Elements of Geometry and Trigonometry |
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Page 16
E D FB A For , these triangles may be so applied to each other , that they shall exactly coincide . Let the triangle EDF , be placed upon the triangle BAC , so that the point E shall fall upon B , and the side ED on the equal side BA ...
E D FB A For , these triangles may be so applied to each other , that they shall exactly coincide . Let the triangle EDF , be placed upon the triangle BAC , so that the point E shall fall upon B , and the side ED on the equal side BA ...
Page 17
DF is equal to AC ; therefore , the point F will fall on C , and the third side EF , will coincide with the third side BC ( Ax . 11. ) : therefore , the triangle EDF is equal to the triangle BAC ( Ax . 13. ) . Cor .
DF is equal to AC ; therefore , the point F will fall on C , and the third side EF , will coincide with the third side BC ( Ax . 11. ) : therefore , the triangle EDF is equal to the triangle BAC ( Ax . 13. ) . Cor .
Page 19
Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon ... If the point G fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) ...
Now , there may be three cases in the proposition , according as the point G falls without the triangle ABC , or upon ... If the point G fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) ...
Page 22
If from a point without a straight line , a perpendicular be let fall on the line , and oblique lines be drawn to different points : 1st , The perpendicular will be shorter than any oblique line . 2d , Any two oblique lines , drawn on ...
If from a point without a straight line , a perpendicular be let fall on the line , and oblique lines be drawn to different points : 1st , The perpendicular will be shorter than any oblique line . 2d , Any two oblique lines , drawn on ...
Page 25
For , if they could meet in a point Q , on either side of AB , there would be two per- B D pendiculars OA , OB , let fall from the same point on the same straight line ; which is impossible ( Prop . XIV . ) . PROPOSITION XIX . THEOREM .
For , if they could meet in a point Q , on either side of AB , there would be two per- B D pendiculars OA , OB , let fall from the same point on the same straight line ; which is impossible ( Prop . XIV . ) . PROPOSITION XIX . THEOREM .
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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 |