Elements of Geometry and Trigonometry |
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Page 5
The Proportions of Figures and the Measurement of Areas , - Problems relating to the Fourth Book , 41 57 98 88888 68 BOOK V. Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII .
The Proportions of Figures and the Measurement of Areas , - Problems relating to the Fourth Book , 41 57 98 88888 68 BOOK V. Regular Polygons and the Measurement of the Circle , 109 BOOK VI . Planes and Solid Angles , 126 BOOK VII .
Page 108
... since 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 .
... since 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
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 : the equi- lateral ...
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 : the equi- lateral ...
Page 110
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 centre being O , and OP the perpendicular let fall ...
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 centre being O , and OP the perpendicular let fall ...
Page 111
... hence likewise the triangles AOB , BOC , COD , must ED A B be equal , because the sides are equal each to each ; hence all the angles ABC , BCD , CDE , & c . will be equal ; hence the figure ABCDEH , will be a regular polygon .
... hence likewise the triangles AOB , BOC , COD , must ED A B be equal , because the sides are equal each to each ; hence all the angles ABC , BCD , CDE , & c . will be equal ; hence the figure ABCDEH , will be a regular polygon .
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Edition | 4 |
| Publisher | A.S. Barnes and Company, 1834 |
| Original from | the University of California |
| Digitized | 14 Oct 2010 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |