## 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 equilateral ... 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**... polygon ( 79 ) . 266. Every regular ... 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 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 1 greater segment OM , and AB ... Page 83

... , 120 , & c . , sides . * * It was supposed , for a long time , that these were the only

... , 120 , & c . , sides . * * It was supposed , for a long time , that these were the only

**polygons**which could be inscribed by the processes of elementary geomFig . 160 PROBLEM . 277. A**regular**inscribed**polygon**ABCD Problems . 83.### Other editions - View all

### Common terms and phrases

ABC fig ABCD adjacent altitude angle ACB applied base called centre chord circ circle circumference circumscribed common cone consequently considered construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces figure follows formed four give given greater half hence homologous sides inclination inscribed join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment sides similar solid angle Solution sphere spherical square straight line suppose surface taken THEOREM third triangle ABC triangular pyramids vertex vertices whence