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
... Regular Polygons - Measurement of the Circle , PAGE . 9 13 20 50 50 82 8889 59 93 129 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons ,. 178 Cylinder , Couc , and Sphere , BOOK VIII .
... Regular Polygons - Measurement of the Circle , PAGE . 9 13 20 50 50 82 8889 59 93 129 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons ,. 178 Cylinder , Couc , and Sphere , BOOK VIII .
Page 15
... Polygons are classified according to the number of their sides or angles . A Polygon of three sides is called a ... REGULAR POLYGON , is one which is both equilateral and equiangular . 21. Two polygons are mutually equilateral , when ...
... Polygons are classified according to the number of their sides or angles . A Polygon of three sides is called a ... REGULAR POLYGON , is one which is both equilateral and equiangular . 21. Two polygons are mutually equilateral , when ...
Page 135
... . On X as a side , homologous to A or B , construct a polygon similar to the given polygons , and it will be equal to their sum or difference ( P. XXVII . , C. 2 ) . BO.OK V. REGULAR POLYGONS . -AREA OF THE CIRCLE . BOOK IV . 135.
... . On X as a side , homologous to A or B , construct a polygon similar to the given polygons , and it will be equal to their sum or difference ( P. XXVII . , C. 2 ) . BO.OK V. REGULAR POLYGONS . -AREA OF THE CIRCLE . BOOK IV . 135.
Page 136
... REGULAR POLYGONS . -AREA OF THE CIRCLE . DEFINITION . 1. A REGULAR POLYGON is a polygon which is both equilateral and equiangular . PROPOSITION I. THEOREM . Regular polygons of the same number of sides are similar . Let ABCDEF and abcdef be ...
... REGULAR POLYGONS . -AREA OF THE CIRCLE . DEFINITION . 1. A REGULAR POLYGON is a polygon which is both equilateral and equiangular . PROPOSITION I. THEOREM . Regular polygons of the same number of sides are similar . Let ABCDEF and abcdef be ...
Page 145
... regular circumscribed polygon of double the number of sides , because the whole is greater than any of its parts ... polygons of 8 , 16 , 32 , & c . , sides . By means of the regular hexagon , we may , in like manner , construct regular ...
... regular circumscribed polygon of double the number of sides , because the whole is greater than any of its parts ... polygons of 8 , 16 , 32 , & c . , sides . By means of the regular hexagon , we may , in like manner , construct regular ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence