## Elements of Geometry and Trigonometry |

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Page 114

Adrien Marie Legendre Charles Davies. PROPOSITION VI . PROBLEM . A regular

Adrien Marie Legendre Charles Davies. PROPOSITION VI . PROBLEM . A regular

**inscribed polygon**being given , to circumscribe a sim- ilar polygon about the same circle . Let CBAFED be a regular polygon . At T , the middle point of the ... Page 115

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**inscribed polygon**. An easier solution of this problem would be simply to join the points of contact T , N , P , & c . by the chords TN , NP , & c . which likewise would form an**inscribed polygon**similar to the circumscribed one ... Page 117

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**inscribed**poly- gons may always be made less than a given surface . Cor . 1. A circumscribed regular**polygon**, having a given number of sides , is greater than the circie , because the circle makes up but a part of the**polygon**: and for ... Page 118

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**inscribed polygon**, and since the two polygons are regular , they will be similar ( Prop . I. ) ; and therefore when they become equal , they will exactly coin- cide , and have a common perimeter . But as the sides of the circumscribed ... Page 119

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**inscribed**circle ; let ab , in like manner , be a side of the other**polygon**, o its centre , oa and od the radii of the circumscribed and the**inscribed**circles . The perimeters of D B the two**polygons**are to each other as the sides AB ...### Other editions - View all

### Common terms and phrases

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