Elements of Geometry and Trigonometry |
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Page 11
Thus , in the triangle ABC , right - angled at A , the side BC is the hypothenuse . B ЈА 17. Among the quadrilaterals , we distinguish : The square , which has its sides equal , and its an- gles right - angles .
Thus , in the triangle ABC , right - angled at A , the side BC is the hypothenuse . B ЈА 17. Among the quadrilaterals , we distinguish : The square , which has its sides equal , and its an- gles right - angles .
Page 18
Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . ... If from any point within a triangle , two straight lines be drawn to the extremities of either side , their sum will be ...
Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . ... If from any point within a triangle , two straight lines be drawn to the extremities of either side , their sum will be ...
Page 19
triangle GAC is equal to DEF , since , by construction , they have an equal angle in each , contained by equal sides ... Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or ...
triangle GAC is equal to DEF , since , by construction , they have an equal angle in each , contained by equal sides ... Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or ...
Page 21
Conversely , if two angles of a triangle are equal , the sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB .
Conversely , if two angles of a triangle are equal , the sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB .
Page 29
Let ABC be any triangle : then will the an- gle C + A + B be equal to two right angles . ... and AB cuts them , the alternate angles ABC , BAE , will be equal : hence the three angles of the triangle ABC make up the same sum as the ...
Let ABC be any triangle : then will the an- gle C + A + B be equal to two right angles . ... and AB cuts them , the alternate angles ABC , BAE , will be equal : hence the three angles of the triangle ABC make up the same sum as the ...
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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 |