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 arc AD .
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 arc AD .
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 po- sitions 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 po- sitions 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 pro- ducts 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 pro- ducts 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 have their angles equal each to each , namely , BAC - CDE , ABC - DCE and ACB DEC ; then the homologous ...
Two equiangular triangles have their homologous sides propor- tional , and are similar . -- Let ABC , CDE be two triangles which have their angles equal each to each , namely , BAC - CDE , ABC - DCE and 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 ...
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 ...
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied 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 shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole
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, 1834 |
| Original from | the University of California |
| Digitized | 14 Oct 2010 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |