Elements of Geometry and Trigonometry |
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Page vii
... SPHERICAL TRIGONOMETRY . PAGE 55 57-59 60-62 63 64-66 67 68-70 71 Spherical Trigonometry Defined , 73 General Principles , 73 Formulas for Right - angled Triangles , 74-76 Napier's Circular Parts , 77 Solution of Right - angled Spherical ...
... SPHERICAL TRIGONOMETRY . PAGE 55 57-59 60-62 63 64-66 67 68-70 71 Spherical Trigonometry Defined , 73 General Principles , 73 Formulas for Right - angled Triangles , 74-76 Napier's Circular Parts , 77 Solution of Right - angled Spherical ...
Page 235
... - circumferences of two great circles . 5. A SPHERICAL WEDGE is a portion of a sphere bounded by a lune and two semicircles meeting in a diameter of the sphere . 6. A SPHERICAL PYRAMID is a portion of of a BOOK IX Spherical Geometry,
... - circumferences of two great circles . 5. A SPHERICAL WEDGE is a portion of a sphere bounded by a lune and two semicircles meeting in a diameter of the sphere . 6. A SPHERICAL PYRAMID is a portion of of a BOOK IX Spherical Geometry,
Page 236
... spherical polygon and sectors of circles whose common centre is the centre of the sphere . The spherical polygon is ... triangle is less than the sum of the other two . Let ABC be a spherical triangle situated on a sphere whose centre is ...
... spherical polygon and sectors of circles whose common centre is the centre of the sphere . The spherical polygon is ... triangle is less than the sum of the other two . Let ABC be a spherical triangle situated on a sphere whose centre is ...
Page 241
... spherical triangle , as poles , arcs be described forming a spherical triangle , the vertices of the angles of this second triangle will be respectively poles of the sides of the first : From the vertices A , B , C , as poles , let the ...
... spherical triangle , as poles , arcs be described forming a spherical triangle , the vertices of the angles of this second triangle will be respectively poles of the sides of the first : From the vertices A , B , C , as poles , let the ...
Page 243
... triangle thus formed will be equal to those of the given triangle , each to each . Let ABC be a spherical triangle situated on a sphere whose centre is 0 , CED and CFD arcs of circles described about B and A as poles , and let DA and DB ...
... triangle thus formed will be equal to those of the given triangle , each to each . Let ABC be a spherical triangle situated on a sphere whose centre is 0 , CED and CFD arcs of circles described about B and A as poles , and let DA and DB ...
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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
ABē ABCD ACē 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...