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 iv
... corresponds more exactly to the idea intended . Many other departures have been made from the original text , the value and utility of which have been made manifest in the practical tests to which the work has been sub- jected . In the ...
... corresponds more exactly to the idea intended . Many other departures have been made from the original text , the value and utility of which have been made manifest in the practical tests to which the work has been sub- jected . In the ...
Page 46
... corresponding exterior angle , is equal D B C / c to two right angles ( P. I. ) : hence , the sum of all the inte- rior and exterior angles is equal to two right angles taken as many times as the polygon has sides . But 46 GEOMETRY .
... corresponding exterior angle , is equal D B C / c to two right angles ( P. I. ) : hence , the sum of all the inte- rior and exterior angles is equal to two right angles taken as many times as the polygon has sides . But 46 GEOMETRY .
Page 49
... corresponding sides of the other ; they are , therefore , equal : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . BOOK II . RATIOS AND PROPORTIONS . DEFINITIONS . 1. BOOK ...
... corresponding sides of the other ; they are , therefore , equal : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . BOOK II . RATIOS AND PROPORTIONS . DEFINITIONS . 1. BOOK ...
Page 57
... corresponding consequent . From the definition of a continued proportion ( D. 3 ) , A : B :: C : D :: E : hence , F :: G : II , & c . , ཁ | ཊ B B 31 A B = A ; whence , BA = AB ; D = ; whence , BC AD ; A B F = Α A E ; whence , BE = AF ...
... corresponding consequent . From the definition of a continued proportion ( D. 3 ) , A : B :: C : D :: E : hence , F :: G : II , & c . , ཁ | ཊ B B 31 A B = A ; whence , BA = AB ; D = ; whence , BC AD ; A B F = Α A E ; whence , BE = AF ...
Page 58
... corresponding terms of two proportions are equal , each term of the resulting proportion will be the square of the corresponding term in either of the given pro- portions hence , If four quantities are proportional , their squares will ...
... corresponding terms of two proportions are equal , each term of the resulting proportion will be the square of the corresponding term in either of the given pro- portions hence , If four quantities are proportional , their squares will ...
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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