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 v
... Measurement of Angles , .... Problems relating to the First and Third Books ,. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , 82 ...
... Measurement of Angles , .... Problems relating to the First and Third Books ,. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , 82 ...
Page 9
... measured . The To measure a thing is to find how many times it contains some other thing of the same kind , 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 ...
... measured . The To measure a thing is to find how many times it contains some other thing of the same kind , 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 ...
Page 26
... measured on any broken line AB , BC , A4 C is greater than the distance measured on the straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ; which was to be proved . Cor . If from both members of the inequality ...
... measured on any broken line AB , BC , A4 C is greater than the distance measured on the straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ; which was to be proved . Cor . If from both members of the inequality ...
Page 58
... extended to three or more proportions , and the corresponding terms of each be supposed equal , it will follow that , like powers of proportional quantities are proportionals . ВО ОК III . THE CIRCLE , AND THE MEASUREMENT 58 GEOMETRY .
... extended to three or more proportions , and the corresponding terms of each be supposed equal , it will follow that , like powers of proportional quantities are proportionals . ВО ОК III . THE CIRCLE , AND THE MEASUREMENT 58 GEOMETRY .
Page 59
... MEASUREMENT OF ANGLES . DEFINITIONS . 1. A CIRCLE is a plane figure , bounded by a curved line , every point of which is equally distant from a point within , called the centre . The bounding line is called the cir- cumference . D 2. A ...
... MEASUREMENT OF ANGLES . DEFINITIONS . 1. A CIRCLE is a plane figure , bounded by a curved line , every point of which is equally distant from a point within , called the centre . The bounding line is called the cir- cumference . D 2. A ...
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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