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 vii
... Polygon , Area of a Regular Polygon ,. To find the Circumference of a Circle , ........ To find the Diameter of a Circle , ... To find the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a ...
... Polygon , Area of a Regular Polygon ,. To find the Circumference of a Circle , ........ To find the Diameter of a Circle , ... To find the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a ...
Page viii
... Polygon , ... 137 Volume of a Prism , 138 Volume of a Pyramid , ........ 189 Volume of the Frustum of a Pyramid , 139 Volume of a Sphere , 141 Volume of a Wedge , 141 Volume of a Prismoid , 144 Volumes of Regular Polyedrons , 146 ...
... Polygon , ... 137 Volume of a Prism , 138 Volume of a Pyramid , ........ 189 Volume of the Frustum of a Pyramid , 139 Volume of a Sphere , 141 Volume of a Wedge , 141 Volume of a Prismoid , 144 Volumes of Regular Polyedrons , 146 ...
Page 15
... POLYGON is a plane figure bounded by straight lines . The bounding lines are called sides of the polygon . The ... REGULAR POLYGON is one which is both equilateral and equiangular . 21. Two polygons are mutually equilateral , when their ...
... POLYGON is a plane figure bounded by straight lines . The bounding lines are called sides of the polygon . The ... REGULAR POLYGON is one which is both equilateral and equiangular . 21. Two polygons are mutually equilateral , when their ...
Page 142
... 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 ...
... 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 ...
Page 143
... regular polygon ; a circle may also be inscribed in it . 1 ° . Let ABCF be a regular polygon : then can the cir- cumference of a circle be circumscribed about it . For , through three consecutive ver- tices A , B , C , describe the ...
... regular polygon ; a circle may also be inscribed in it . 1 ° . Let ABCF be a regular polygon : then can the cir- cumference of a circle be circumscribed about it . For , through three consecutive ver- tices A , B , C , describe the ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence