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 17. Among the quadrilaterals , we distinguish : The square , which has its sides equal , and its angles right - angles . A The rectangle , which has ...
Thus , in the triangle ABC , right - angled at A , the side BC is the hypothenuse . B 17. Among the quadrilaterals , we distinguish : The square , which has its sides equal , and its angles right - angles . A The rectangle , which has ...
Page 18
The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the B sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the shortest ...
The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the B sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the shortest ...
Page 19
triangle GAC is equal to DEF , since , by construction , they have an equa angle in each , contained by equal ... Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon its ...
triangle GAC is equal to DEF , since , by construction , they have an equa angle in each , contained by equal ... Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon its ...
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 ; A 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 ; A then will the side AC be equal to the side AB .
Page 29
B V D Let ABC be any triangle : then will the angle 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 ...
B V D Let ABC be any triangle : then will the angle 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 angled triangle base become Book called centre chord circle circumference circumscribed common cone consequently contained corresponding 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 logarithm manner means measured meet middle multiplied number of sides 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 sides similar sine solid solid angle sphere spherical triangle square straight line suppose taken tang tangent THEOREM third triangle triangle ABC unit vertex whole
Popular passages
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 31 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon...
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.
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, 1837 |
| Original from | the University of Michigan |
| Digitized | 9 Jun 2007 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |