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 138
... number of sides of the polygon . 3. The APOTHEM , is the shortest distance from the centre to either side . The apothegm is equal to the radius of the inscribed circle . cle . PROPOSITION III . PROBLEM . To inscribe a 138 GEOMETRY .
... number of sides of the polygon . 3. The APOTHEM , is the shortest distance from the centre to either side . The apothegm is equal to the radius of the inscribed circle . cle . PROPOSITION III . PROBLEM . To inscribe a 138 GEOMETRY .
Page 145
... apothem . Let GHIK be a regular polygon , O its centre , and OT its apothem , or the radius of the inscribed circle : then will the area of the polygon be equal to half the product of the perimeter and the apothem . For , draw lines ...
... apothem . Let GHIK be a regular polygon , O its centre , and OT its apothem , or the radius of the inscribed circle : then will the area of the polygon be equal to half the product of the perimeter and the apothem . For , draw lines ...
Page 149
... apothem . PROPOSITION XI . PROBLEM . The area of a regular inscribed polygon , and that of a similar circumscribed polygon being given , to find the areas of the regular inscribed and circumscribed polygons having double the number of ...
... apothem . PROPOSITION XI . PROBLEM . The area of a regular inscribed polygon , and that of a similar circumscribed polygon being given , to find the areas of the regular inscribed and circumscribed polygons having double the number of ...
Page 154
... half the product of the circumference and radius . For , inscribe in it a regular poly- gon ACDE Then will the area of this polygon be equal to half the pro- duct of its perimeter and apothem , whatever may be 154 GEOMETRY .
... half the product of the circumference and radius . For , inscribe in it a regular poly- gon ACDE Then will the area of this polygon be equal to half the pro- duct of its perimeter and apothem , whatever may be 154 GEOMETRY .
Page 155
... apothem , whatever may be the number of its sides ( P. VIII . ) . If the number of sides be made infinite , the polygon will coincide with the circle , the perimeter with the circumference , and the apothem with the radius : hence , the ...
... apothem , whatever may be the number of its sides ( P. VIII . ) . If the number of sides be made infinite , the polygon will coincide with the circle , the perimeter with the circumference , and the apothem with the radius : hence , the ...
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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