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 iii
... taken to represent any one of the class to which it belongs . By this arrangement , the difficulty experienced by beginners in comprehending abstract truths , is lessened , without in any manner impairing the gener ality of the truths ...
... taken to represent any one of the class to which it belongs . By this arrangement , the difficulty experienced by beginners in comprehending abstract truths , is lessened , without in any manner impairing the gener ality of the truths ...
Page 9
... taken as a standard . assumed standard is called the unit of measure . 2. Since the unit of measure is of the same kind as the thing measured , there are as many kinds of units as there are species of quantity . In Geometry , there are ...
... taken as a standard . assumed standard is called the unit of measure . 2. Since the unit of measure is of the same kind as the thing measured , there are as many kinds of units as there are species of quantity . In Geometry , there are ...
Page 10
... taken . or When a compound quantity is to be operated upon as a single quantity , its parts are connected by a ... taken . Thus , 3 ( A + B ) , indicates that the sum of A and B is to be taken three times . The Sign of Equality ...
... taken . or When a compound quantity is to be operated upon as a single quantity , its parts are connected by a ... taken . Thus , 3 ( A + B ) , indicates that the sum of A and B is to be taken three times . The Sign of Equality ...
Page 15
... equilateral , or mutually equilateral , when their sides , taken in the same order , are equal , each to each that is , following their perimeters in the same in the direction , the first side of the one is equal BOOK I. 15.
... equilateral , or mutually equilateral , when their sides , taken in the same order , are equal , each to each that is , following their perimeters in the same in the direction , the first side of the one is equal BOOK I. 15.
Page 16
... taken in the same order , are equal , each to each . 23. A DIAGONAL of a polygon is a line joining the ver tices of two angles , not consecutive . 24. A BASE of a polygon is any one polygon is any one of its sides on which the polygon ...
... taken in the same order , are equal , each to each . 23. A DIAGONAL of a polygon is a line joining the ver tices of two angles , not consecutive . 24. A BASE of a polygon is any one polygon is any one of its sides on which the polygon ...
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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