Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 30
Page 17
... solution of plane triangles . In every plane triangle there are six parts : three sides and three angles . When three of these parts are given , one being a side , the remaining parts may be found by comput- ation . The operation of ...
... solution of plane triangles . In every plane triangle there are six parts : three sides and three angles . When three of these parts are given , one being a side , the remaining parts may be found by comput- ation . The operation of ...
Page 27
... SOLUTION OF RIGHT - ANGLED TRIANGLES . 37. In what follows , we shall designate the three angles of every triangle , by the capital letters A , B , and C , A denoting the right angle ; and the sides lying opposite the angles , by the ...
... SOLUTION OF RIGHT - ANGLED TRIANGLES . 37. In what follows , we shall designate the three angles of every triangle , by the capital letters A , B , and C , A denoting the right angle ; and the sides lying opposite the angles , by the ...
Page 28
... solution of every case of right - angled tri- angles . When the table of logarithmic sines is used , in the solution , Formulas ( 1 ) to ( 6 ) must be made homogeneous , by substituting for sin C , cos C , and tan C , respectively , sin ...
... solution of every case of right - angled tri- angles . When the table of logarithmic sines is used , in the solution , Formulas ( 1 ) to ( 6 ) must be made homogeneous , by substituting for sin C , cos C , and tan C , respectively , sin ...
Page 32
... the right angle , to find the re- maining parts . 40. The angle at the base may be found by Formula ( 12 ) , and the solution may be completed as in Case II . EXAMPLES . 1. Given b = 26 , and c 32 PLANE TRIGONOMETRY .
... the right angle , to find the re- maining parts . 40. The angle at the base may be found by Formula ( 12 ) , and the solution may be completed as in Case II . EXAMPLES . 1. Given b = 26 , and c 32 PLANE TRIGONOMETRY .
Page 35
... 53 ° 7 ′ 49 ′′ , and c = 80 . 4. Given a = 19.209 , and b . and c = 15 , to find B , C , Ans . B = 38 ° 39 ′ 30 ′′ , C = 51 ° 20 ' 30 " , b = 12 . SOLUTION OF OBLIQUE - ANGLED TRIANGLES . 42. In the PLANE TRIGONOMETRY . 35.
... 53 ° 7 ′ 49 ′′ , and c = 80 . 4. Given a = 19.209 , and b . and c = 15 , to find B , C , Ans . B = 38 ° 39 ′ 30 ′′ , C = 51 ° 20 ' 30 " , b = 12 . SOLUTION OF OBLIQUE - ANGLED TRIANGLES . 42. In the PLANE TRIGONOMETRY . 35.
Other editions - View all
Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. 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 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...