## Elements of Geometry and Trigonometry |

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Page 116

Cor It is evident that the

Cor It is evident that the

**circumscribed**square is greater than the**circumscribed**octagon by the four triangles , Cnp , kDg , hEf , Git ; and if a regular polygon of sixteen sides be**circumscribed**about the circle , we may prove in a ... Page 117

Let P represent the

Let P represent the

**circumscribed**polygon , and p the inscribed polygon : then , since the triangles aOb , AOB , are like parts of P and p , we shall have aOb · AOB :: P : p ( Book II . Prop . XI . ) : But the triangles being similar ... Page 118

Since the

Since the

**circumscribed**polygon has the same number of sides as the corresponding inscribed polygon , and since the two polygons are regular , they will be similar ( Prop . I. ) ; and therefore when they become equal , they will exactly ... Page 119

The perimeters of two regular polygons , having the same number of sides , are to each other as the radii of the

The perimeters of two regular polygons , having the same number of sides , are to each other as the radii of the

**circumscribed**circles , and also , as the radii of the inscribed circles ; and their areas are to each other as the squares ... Page 120

... until the number of sides of the polygons shall be indefinitely increased , the perimeters of the polygons will become equal to the circumferences of the

... until the number of sides of the polygons shall be indefinitely increased , the perimeters of the polygons will become equal to the circumferences of the

**circumscribed**circles ( Prop . VIII . Cor . 2. ) , and we shall have circ .### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole