Elements of Geometry and Trigonometry |
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Page 4
The proposition in Book V. , which proves that a polygon and circle may be made to coincide so nearly , as to differ from each other by less than any assignable quantity , has been taken from the Edinburgh Encyclopedia .
The proposition in Book V. , which proves that a polygon and circle may be made to coincide so 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 called 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 called 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 BO be produced till it meets the side AC , in D ...
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 BO be produced till it meets the side AC , in D ...
Page 19
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 the ...
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 the ...
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 contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |