Elements of Geometry and Trigonometry |
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Page 5
Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 BOOK VIII . The three round bodies , 166 BOOK IX . Of Spherical Triangles and Spherical Polygons , 186 · APPENDIX . The regular Polyedrons , 205 PLANE TRIGONOMETRY .
Planes and Solid Angles , 126 BOOK VII . Polyedrons , 142 BOOK VIII . The three round bodies , 166 BOOK IX . Of Spherical Triangles and Spherical Polygons , 186 · APPENDIX . The regular Polyedrons , 205 PLANE TRIGONOMETRY .
Page 9
A solid or body is that which has length , breadth , and thickness ; and therefore combines the three dimensions of extension . 9. When two straight lines , AB , AC , 2 The principles,
A solid or body is that which has length , breadth , and thickness ; and therefore combines the three dimensions of extension . 9. When two straight lines , AB , AC , 2 The principles,
Page 96
VI . ) ; there- fore the product of three sides of a triangle is equal to its area multiplied by twice the diameter of the circumscribed circle . ` The product of three lines is sometimes called a solid , for a reason that shall be seen ...
VI . ) ; there- fore the product of three sides of a triangle is equal to its area multiplied by twice the diameter of the circumscribed circle . ` The product of three lines is sometimes called a solid , for a reason that shall be seen ...
Page 125
... or the whole circumference must be 3.1415926 , when the diameter is 1 : hence the ratio of the circumference to the diameter , formerly expressed by π , is equal to 3.1415926 . L * BOOK VI . PLANES AND SOLID ANGLES .
... or the whole circumference must be 3.1415926 , when the diameter is 1 : hence the ratio of the circumference to the diameter , formerly expressed by π , is equal to 3.1415926 . L * BOOK VI . PLANES AND SOLID ANGLES .
Page 126
PLANES AND SOLID ANGLES . Definitions , 1. A straight line is perpendicular to a plane , when it is per- pendicular to all the straight lines which pass through its foot in the plane . Conversely , the plane is perpendicular to the line ...
PLANES AND SOLID ANGLES . Definitions , 1. A straight line is perpendicular to a plane , when it is per- pendicular to all the straight lines which pass through its foot in the plane . Conversely , the plane is perpendicular to the line ...
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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 |