## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |

### From inside the book

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Page 163

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**polygons**ABCDEF and GHIKLM are equiangular to one another ; and since they are equilateral , the sides about the equal angles are proportion- als ; the**polygon**ABCD is therefore similar to the**polygon**GHIKLM ( def . 1.6 . ) . And ... Page 164

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**polygon**ABCDEF is to the**polygon**GHIKLM as the square of AD to the square of GK ; and they have also been shewn to be similar . Therefore , & c . Q. E. D. COR . Every equilateral**polygon**inscribed in a circle is also equi- angular : For ... Page 165

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**polygon**, and equilateral**polygon**may be described about the circle , the sides of which will each be equal to KL , and will be equal in number to the sides of the inscribed**polygon**. Therefore , KL is the side of an equilateral ... Page 166

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**polygon**inscribed in the circle ABC . Wherefore also , HL is the side of an equilateral**polygon**, of the same number of sides , described about ABC ( 3. 1. Sup . ) . Let the**polygon**described about the circle be called , M and the ... Page 167

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**polygon**M to the difference of the**polygons**; therefore , since the square of AC is greater than M , the square of AF is greater than the difference of the**polygons**( 14.5 ) . The difference of the poly- gons is therefore less than the ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore