Elements of Geometry and Trigonometry |
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Page 4
The propo- sition in Book V. , which proves that a polygon and circle may be made to coincide sò nearly , as to differ from each other by less than any assignable quantity , has been taken from the Edinburgh Encyclopedia .
The propo- sition in Book V. , which proves that a polygon and circle may be made to coincide sò nearly , as to differ from each other by less than any assignable quantity , has been taken from the Edinburgh Encyclopedia .
Page 10
When two straight lines , AB , AC , meet each other , their inclination or opening is call- ed an angle , which is greater or less as the lines are more or less inclined or opened . The point of intersection A is the vertex of the angle ...
When two straight lines , AB , AC , meet each other , their inclination or opening is call- ed an angle , which is greater or less as the lines are more or less inclined or opened . The point of intersection A is the vertex of the angle ...
Page 18
If from any point within a triangle , two straight lines be drawn to the extremities of either side , their sum will be less than the sum of the two other sides of the triangle . Let any point , as O , be taken within the trian- gle BAC ...
If from any point within a triangle , two straight lines be drawn to the extremities of either side , their sum will be less than the sum of the two other sides of the triangle . Let any point , as O , be taken within the trian- gle BAC ...
Page 19
E F For , if not , the angle BAC must be equal to EDF , or less than it . In the first case , the side BC would be equal to EF , ( Prop . V. Cor . ) ; in the second , CB would be less than EF ; but either of these results contradicts ...
E F For , if not , the angle BAC must be equal to EDF , or less than it . In the first case , the side BC would be equal to EF , ( Prop . V. Cor . ) ; in the second , CB would be less than EF ; but either of these results contradicts ...
Page 20
... if the angle D were less than A , it would follow , that the side EF must be less than BC : but EF is equal to BC , by hypothesis ; therefore , the angle D can neither be greater nor less than A ; therefore it must be equal to it .
... if the angle D were less than A , it would follow , that the side EF must be less than BC : but EF is equal to BC , by hypothesis ; therefore , the angle D can neither be greater nor less than A ; therefore it must be equal to it .
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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 |