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 ii
... Equations of the Point , the Straight Line , the Conic Sections , and Surfaces of the first and second order . Babies ' Bifferential AND Entegral Calculus . Davies ' Descriptive Geometry - With its application to Spherical Trigonome ...
... Equations of the Point , the Straight Line , the Conic Sections , and Surfaces of the first and second order . Babies ' Bifferential AND Entegral Calculus . Davies ' Descriptive Geometry - With its application to Spherical Trigonome ...
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 , A < / B , indicates that the square root of A is less than the cube root ...
... 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 , A < / B , indicates that the square root of A is less than the cube root ...
Page 52
... AD = BC , by changing the members of the equation , we have , BC = AD ; dividing both members by AC , we have , B D = or A B :: ≈ : D ; A C which was to be proved . PROPOSITION III . THEOREM . If four quantities are in 52 GEOMETRY ,
... AD = BC , by changing the members of the equation , we have , BC = AD ; dividing both members by AC , we have , B D = or A B :: ≈ : D ; A C which was to be proved . PROPOSITION III . THEOREM . If four quantities are in 52 GEOMETRY ,
Page 58
... equations , member by member , we have , BF AE = DH 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 of ...
... equations , member by member , we have , BF AE = DH 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 of ...
Page 109
... equations , member to member ( A. 2 ) , recollect- ing that BE is equal to EC , we have , AB2 + 4012 で 2 = + 2BE2 2EA2 ; which was to be proved . Cor . Let ABCD b . parallelogram , and BD , AC , its diagonals . Then , since the ...
... equations , member to member ( A. 2 ) , recollect- ing that BE is equal to EC , we have , AB2 + 4012 で 2 = + 2BE2 2EA2 ; which was to be proved . Cor . Let ABCD b . parallelogram , and BD , AC , its diagonals . Then , since the ...
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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