Elements of Geometry and Trigonometry |
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Page 109
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 ...
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 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 ...
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 ...
... 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 114
Adrien Marie Legendre. 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 arc AB , apply the ...
Adrien Marie Legendre. 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 arc AB , apply the ...
Page 115
... polygon similar to the circumscribed one . Cor . 2. Hence we may circumscribe about a circle any regular polygon , which can be inscribed within it , and con- versely . Cor . 3. It is plain that NH + HT = HT + TG = HG , one of the equal ...
... polygon similar to the circumscribed one . Cor . 2. Hence we may circumscribe about a circle any regular polygon , which can be inscribed within it , and con- versely . Cor . 3. It is plain that NH + HT = HT + TG = HG , one of the equal ...
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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