Elements of Geometry and Trigonometry |
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Page 210
... SPHERE . DEFINITIONS . E A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . Thus , if the rectangle ABCD be turned about the side . AB , as an axis , it will generate the cylinder ...
... SPHERE . DEFINITIONS . E A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . Thus , if the rectangle ABCD be turned about the side . AB , as an axis , it will generate the cylinder ...
Page 214
... SPHERE is a volume bounded by a surface , every point of which is equally distant from a point within called the centre . A sphere may be generated by a semicircle revolving about its diameter as an axis . 13. A RADIUS of a sphere is a ...
... SPHERE is a volume bounded by a surface , every point of which is equally distant from a point within called the centre . A sphere may be generated by a semicircle revolving about its diameter as an axis . 13. A RADIUS of a sphere is a ...
Page 215
... sphere , the zone has but one base . 17 . A SPHERICAL SEGMENT is a portion of a sphere in- cluded between two parallel planes . The sections made by the planes are called bases of the segment , and the distance between them is called ...
... sphere , the zone has but one base . 17 . A SPHERICAL SEGMENT is a portion of a sphere in- cluded between two parallel planes . The sections made by the planes are called bases of the segment , and the distance between them is called ...
Page 221
... sphere made by a plane , is a circle . Let C be the centre of a sphere , CA radii , and AMB any section made by a plane this section be a circle . perpen- For , draw a radius CO dicular to the cutting plane , and let it pierce the plane ...
... sphere made by a plane , is a circle . Let C be the centre of a sphere , CA radii , and AMB any section made by a plane this section be a circle . perpen- For , draw a radius CO dicular to the cutting plane , and let it pierce the plane ...
Page 222
Adrien Marie Legendre Charles Davies. is called a small circle of the sphere . All great circles of the same , or of equal spheres , are equal . Cor . 2. Any great circle divides the sphere , and also the surface of the sphere , into ...
Adrien Marie Legendre Charles Davies. is called a small circle of the sphere . All great circles of the same , or of equal spheres , are equal . Cor . 2. Any great circle divides the sphere , and also the surface of the sphere , into ...
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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
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...