the circumference of a great circle.

Page 56 - Mathematics which treats of the solution of plane triangles. In every plane triangle there are six parts : three sides and three angles. When three of these parts are given, one being a side, the remaining parts may be found by computation. The operation of finding the unknown parts is called the solution of the triangle.

Page 57 - ... the three interior angles of a triangle are together equal to two right angles.

Page 12 - 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 143 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.

Page 27 - For example, let it be required to prove the formula sin ( A - B) = sin A. cos В - cos A. sin В from the annexed figure, where ВАC' = A, and C'AD — В ; each angle being greater than a right angle.

Page 5 - ... stretched taut from one point to the other. The string will not lie on the parallel, but will evidently be in a plane which passes through the centre of the sphere. If the two points be on a meridian, the stretched string will lie on the meridian. By angular distance between two points on a sphere is meant the angle subtended at the centre of the sphere by the arc joining the given points. Thus in Fig. 4 the angle NOA is the angular distance of A from N.

Page 6 - If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall be together greater than the third.

Page 200 - Three circles whose radii are a, b, c touch each other externally ; prove that the tangents at the points of contact meet in a point whose distance from any one of them is (aba Nj a+b + cj 12.