Elements of Geometry and Trigonometry |
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Page 12
A scholium is a remark on one or several preceding propo- sitions , which tends to point out their connexion , their use , their restriction , or their extension .
A scholium is a remark on one or several preceding propo- sitions , which tends to point out their connexion , their use , their restriction , or their extension .
Page 16
Scholium . The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the ...
Scholium . The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the ...
Page 17
Scholium . Two triangles are said to be equal , when being applied to each other , they will exactly coincide ( Ax . 13. ) . Hence , equal triangles have their like parts equal , each to each , since those parts must coincide with ...
Scholium . Two triangles are said to be equal , when being applied to each other , they will exactly coincide ( Ax . 13. ) . Hence , equal triangles have their like parts equal , each to each , since those parts must coincide with ...
Page 19
... and its equal AB from the other , there will remain GC < BC or BC > EF , B Scholium . Conversely , if two sides BA , AC , of the triangle BAC , are equal to the two ED , DF , of the triangle EDF , each to each , while the third side ...
... and its equal AB from the other , there will remain GC < BC or BC > EF , B Scholium . Conversely , if two sides BA , AC , of the triangle BAC , are equal to the two ED , DF , of the triangle EDF , each to each , while the third side ...
Page 20
Scholium . It may be observed that the equal angles lie op- posite the equal sides : thus , the equal angles D and A , lie op- posite the equal sides EF and BC . PROPOSITION XI . THEOREM . In an isosceles triangle ...
Scholium . It may be observed that the equal angles lie op- posite the equal sides : thus , the equal angles D and A , lie op- posite the equal sides EF and BC . PROPOSITION XI . THEOREM . In an isosceles triangle ...
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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 |