Elements of Geometry and Trigonometry |
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Page 53
By a process of reasoning entirely similar , it may be shown that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB : angle ACD : : arc AB ...
By a process of reasoning entirely similar , it may be shown that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB : angle ACD : : arc AB ...
Page 68
Similar figures are those which have the angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . 2. Any two sides , or any two angles , which have like positions in two ...
Similar figures are those which have the angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . 2. Any two sides , or any two angles , which have like positions in two ...
Page 73
that the area of any other rectangle is computed in a similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two products is the same as that of the rectangles ...
that the area of any other rectangle is computed in a similar manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two products is the same as that of the rectangles ...
Page 84
Two equiangular triangles have their homologous sides propor . tional , and are similar . Let ABC , CDE be two triangles which E have their angles equal each to each , namely , BAC = CDE , ABC - DCE and А ACB = DEC ; then the homologous ...
Two equiangular triangles have their homologous sides propor . tional , and are similar . Let ABC , CDE be two triangles which E have their angles equal each to each , namely , BAC = CDE , ABC - DCE and А ACB = DEC ; then the homologous ...
Page 85
Observe , that in similar triangles , the homolo gous sides are opposite to the equal angles ; thus the angle ACB being equal to DEC , the side AB is homologous to DC ; in like manner , AC and DE are homologous , because opposite to the ...
Observe , that in similar triangles , the homolo gous sides are opposite to the equal angles ; thus the angle ACB being equal to DEC , the side AB is homologous to DC ; in like manner , AC and DE are homologous , because opposite to 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 |