## Elements of Plane Trigonometry, Surveying and Navigation |

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base line bearing Begin calculate called centre chain column compass computed construction convenient corner cosine course departure determined difference direction distance divided division draw drawn earth east employed equal evident example explained extended extreme feet field field book figure given gives ground half height hill horizontal land latitude length logarithm longitude manner mark means measured meridian method miles minutes notes objects observed obtain offsets operations parallel passing perpendicular plane plot position preceding primary principal proceed proportion radius remaining represented respectively right angled river road sailed scale secant seen ship sides sight sine square star station sufficient supposed surface survey taken tangent tion triangle true vertical

### 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 59 - Ans. 23° 3' 55". 4. 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 59 - A line of 36 yards long will exactly reach from the top of a fort to the opposite bank of a river, known to be 24 yards broad ; the height of the wall is required.

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

Page 25 - The CO-SINE of an arc is the sine of the complement of that arc as L.

Page 202 - Radius, is to the tangent of the course; as the meridional difference of latitude, is to the Difference of longitude.

Page 54 - Ans. 22| rods. We may find the distance between two objects which are in the same vertical plane with the perpendicular, by calculating the distance of each from the perpendicular. Thus, AG (Fig. 2.) is equal to the difference between AB and GB. PROBLEM II. To find the HEIGHT of an accessible object standing on an INCLINED PLANE. 9. MEASURE THE DISTANCE FROM THE OBJECT TO A CONVENIENT STATION, AND TAKE THE ANGLES WHICH THIS BASE MAKES WITH LINES DRAWN FROM ITS TWO ENDS TO THE TOP OF THE OBJECT. If...

Page 61 - ... and 63° 41'. Find the distance of each ship from the fort. 235. 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 60 - 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'.

Page 61 - ... to be on a level with the place where I stood, close by the side of the river ; and not having room to measure backward...