Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 9
... FACES , VOLUMES , and ANGLES : hence , there are four kinds of units of measure , viz . , Units of Length , Units of Surface , Units of Volume , and Units of Angular Measure . 3. GEOMETRY is that branch of Mathematics which treats of ...
... FACES , VOLUMES , and ANGLES : hence , there are four kinds of units of measure , viz . , Units of Length , Units of Surface , Units of Volume , and Units of Angular Measure . 3. GEOMETRY is that branch of Mathematics which treats of ...
Page 148
... face ; which was to be proved . Cor . 1. If the number of sides of the polygons be made greater than any assignable number ; that is , infinite , the difference between their areas will be less than any assignable surface ; that is , it ...
... face ; which was to be proved . Cor . 1. If the number of sides of the polygons be made greater than any assignable number ; that is , infinite , the difference between their areas will be less than any assignable surface ; that is , it ...
Page 157
... faces of the angle . The measure of a diedral angle is the same as that of a plane angle formed by two lines , one drawn in each face , and both perpendicular to the edge at the same point . A diedral angle may be acute , obtuse , or a ...
... faces of the angle . The measure of a diedral angle is the same as that of a plane angle formed by two lines , one drawn in each face , and both perpendicular to the edge at the same point . A diedral angle may be acute , obtuse , or a ...
Page 158
... faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , and whose faces are ASB , BSC , CSD , DSA . A polyedral angle which has but three faces , is called a triedral angle . A ne lines ...
... faces of the angle . Thus , S is the vertex of the polyedral angle , whose edges are SA , SB , SC , SD , and whose faces are ASB , BSC , CSD , DSA . A polyedral angle which has but three faces , is called a triedral angle . A ne lines ...
Page 175
... faces in the lines AB , BC , CD , DE , and EA . From any point within the polygon thus formed , as 0 , draw the straight lines OA , OB , OC , OD , and OE . B D both having com- Now , in the set We then have two sets of triangles , one ...
... faces in the lines AB , BC , CD , DE , and EA . From any point within the polygon thus formed , as 0 , draw the straight lines OA , OB , OC , OD , and OE . B D both having com- Now , in the set We then have two sets of triangles , one ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence