Elements of Geometry and Trigonometry |
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Page 5
... Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 BOOK VIII . The three round bodies , 16 BOOK IX . Of Spherical Triangles and Spherical Polygons , The regular ...
... Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 BOOK VIII . The three round bodies , 16 BOOK IX . Of Spherical Triangles and Spherical Polygons , The regular ...
Page 108
... these two lines are to each other :: √2 : 1 ( Prop . XI . Cor . 4. ) , but which acquires a greater degree of clearness by the geometrical investigation . BOOK V. REGULAR POLYGONS , AND THE MEASUREMENT OF THE 108 GEOMETRY .
... these two lines are to each other :: √2 : 1 ( Prop . XI . Cor . 4. ) , but which acquires a greater degree of clearness by the geometrical investigation . BOOK V. REGULAR POLYGONS , AND THE MEASUREMENT OF THE 108 GEOMETRY .
Page 109
... regular polygon . Regular polygons may have any number of sides : the equi- lateral triangle is one of three sides ; the square is one of four . PROPOSITION I. THEOREM . Two regular polygons of the same number of sides are similar ...
... regular polygon . Regular polygons may have any number of sides : the equi- lateral triangle is one of three sides ; the square is one of four . PROPOSITION I. THEOREM . Two regular polygons of the same number of sides are similar ...
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 ...
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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