Elements of Geometry |
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Page 4
... Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will ... fall upon A , and the point F upon B. These two lines , thus placed , will co- incide with each other throughout ...
... Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will ... fall upon A , and the point F upon B. These two lines , thus placed , will co- incide with each other throughout ...
Page 7
... let the angle A be equal to the angle D , the side AB equal to the side DE , and the side AC equal to the side DF ... fall upon A , and the point E upon B. But , since the angle D is equal to the angle A , when the side DE is placed upon ...
... let the angle A be equal to the angle D , the side AB equal to the side DE , and the side AC equal to the side DF ... fall upon A , and the point E upon B. But , since the angle D is equal to the angle A , when the side DE is placed upon ...
Page 9
... fall upon the side BC , then Fig . 26 it is evident that GC , or its equal EF , is less than BC . Case III . If the ... Let the side AB = DE ( fig . 23 ) , AC = DF , Fig . 23 . BC = EF ; then the angles will be equal , namely , A = D ...
... fall upon the side BC , then Fig . 26 it is evident that GC , or its equal EF , is less than BC . Case III . If the ... Let the side AB = DE ( fig . 23 ) , AC = DF , Fig . 23 . BC = EF ; then the angles will be equal , namely , A = D ...
Page 17
... fall upon the case of the pre- ceding proposition . Let us suppose , then , that they are unequal ; and that , through the point F , the vertex of the greater , we let fall upon AB a perpendicular FG . In the triangle EFG , the sum of ...
... fall upon the case of the pre- ceding proposition . Let us suppose , then , that they are unequal ; and that , through the point F , the vertex of the greater , we let fall upon AB a perpendicular FG . In the triangle EFG , the sum of ...
Page 26
... fall upon G ; therefore the chord AD is equal to the chord EG . Conversely , AC being supposed equal to EO , if the ... Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD and AH , and the radii CD , CH , be drawn ...
... fall upon G ; therefore the chord AD is equal to the chord EG . Conversely , AC being supposed equal to EO , if the ... Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD and AH , and the radii CD , CH , be drawn ...
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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 |