Elements of Geometry and Trigonometry |
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Page 158
... of the plane , that line will lie wholly in the plane . Scholium . If any two points of a plane be joined by a straight line , the plane may be turned about that line as an axis , so as to take an infinite number of 158 GEOMETRY .
... of the plane , that line will lie wholly in the plane . Scholium . If any two points of a plane be joined by a straight line , the plane may be turned about that line as an axis , so as to take an infinite number of 158 GEOMETRY .
Page 159
Adrien Marie Legendre Charles Davies. axis , so as to take an infinite number of positions . Hence , we infer that an infinite number of planes may be passed through a given line . PROPOSITION II . THEOREM . Through three points , not in ...
Adrien Marie Legendre Charles Davies. axis , so as to take an infinite number of positions . Hence , we infer that an infinite number of planes may be passed through a given line . PROPOSITION II . THEOREM . Through three points , not in ...
Page 180
... axis of the pyramid . 12. The SLANT HEIGHT of a right pyramid , is the per- pendicular distance from the vertex to any side of the base . 13. A TRUNCATED PYRAMID is that portion of a pyramid included between the base and any plane which ...
... axis of the pyramid . 12. The SLANT HEIGHT of a right pyramid , is the per- pendicular distance from the vertex to any side of the base . 13. A TRUNCATED PYRAMID is that portion of a pyramid included between the base and any plane which ...
Page 210
... axis . Thus , if the rectangle ABCD be turned about the side . AB , as an axis , it will generate the cylinder FGCQ - P . The fixed line AB is called the axis of the cylinder ; the curved surface generated by the side CD , opposite the ...
... axis . Thus , if the rectangle ABCD be turned about the side . AB , as an axis , it will generate the cylinder FGCQ - P . The fixed line AB is called the axis of the cylinder ; the curved surface generated by the side CD , opposite the ...
Page 211
... axes of similar cylinders are proportional to the radii of their bases ( B. IV . , D. 1 ) ; they are also proportional to any other homologous lines of the cylinders . 3 ... axis . Thus , if the triangle SAB , right - angled BOOK VIII . 211.
... axes of similar cylinders are proportional to the radii of their bases ( B. IV . , D. 1 ) ; they are also proportional to any other homologous lines of the cylinders . 3 ... axis . Thus , if the triangle SAB , right - angled BOOK VIII . 211.
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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...