Elements of Geometry and Trigonometry |
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Page 190
... lower base , and their upper bases between the same parallels , they are equal in volume . Let the parallelopipedons AG and AL have the com- mon lower base ABCD , and their upper bases EFGH and IKLM , between the same parallels EK and ...
... lower base , and their upper bases between the same parallels , they are equal in volume . Let the parallelopipedons AG and AL have the com- mon lower base ABCD , and their upper bases EFGH and IKLM , between the same parallels EK and ...
Page 191
... lower base and the same altitude , they will be equal in volume . Let the parallelopipedons AG and AL have the com- mon lower base ABCD and the same altitude : then will they be equal in volume . Because they have the same altitude ...
... lower base and the same altitude , they will be equal in volume . Let the parallelopipedons AG and AL have the com- mon lower base ABCD and the same altitude : then will they be equal in volume . Because they have the same altitude ...
Page 193
... lower base , are to each other as their altitudes . Let the parallelopipedons AG and AL have the com‐ mon lower base ABCD : then will they be to each other as their altitudes AE and AI 1o . Let the altitudes be commensurable , and ...
... lower base , are to each other as their altitudes . Let the parallelopipedons AG and AL have the com‐ mon lower base ABCD : then will they be to each other as their altitudes AE and AI 1o . Let the altitudes be commensurable , and ...
Page 202
... base of the given pyramid : hence , the volume of the given pyramid is equal to one- third of the product of its ... lower base of the frustum , the upper base of the frustum , and a mean proportional between the two bases . Let FGH - h ...
... base of the given pyramid : hence , the volume of the given pyramid is equal to one- third of the product of its ... lower base of the frustum , the upper base of the frustum , and a mean proportional between the two bases . Let FGH - h ...
Page 203
... 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 - fgh , has for its base the upper base fgh of the frustum , and 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 - fgh , has for its base the upper base fgh of the frustum , and its ...
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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...