Elements of Geometry and Trigonometry |
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Page 251
Wanting to know the distance between two inaccessible objects which lie in a direct line from the bottom of a tower of 120 feet in height , the angles of depression are measured , and found to be , of the nearest , 57 ° ; of the most ...
Wanting to know the distance between two inaccessible objects which lie in a direct line from the bottom of a tower of 120 feet in height , the angles of depression are measured , and found to be , of the nearest , 57 ° ; of the most ...
Page 274
Thus , when we say that a square yard contains 9 square feet , we should understand that one square foot is taken for the unit of measure , and that this unit is contained 9 times in the square yard . The most convenient unit of measure ...
Thus , when we say that a square yard contains 9 square feet , we should understand that one square foot is taken for the unit of measure , and that this unit is contained 9 times in the square yard . The most convenient unit of measure ...
Page 275
To find the area of a triangle , whose base is 625 and altitude 520 feet . Ans . 162500 sq . ft . 2. To find the number of square yards in a triangle , whose base is 40 and altitude 30 feet . Ans . 663 . 3. To find the number of square ...
To find the area of a triangle , whose base is 625 and altitude 520 feet . Ans . 162500 sq . ft . 2. To find the number of square yards in a triangle , whose base is 40 and altitude 30 feet . Ans . 663 . 3. To find the number of square ...
Page 276
What is the number of square yards in a triangle of which the sides are 25 feet and 21.25 feet , and their included angle 45 ° ? Ans . 20.8694 CASE III . B When the three sides are known . RULE . — 1 . Add the three sides together ...
What is the number of square yards in a triangle of which the sides are 25 feet and 21.25 feet , and their included angle 45 ° ? Ans . 20.8694 CASE III . B When the three sides are known . RULE . — 1 . Add the three sides together ...
Page 277
2 ) 90 45 half - sum . Then , 45 x 25 x 15 x 5 = 84375 . The square root of which is 290.4737 , the required area . 2. How many square yards of plastering are there in a tri . angle whose sides are 30 , 40 , and 50 feet ? Ans . 66 ) .
2 ) 90 45 half - sum . Then , 45 x 25 x 15 x 5 = 84375 . The square root of which is 290.4737 , the required area . 2. How many square yards of plastering are there in a tri . angle whose sides are 30 , 40 , and 50 feet ? Ans . 66 ) .
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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 |