Elements of Geometry and Trigonometry |
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Page 19
triangle GAC is equal to DEF , since , by construction , they have an equal angle in each , contained by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the ...
triangle GAC is equal to DEF , since , by construction , they have an equal angle in each , contained by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the ...
Page 34
If the other magnitude contain a certain number of those units , it also may be expressed by the number of its units ... there may perhaps be a smaller unit which will be contained an exact number of times in each of the magnitudes .
If the other magnitude contain a certain number of those units , it also may be expressed by the number of its units ... there may perhaps be a smaller unit which will be contained an exact number of times in each of the magnitudes .
Page 51
In the same circle , or in equal circles , equal angles having their vertices at the centre , intercept equal arcs on the circumference : and conversely , if the arcs intercepted are equal , the angles * contained by the radii will also ...
In the same circle , or in equal circles , equal angles having their vertices at the centre , intercept equal arcs on the circumference : and conversely , if the arcs intercepted are equal , the angles * contained by the radii will also ...
Page 52
Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is contained times in the angle ACB , and 4 times in ...
Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is contained times in the angle ACB , and 4 times in ...
Page 60
... and the angle which they contain , being given , to describe the triangle . Let the lines B and C be equal to TB TC the given sides , and A the given an- gle . Having drawn the indefinite line DE , at the point D , make the angle .
... and the angle which they contain , being given , to describe the triangle . Let the lines B and C be equal to TB TC the given sides , and A the given an- gle . Having drawn the indefinite line DE , at the point D , make the angle .
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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 |