## The Elements of Plane Trigonometry |

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addition angle AP AP base becomes called centre circle circumference circumscribed considered cos A cos cosec cosine cot A cot diameter difference distance Divide draw elevation equal equation equilateral express feet figure formula four given gives greater half height hence hexagon inscribed length less logarithms manner measured miles multiply nearly negative object observed opposite perimeter perpendicular plane triangle polygon positive prove quadrant radii radius ratio regular right angle sector shew sides sin A cos sin A sin sine sine and cosine sinš SITY square subtend subtracted suppose taken tangent tanš touch tower triangle triangle ABC unity UNIV values whole пф

### Popular passages

Page 99 - From a window near the bottom of a house, which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple, equal to 40° ; then from another window, 18 feet directly above the former, the like angle was 37° 30'.

Page 88 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.

Page 100 - Wanting to know my distance from an- inaccessible object 0, on the other side of a river ; and having no instrument for taking angles, but only a chain or cord for measuring distances ; from each of two stations, A and B, which were taken at 500 yards asunder, I measured in a direct line from the object 0 100 yards, viz. AC and BD each equal to 100 yards ; also the diagonal AD measured 550 yards, and the diagonal BC 560.

Page 53 - It depends on the principle, that the difference of the squares of two quantities is equal to the product of the sum and difference of the quantities.

Page 65 - If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from, the point of their intersection lines be drawn perpendicular to the sides which contain the opposite angle...

Page 89 - The square on the side of a regular pentagon inscribed in a circle is equal to the sum of the squares on the sides of the regular hexagon and decagon inscribed in the same circle.

Page 95 - To THEIR DIFFERENCE ; - So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE.

Page 99 - Being on a horizontal plane, and wanting to know the height of a tower placed on the top of an inaccessible hill : I took the angle of elevation of the top of the hill 40°, and of the top of the tower 51°; then measuring in a line directly from it to the distance of 200 feet farther, I found the angle at the top of the tower to be 33

Page 103 - The hypotenuse AB of a right-angled triangle ABC is trisected in the points D, E; prove that if CD, CE be joined, the sum of the squares on the sides of the triangle CDE is equal to two-thirds of the square on AB.

Page 115 - CE is equal to the difference of the segments of the base made by the perpendicular.