Elements of Geometry and Trigonometry |
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Page 182
Adrien Marie Legendre Charles Davies. PROPOSITION II . THEOREM . In any prism , the sections made by parallel planes are equal polygons . Let the prism AH be intersected by the parallel planes . NP , SV : then are the sections NOPQR ...
Adrien Marie Legendre Charles Davies. PROPOSITION II . THEOREM . In any prism , the sections made by parallel planes are equal polygons . Let the prism AH be intersected by the parallel planes . NP , SV : then are the sections NOPQR ...
Page 186
... prism are equal to the three faces which include a triedral an- gle of a second prism , each to each , and are like placed , the two prisms are equal in all their parts . Let B and b be the vertices of two triedral angles , included by ...
... prism are equal to the three faces which include a triedral an- gle of a second prism , each to each , and are like placed , the two prisms are equal in all their parts . Let B and b be the vertices of two triedral angles , included by ...
Page 188
... prisms . Let ABCD - N be a parallelopipedon , and let a plane be passed through the edges BF and DH : then will the prisms ABD - H and BCD - H be equal in volume . For , through the vertices F and B let planes be passed perpendicular to ...
... prisms . Let ABCD - N be a parallelopipedon , and let a plane be passed through the edges BF and DH : then will the prisms ABD - H and BCD - H be equal in volume . For , through the vertices F and B let planes be passed perpendicular to ...
Page 189
... prism BAD - H and if from the same polyedron we take away the part Feh - H , there will remain the prism Bad - h hence , these prisms are equal in volume . In like manner , it may be shown that the prisms BCD - H and Bcd - h are equal ...
... prism BAD - H and if from the same polyedron we take away the part Feh - H , there will remain the prism Bad - h hence , these prisms are equal in volume . In like manner , it may be shown that the prisms BCD - H and Bcd - h are equal ...
Page 190
... prisms AEI - M and B BFK - L , we have the line AE equal and parallel to BF , and EI equal to FK ; hence , the face ... prism AEI - M , there will remain the parallelopipedon AL : hence , these parallelopipedons are equal in volume ( A ...
... prisms AEI - M and B BFK - L , we have the line AE equal and parallel to BF , and EI equal to FK ; hence , the face ... prism AEI - M , there will remain the parallelopipedon AL : hence , these parallelopipedons are equal in volume ( A ...
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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...