## Elements of Geometry and Trigonometry |

### From inside the book

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Page 109

Adrien Marie Legendre. BOOK V.

Adrien Marie Legendre. BOOK V.

**REGULAR POLYGONS**, AND THE MEASUREMENT OF THE CIRCLE . Definition . A POLYGON , which is at once equilateral and equiangular , is called a**regular polygon**.**Regular polygons**may have any number of sides ... Page 110

Adrien Marie Legendre. PROPOSITION II . THEOREM . Any

Adrien Marie Legendre. PROPOSITION II . THEOREM . Any

**regular polygon**may be inscribed in a circle , and circum- scribed about one . Let ABCDE & c . be a regular poly- gon : describe a circle through the three points A , B , C , the ... Page 111

...

...

**regular polygon**. PROPOSITION III . PROBLEM . To inscribe a square in a given circle . Draw two diameters AC , BD , cut- ting each other at right angles ; join their extremities A , B , C , D : the figure ABCD will be a square . For the ... Page 112

... regular decagon ; then a pentagon , and also a

... regular decagon ; then a pentagon , and also a

**regular polygon**of fifteen sides . Divide the radius AO in extreme and mean ratio at 112 GEOMETRY . Page 113

... It is further evident , that any of the inscribed

... It is further evident , that any of the inscribed

**polygons**will be less than the inscribed**polygon**of double the number of sides , since a part is less than the whole . H PROPOSITION VI . PROBLEM . A**regular**inscribed**polygon**being BOOK V.### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex