## Elements of Plane Trigonometry: With Its Application to Mensuration of Heights and Distances, Surveying and Navigation |

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bearing calculation called centre chain chords circle compass considered construction convenient corresponding course departure determined difference difference of latitude direction distance divided draw drawn east equal evident example expression extended extremity feet field figure given gives ground half height horizontal hypothenuse known latitude length less logarithm longitude manner marked means measure meridian method miles minutes multiply notes object observed obtain opposite parallel passes perpendicular plane plot position principal proportion proposed quadrant radius remaining represent respectively river road sailed scale secant ship side side AC sight similar sine sines and cosines square star station subtracting sufficient supposed survey taken tangent triangle ABC whence yards

### Popular passages

Page 39 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.

Page 58 - From the edge of a ditch 18 feet wide, surrounding a fort, I took the angle of elevation of the top of the wall and found it 62° 40...

Page 48 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 21 - ... the side opposite the given angle is less than the other given side, the solution is impossible.

Page 173 - Radius, is to the tangent of the course; as the meridional difference of latitude, is to the Difference of longitude.

Page 58 - A line 27 yards long, will exactly reach from the top of a fort to the opposite bank of a river, which is known to be 23 yards broad ; what is the height of the fort?

Page 46 - ... others ; thus, 0,17032 2,30103 9,86763 2,33898 the same as before. t Of the manner of measuring the necessary angles and sides and of the instruments that are used for this purpose an account is given in a note subjoined to this part. In the solution of this problem we have made use of the theorem, the sines of the angles are to each other as the sides opposite to these angles.

Page 17 - For this purpose it is divided into 360 equal parts called degrees, each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds. The degrees, minutes, and seconds are marked thus ° ' " ; and 9° 18' 16", are read, 9 degrees 18 minutes and 16 seconds.

Page 60 - From the summit of a tower, whose height is 108 feet, the angles of depression of the top and bottom of a vertical column, standing in the horizontal plane, are found to be 30° and 60° respectively.

Page 59 - Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it ; and at each end of this line I .found the angles subtended by the other end and a tree, close to the bank on the other side of the river, to be 53° and 79° 12'.