## The Elements of Plane Trigonometry |

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angle ACB angle is equal angle of elevation angular arithmetical progression bisecting book of Euclid centre circular measure circumference circumscribed circle complement cos\A cos2 cosB cosec cosM coss cosy cot A cot cot2 decagon diagonal diameter difference distance Divide dodecagon equation equilateral triangle Euclid feet Find the number find the sides formula given height Hence hexagon inscribed circle Inverse trigonometrical functions Let the angle log cot logarithms miles multiply negative nth root number of degrees number of sides Oa cot perimeter plane triangle positive prove quadrant quadrilateral radii radius ratio regular polygon right angle right-angled triangle sec2 secant segment shew sin'A sin2 sin4 sinB sine and cosine sinM square subtend subtracted tan2 tangent tanM tanx tower triangle ABC Trigonometry unity values versed sine whole number

### Popular passages

Page 97 - 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 97 - Wanting to know the height of an inaccessible tower; at the least distance from it, on the same horizontal plane, I took its angle of elevation equal to 58°; then going 300 feet directly from it, found the angle there to be only 32°: required its height, and my distance from it at the first station?

Page 86 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.

Page 51 - 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 63 - 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 87 - 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 93 - To THEIR DIFFERENCE ; - So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE.

Page 98 - 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. What then was the distance of the object 0 from each, station A and B ? . C AO...

Page 97 - 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° 45'.

Page 101 - 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.