Elements of Geometry and Trigonometry |
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Page 96
For , drawing AE , the triangles ABD , AEC , are right angled , the one at D , the E other at A : also the angle B = E ; these ... The product of three lines is sometimes called a solid , for a reason that shall be seen afterwards .
For , drawing AE , the triangles ABD , AEC , are right angled , the one at D , the E other at A : also the angle B = E ; these ... The product of three lines is sometimes called a solid , for a reason that shall be seen afterwards .
Page 126
PLANES AND SOLID ANGLES . Definitions , 1. A straight line is perpendicular to a plane , when it is per- pendicular to all the straight lines which pass through its foot in the plane . Conversely , the plane is perpendicular to the line ...
PLANES AND SOLID ANGLES . Definitions , 1. A straight line is perpendicular to a plane , when it is per- pendicular to all the straight lines which pass through its foot in the plane . Conversely , the plane is perpendicular to the line ...
Page 138
If a solid angle is formed by three plane angles , the sum of any two of these angles will be greater than the third . The proposition requires demonstra- tion only when the plane angle , which is compared to the sum of the other two ...
If a solid angle is formed by three plane angles , the sum of any two of these angles will be greater than the third . The proposition requires demonstra- tion only when the plane angle , which is compared to the sum of the other two ...
Page 139
The sum of the plane angles which form a solid angle is always less than four right angles . Cut the solid angle S by any plane ABCDE ; from O , a point in that plane , draw to the several angles the straight lines AO , OB , OC , OD ...
The sum of the plane angles which form a solid angle is always less than four right angles . Cut the solid angle S by any plane ABCDE ; from O , a point in that plane , draw to the several angles the straight lines AO , OB , OC , OD ...
Page 140
Let the angle ASC = DTF , the angle ASB DTE , and the an- gle BSC = ETF ; then will the inclination of the planes ASC ... If two solid angles are contained by three plane angles , respectively equal to each other , and if 140 GEOMETRY .
Let the angle ASC = DTF , the angle ASB DTE , and the an- gle BSC = ETF ; then will the inclination of the planes ASC ... If two solid angles are contained by three plane angles , respectively equal to each other , and if 140 GEOMETRY .
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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 |