Elements of Geometry and Trigonometry |
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Page 11
... equation . The part on the left of the sign of equality , is called the first member ; that on the right , the second member . The Sign of Inequality , < : Thus , AB , indicates that the square root of A is less than the cube root of B ...
... equation . The part on the left of the sign of equality , is called the first member ; that on the right , the second member . The Sign of Inequality , < : Thus , AB , indicates that the square root of A is less than the cube root of B ...
Page 58
... equations , member by member , we have , BF DH = AE CG ; BF :: whence , AE : which was to be proved . CG : DH ; Cor . 1. If the corresponding terms of two proportions are equal , each term of the resulting proportion will be the square ...
... equations , member by member , we have , BF DH = AE CG ; BF :: whence , AE : which was to be proved . CG : DH ; Cor . 1. If the corresponding terms of two proportions are equal , each term of the resulting proportion will be the square ...
Page 109
... equations , member to member ( A. 2 ) , recollect- ing that BE is equal to EC , we have , AB2 + AC2 = 2BE2EA2 ; which was to be proved . Cor . Let ABCD be a parallelogram , and BD , AC , its diagonals . Then , since the diagonals ...
... equations , member to member ( A. 2 ) , recollect- ing that BE is equal to EC , we have , AB2 + AC2 = 2BE2EA2 ; which was to be proved . Cor . Let ABCD be a parallelogram , and BD , AC , its diagonals . Then , since the diagonals ...
Page 151
... Equation ( 2 ) , we can find P ' . PROPOSITION XII . PROBLEM . To find the approximate area of a circle whose radius ... Equations ( 1 ) and ( 2 ) of Proposition XI . , inscribed octagon , p ' = √8 = 2.8284271 P ' = 2+ 8 16 = 3.3137085 ...
... Equation ( 2 ) , we can find P ' . PROPOSITION XII . PROBLEM . To find the approximate area of a circle whose radius ... Equations ( 1 ) and ( 2 ) of Proposition XI . , inscribed octagon , p ' = √8 = 2.8284271 P ' = 2+ 8 16 = 3.3137085 ...
Page 152
... equations , p ' = 3.0614674 • • inscribed polygon of 16 sides . P ' = 3.1825979 • circumscribed polygon of 16 sides . By a continued application of these equations , we find the areas indicated below , NUMBER OF SIDES . INSCRIBED ...
... equations , p ' = 3.0614674 • • inscribed polygon of 16 sides . P ' = 3.1825979 • circumscribed polygon of 16 sides . By a continued application of these equations , we find the areas indicated below , NUMBER OF SIDES . INSCRIBED ...
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Common terms and phrases
ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence