Elements of Geometry and Trigonometry |
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Page 11
The side opposite the right angle is called the hypothenuse . 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 ...
The side opposite the right angle is called the hypothenuse . 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 ...
Page 24
If a straight line have two points D and F , equally distant from the extremities A and B , it will be perpendicular to AB at the middle point C. PROPOSITION XVII . THEOREM . If two right angled triangles have the hypothenuse and a side ...
If a straight line have two points D and F , equally distant from the extremities A and B , it will be perpendicular to AB at the middle point C. PROPOSITION XVII . THEOREM . If two right angled triangles have the hypothenuse and a side ...
Page 47
DA In the right angled triangles CAF , с DCG , the hypothenuses CĂ , CD , are equal ; and the side AF , the half of AB , is equal to the side DG , the half of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop .
DA In the right angled triangles CAF , с DCG , the hypothenuses CĂ , CD , are equal ; and the side AF , the half of AB , is equal to the side DG , the half of DE : hence the triangles are equal , and CF is equal to CG ( Book I. Prop .
Page 64
... be always two equal tangents AB , AD , passing through the point A : they are equal , because the right angled triangles CBA , CDA , have the hypothenuse CA common , and the side CB = CD ; hence they are equal ( Book I. Prop .
... be always two equal tangents AB , AD , passing through the point A : they are equal , because the right angled triangles CBA , CDA , have the hypothenuse CA common , and the side CB = CD ; hence they are equal ( Book I. Prop .
Page 78
The square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on the other two sides . > Let the triangle ABC be right angled at A. Having described squares on the three sides ...
The square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on the other two sides . > Let the triangle ABC be right angled at A. Having described squares on the three sides ...
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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 |