Elements of Geometry and Trigonometry |
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Page 12
The sign = is the sign of equality ; thus , the expression A = B , signifies that A is equal to B. To signify that A is ... To signify that A is greater than B , the expression A > B is used ; the smaller quantity being always at the ...
The sign = is the sign of equality ; thus , the expression A = B , signifies that A is equal to B. To signify that A is ... To signify that A is greater than B , the expression A > B is used ; the smaller quantity being always at the ...
Page 13
... but this expression should not be employed , wher there is any danger of confounding it with that of the line AB , which expresses the distance between the points A and B. The expression A x ( B + C - D ) represents the product of A ...
... but this expression should not be employed , wher there is any danger of confounding it with that of the line AB , which expresses the distance between the points A and B. The expression A x ( B + C - D ) represents the product of A ...
Page 30
each of its angles will be equal to the third part of two right angles ; so that , if the right angle is expressed by unity , the angle of an equilateral triangle will be expressed by . Cor . 6. In every triangle ABC , the exterior ...
each of its angles will be equal to the third part of two right angles ; so that , if the right angle is expressed by unity , the angle of an equilateral triangle will be expressed by . Cor . 6. In every triangle ABC , the exterior ...
Page 34
Thus , if A and B represent quantities of the same kind , the ratio of A to B is exB pressed by A The ratios of magnitudes may be expressed by numbers , either exactly or approximatively ; and in the latter case , the approximation may ...
Thus , if A and B represent quantities of the same kind , the ratio of A to B is exB pressed by A The ratios of magnitudes may be expressed by numbers , either exactly or approximatively ; and in the latter case , the approximation may ...
Page 35
In the same manner , the ratio of any other two magnitudes C and D may be expressed by PxC to Q x C ' , P and Q being also integral numbers , and their ratio will be the same as that of P to Q. 2. If there be four magnitudes A ...
In the same manner , the ratio of any other two magnitudes C and D may be expressed by PxC to Q x C ' , P and Q being also integral numbers , and their ratio will be the same as that of P to Q. 2. If there be four magnitudes A ...
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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 |