Elements of Plane Trigonometry: And Their Application to the Measurement of Heights and Distances, Surveying of Land, and Levellings : Particularly Adapted to the Use of High Schools and Academies


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Side 14 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Side 66 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?
Side 52 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Side 27 - In every plane triangle there are six parts : three sides and three angles. Of these, any three being given, provided one of them is a side, the others may be determined. In a right-angled triangle, one of the six parts, viz., the right angle, is always given ; and if one of the acute angles is given, the other is, of course, known. Hence the number of parts to be considered in a right-angled triangle is reduced to four, any two of which being given, the others may be found. It is desirable to have...
Side 7 - BY LOGARITHMS. RULE. From, the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.
Side 15 - QUADRANT. NB The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right-hand column, belong to the degrees below.
Side 14 - A circle is a plane figure bounded by a curved line called the circumference, every point of which is equally distant from a point within called the center, Fig.
Side 12 - In a Right-angled Triangle, the side opposite the right angle is called the Hypothenuse ; and the other two sides are called the Legs, and sometimes the Base and Perpendicular.
Side 11 - A polygon of three sides is called a TRIANGLE ; one of four sides, a QUADRILATERAL ; one of five, a PENTAGON ; one of six, a HEXAGON ; one of seven, a HEPTAGON ; one of eight, an OCTAGON ; one of nine, a NONAGON ; one of ten, a DECAGON ; one of eleven, an UNDECAGON ; one of twelve, a DODECAGON ; and so on.
Side 70 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

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