Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 ...
... 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 ...
Page 157
... faces of the angle . A 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 ...
... faces of the angle . A 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 ...
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 . he 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 . he 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 We then have two sets of triangles , one set having a common vertex S , the ...
... 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 We then have two sets of triangles , one set having a common vertex S , the ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface 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 multiplied 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 similar 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 write the following