## Elements of Geometry and Trigonometry |

### From inside the book

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Page 42

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**inscribed**figure is one , of which all the angles have their vertices in the circumference . The circle is then said ...**polygon**is circumscribed about a circle , when all its sides are tangents to the circumference : in the same case , the ... Page 110

Adrien Marie Legendre Charles Davies. PROPOSITION II . THEOREM . Any regular

Adrien Marie Legendre Charles Davies. 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 ... Page 111

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**polygon**has sides : for the arcs being equal , ora CA the chords AB , BC ...**polygon**. Toget erms of Jaupo vllandum gaiod bas : A slymint oil condo lege od tem ...**inscribed**square is to the radius , as the square root of 2 , is to unity ... Page 112

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**inscribed**hexagon is equal to the radius . Hence to inscribe a regular ...**inscribed**, the equilateral triangle ACE may be formed by joining the vertices of ...**polygon**of fifteen sides . Divide the radius AO in extreme and mean ratio at ... Page 113

... , that any of the

... , 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 . PROPOSITION VI . PROBLEM . A regular**inscribed polygon**being K * 15 BOOK V. 113.### 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