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 . It the angle CB , 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 . It the angle CB , then the side AB = AC ( Prop . XII . ) ; which is also contrary to the supposition .
Page 22
from whence it follows , that between the same two points , A and F , two straight lines can be drawn , which is impossible ( Ax . 11. ) : hence , two perpendiculars cannot be drawn from the same point to the same ...
from whence it follows , that between the same two points , A and F , two straight lines can be drawn , which is impossible ( Ax . 11. ) : hence , two perpendiculars cannot be drawn from the same point to the same ...
Page 32
... is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the opposite sides of a parallelogram are equal . - Again , since the triangles are equal , it follows that the angle A is ...
... is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the opposite sides of a parallelogram are equal . - Again , since the triangles are equal , it follows that the angle A is ...
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 ...
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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 |