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 10
... square root of A , and the cube root of B , are to be taken . or When a compound quantity is to be operated upon as a single quantity , its parts are connected by a vinculum by a parenthesis : Thus , A + B x C , indicates that the sum ...
... square root of A , and the cube root of B , are to be taken . or When a compound quantity is to be operated upon as a single quantity , its parts are connected by a vinculum by a parenthesis : Thus , A + B x C , indicates that the sum ...
Page 11
... square root of A is less than the cube root of B. The opening of the sign is towards the greater quantity . The sign , .. is used as an abbreviation of the word hence , or consequently . 5. The general truths of Geometry are deduced by ...
... square root of A is less than the cube root of B. The opening of the sign is towards the greater quantity . The sign , .. is used as an abbreviation of the word hence , or consequently . 5. The general truths of Geometry are deduced by ...
Page 17
... all right angles . A SQUARE is an equilateral rectangle . 2. A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral rhomboid . AXIOMS . 1. Things which are equal to the same 2 BOOK I. 17.
... all right angles . A SQUARE is an equilateral rectangle . 2. A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral rhomboid . AXIOMS . 1. Things which are equal to the same 2 BOOK I. 17.
Page 52
... square of the mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two quantities is equal to the product of two other quantities , two of them may be made the means , and the other two the ...
... square of the mean is equal to the product of the extremes . PROPOSITION II . THEOREM . If the product of two quantities is equal to the product of two other quantities , two of them may be made the means , and the other two the ...
Page 58
... square of the corresponding term in either of the given pro- portions hence , If four quantities are proportional , their squares will be proportional . Cor . 2. If the principle of the proposition be extended to three or more ...
... square of the corresponding term in either of the given pro- portions hence , If four quantities are proportional , their squares will be proportional . Cor . 2. If the principle of the proposition be extended to three or more ...
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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