Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 12
Page 191
... solidity will be expressed numerically , by the number of times which the solid contains its unit of measure . A ... find a cube double of a given cube , we should have , unity to the cube - root of 2 , as the edge of the given cube to the ...
... solidity will be expressed numerically , by the number of times which the solid contains its unit of measure . A ... find a cube double of a given cube , we should have , unity to the cube - root of 2 , as the edge of the given cube to the ...
Page 225
... solidity of a sphere whose diameter is this same altitude . Let DMB be the ... find the measure of this segment . The solid generated by the circular ... solidity of the segment , we have , XEFX ( 2BE2 + 2DF2 + 2BEXDF + EF2 + 15 ...
... solidity of a sphere whose diameter is this same altitude . Let DMB be the ... find the measure of this segment . The solid generated by the circular ... solidity of the segment , we have , XEFX ( 2BE2 + 2DF2 + 2BEXDF + EF2 + 15 ...
Page 358
... solidity is a cube , the face of which is equal to the superficial unit in ... find the surface of a right prism . Multiply the perimeter of the base by ... find the surface of a cube , the length of each side being 20 feet . Ans ...
... solidity is a cube , the face of which is equal to the superficial unit in ... find the surface of a right prism . Multiply the perimeter of the base by ... find the surface of a cube , the length of each side being 20 feet . Ans ...
Page 359
... find the surface of a right pyramid . Multiply the perimeter of the base by half the slant height , and the product ... solidity of a prism . 1. Find the area of the base . 2. Multiply the area of the base by the altitude , and the ...
... find the surface of a right pyramid . Multiply the perimeter of the base by half the slant height , and the product ... solidity of a prism . 1. Find the area of the base . 2. Multiply the area of the base by the altitude , and the ...
Page 360
... find the solidity of a pyramid . Multiply the area of the base by one - third of the altitude , and the product will be the solidity ( B. VII . , P. 17 ) . Ex . 1. Required the solidity of a square pyramid , each side of its base ...
... find the solidity of a pyramid . Multiply the area of the base by one - third of the altitude , and the product will be the solidity ( B. VII . , P. 17 ) . Ex . 1. Required the solidity of a square pyramid , each side of its base ...
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
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface Cosine Cotang cube cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area find the solidity frustum given angle given line greater hence homologous homologous sides hypothenuse inches inscribed circle intersect less Let ABCD let fall logarithm magnitudes middle point number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle proportional PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles upper base vertex vertices
Popular passages
Page 24 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Page 38 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 43 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the sum of the exterior angles.
Page 215 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 93 - The area of a parallelogram is equal to the product of its base and altitude.
Page 231 - The angles of spherical triangles may be compared together, by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle.
Page 232 - F, be respectively poles of the sides BC, AC, AB. For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...