An introduction to plain trigonometry, with its application to heights and distances

M. Heavisides, for the author, 1792 - 99 pages

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Page 72 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Page xvi - If equal quantities be added to equal quantities, the sums will be equal.
Page 91 - 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 80 - What is the perpendicular height of a hill whose angle of elevation, taken at the bottom of it, was 46° ; and 100 yards farther off, on a level with the bottom of it, the angle was 31° ? Ans., 143.14 yards.
Page 85 - I measured out for a base 400 yards in a right line by the side of the river, and found that the two angles, one at each end of this line, subtended by the other end and the house, were 68° 2
Page 85 - Being on one side of a river and wanting to know the distance to a house, which stood on the other side, I measured 200 yards in a right line by the side of the river, and found that the two angles at each end of this line formed by the other end and the house were 73° 15' and 68° 2'; what was the distance between each station and the house ? Ans.
Page 69 - As the sum of the two sides Is to their difference, So is the tan of half the sum of the unknown angles To the tan of half the difference of the unknown angles. And this tan half difference added to the half sum of two unknown angles gives the greater angle, and subtracted gives the less angle. Taking the example already given (fig. 29) : — AC + AD = 50 + 40...
Page xxv - Triangles on the fame Bafe, and between the fame Parallels, are equal ; becaufe they are Half the circumfcribing Parallelograms.
Page 82 - I meafured from its bottom a diftance of 40 feet, and then took the angle formed by the plane and a line drawn to the top 41"; and going 'on in the fame...
Page 44 - DE, and ercdl the perpendicular DF ; which, it is evident, will be the tangent, and AF the fecant of the arc DE, or angle A, to the radius AD.

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