## Elements of Geometry and Trigonometry |

### From inside the book

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Page viii

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**Frustum**of a Cone , 121 Area of the Surface of a Sphere , 122 Area of a Zone , 122 Area of a Spherical Polygon , Volume of a Prism ,. • Volume of a Pyramid , Volume of the**Frustum**of a Pyramid , Volume of a Sphere , 123 124 124 125 ... Page 180

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**FRUSTUM**OF A PYRAMID , and the inter- section of the cutting plane with the pyramid , is called the upper base of the**frustum**; the base of the pyramid is cal- led the lower base of the**frustum**. 14. The ALTITUDE of a**frustum**of a ... Page 185

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**frustum**, as AEea , is a trapezoid , whose altitude is equal to Ff , the slant height of the**frustum**; E ( EA + ea ) × Ff But the area of the con- A 13 hence , its area is equal to ( B. IV . , P. VII . ) . vex surface of the**frustum**is ... Page 202

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**frustum**, and whose bases are the lower base of the**frustum**, the upper base of the**frustum**, and a mean proportional between the two bases . Let FGH - h be a**frustum**of any triangular pyramid : then will its volume be equal to that ... Page 203

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**frustum**into three pyramids . The pyra- mid g - FGH , has for its base the lower base FGH of the**frustum**, and its al- titude is equal to that of the**frustum**, because its vertex g , is in the plane of the upper base . The pyramid H ...### 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...