## Elements of Geometry |

### From inside the book

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Page 81

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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 82

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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**is deter- mined by the number of ... Page 83

... 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 84

... regular decagon , also a pentagon and a

... regular decagon , also a pentagon 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 will ... Page 85

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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 ...**polygon**of 15 sides . It is man- ifest , at the same time , that the arc CL is a third of CB . 276. Scholium . A ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence