Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 13
Page 179
Adrien Marie Legendre Charles Davies. 5. An OBLIQUE PRISM is one whose ... prism is one whose bases are triangles ; a quadrangular prism is one whose ... triangular pyramid is one whose base is a triangle ; a quadrangular pyramid ...
Adrien Marie Legendre Charles Davies. 5. An OBLIQUE PRISM is one whose ... prism is one whose bases are triangles ; a quadrangular prism is one whose ... triangular pyramid is one whose base is a triangle ; a quadrangular pyramid ...
Page 189
... prism ( D. 2 , 4 ) , as are also the polyedrons Bad - h and Bcd - h . ae e Place the triangle Feh upon Bad , so that F shall coincide with B , with a , and h with d ; then , because eE , hH , are perpendicular to the plane Feh , and aA ...
... prism ( D. 2 , 4 ) , as are also the polyedrons Bad - h and Bcd - h . ae e Place the triangle Feh upon Bad , so that F shall coincide with B , with a , and h with d ; then , because eE , hH , are perpendicular to the plane Feh , and aA ...
Page 190
... triangular prisms AEI - M and BFK - L , we have the line AE equal and parallel to BF , and EI equal to FK ; hence ... prism BFK - L , there will remain the parallelopipedon AG ; and if from the same polyedron we take away the prism ...
... triangular prisms AEI - M and BFK - L , we have the line AE equal and parallel to BF , and EI equal to FK ; hence ... prism BFK - L , there will remain the parallelopipedon AG ; and if from the same polyedron we take away the prism ...
Page 197
... For , through any lateral edge , as AF , pass the planes AH , AI , dividing it into triangular prisms . These prisms will all have a common altitude equal to that of the given prism . Now , the volume of any one of the triangular BOOK VII .
... For , through any lateral edge , as AF , pass the planes AH , AI , dividing it into triangular prisms . These prisms will all have a common altitude equal to that of the given prism . Now , the volume of any one of the triangular BOOK VII .
Page 198
... prism is half that of the parallelopipedon , the volume of the prism is also equal to the pro- duct of its base and altitude : hence , the sum of the triangular prisms , which I K H G F D C B E make up the given prism , is equal to the ...
... prism is half that of the parallelopipedon , the volume of the prism is also equal to the pro- duct of its base and altitude : hence , the sum of the triangular prisms , which I K H G F D C B E make up the given prism , is equal to the ...
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
ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cos²a cosec cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment semi-circumference similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume 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...