Elements of Geometry and Trigonometry |
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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 .
Page 21
For , if the angle C < B , it follows , from what has just been proved , that AB < AC ; which is contrary to the hypothesis . If the angle C - B , then the side AB = AC ( Prop . XII . ) ; which is also contrary to the supposition .
For , if the angle C < B , it follows , from what has just been proved , that AB < AC ; which is contrary to the hypothesis . If the angle C - B , then the side AB = AC ( Prop . XII . ) ; which is also contrary to the supposition .
Page 32
... is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the op- posite sides of a parallelogram are equal . - Again , since the triangles are equal , it follows that the angle ...
... is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the op- posite sides of a parallelogram are equal . - Again , since the triangles are equal , it follows that the angle ...
Page 33
In the case of the rhombus , the sides AB , BC , being equal , the triangles AEB , EBC , have all the sides of the one equal to the corresponding sides of the other , and are therefore equal : whence it follows that the angles AEB ...
In the case of the rhombus , the sides AB , BC , being equal , the triangles AEB , EBC , have all the sides of the one equal to the corresponding sides of the other , and are therefore equal : whence it follows that the angles AEB ...
Page 34
Now , since the unit of measure may be made as small as we please , it follows , that magnitudes may be rep- resented by numbers to any degree of exactness , or they will differ from their numerical representatives by less than any ...
Now , since the unit of measure may be made as small as we please , it follows , that magnitudes may be rep- resented by numbers to any degree of exactness , or they will differ from their numerical representatives by less than any ...
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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 |