## Elements of Geometry |

### From inside the book

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Page 79

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**regular Polygons**and the Measure of the Circle . DEFINITION . 262. A POLYGON , which is at the same time equiangular and equilateral , is called a**regular polygon**.**Regular polygons**admit of any number of sides . The equi- lateral ... Page 80

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**regular polygons**of the same number of sides are to each other as their homologous sides , and their surfaces are as the squares of these sides ( 221 ) . 265. Scholium . The angle of a**regular polygon**...**regular polygon**may be inscribed in a ... Page 81

... polygon is inscribed in this circumference . Furthermore , with respect to this circumference , all the sides AB ...

... polygon is inscribed in this circumference . Furthermore , with respect to this circumference , all the sides AB ...

**regular polygon**of a certain number of sides in a given circle , it is only necessary to divide the circumference into ... Page 82

... regular decagon , also a pen- tagon and a

... regular decagon , also a pen- tagon and a

**regular polygon**of fifteen sides . Solution . Divide the radius AO ( fig . 159 ) in extreme and mean ratio at the point M ( 240 ) , take the chord AB equal to the greater segment OM , and AB ... Page 83

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**regular**deca- gon , which is to be applied ten times round on the circumference . For , by joining MB , we have , by construction , or , because AO OM :: OM : AM , AB = OM , AO AB : AB : AM ...**regular**inscribed**polygon**Problems . 83.### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence