Elements of Geometry |
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Page 2
... opposite to the right angle is called the hypothenuse . Fig . 10. Thus ABC ( fig . 10 ) is a triangle right - angled at A , and the side BC is the hypothenuse . Fig . 11 . Fig . 12 . Fig . 13 . Fig . 14 . Fig . 15 . 17. Among ...
... opposite to the right angle is called the hypothenuse . Fig . 10. Thus ABC ( fig . 10 ) is a triangle right - angled at A , and the side BC is the hypothenuse . Fig . 11 . Fig . 12 . Fig . 13 . Fig . 14 . Fig . 15 . 17. Among ...
Page 6
... opposite angle BCE . It may be demonstrated , in like manner , that the angle ACE is equal to its opposite angle BCD . 35. Scholium . The four angles , formed about a point by two straight lines which cut each other , are together equal ...
... opposite angle BCE . It may be demonstrated , in like manner , that the angle ACE is equal to its opposite angle BCD . 35. Scholium . The four angles , formed about a point by two straight lines which cut each other , are together equal ...
Page 9
... opposite to equal sides ; thus , the equal angles A and D are op- posite to the equal sides BC and EF . THEOREM . 45. In an isosceles triangle , the angles opposite to the equal sides are equal . Demonstration . Let the side AB = AC ...
... opposite to equal sides ; thus , the equal angles A and D are op- posite to the equal sides BC and EF . THEOREM . 45. In an isosceles triangle , the angles opposite to the equal sides are equal . Demonstration . Let the side AB = AC ...
Page 10
... opposite to the greater angle ; and conversely , of the two angles of a triangle , that is the greater , which is opposite to the greater side . Demonstration . 1. Let the angle C > B ( fig . 30 ) , then will the side AB , opposite to ...
... opposite to the greater angle ; and conversely , of the two angles of a triangle , that is the greater , which is opposite to the greater side . Demonstration . 1. Let the angle C > B ( fig . 30 ) , then will the side AB , opposite to ...
Page 11
... opposite sides of the perpendicular , and at equal distances BC , BE , from it , are equal to one another ; 3. Of any two oblique lines AC , AD , or AE , AD , that which is more remote from the perpendicular is the greater ...
... opposite sides of the perpendicular , and at equal distances BC , BE , from it , are equal to one another ; 3. Of any two oblique lines AC , AD , or AE , AD , that which is more remote from the perpendicular is the greater ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence
Bibliographic information
| Title | Elements of Geometry |
| Author | Adrien Marie Legendre |
| Translated by | John Farrar |
| Publisher | Hilliard, Gray, and Company, 1833 |
| Original from | University of Chicago |
| Digitized | 11 Apr 2012 |
| Length | 235 pages |
| Export Citation | BiBTeX EndNote RefMan |