Elements of Geometry |
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Page 2
3 ) meets another straight line CD in such a manner that the adjacent angles BAC , BAD , are equal , each of these angles is called a right angle , and the line AB is said to be perpendicular to CD . 11. Every angle BAC ( fig .
3 ) meets another straight line CD in such a manner that the adjacent angles BAC , BAD , are equal , each of these angles is called a right angle , and the line AB is said to be perpendicular to CD . 11. Every angle BAC ( fig .
Page 3
A diagonal is a line which joins the vertices of two angles not adjacent , as AC ( fig . 42 ) . Fig . 42 19. An equilateral polygon is one which has all its sides equal ; an equiangular polygon is one which has all its angles equal .
A diagonal is a line which joins the vertices of two angles not adjacent , as AC ( fig . 42 ) . Fig . 42 19. An equilateral polygon is one which has all its sides equal ; an equiangular polygon is one which has all its angles equal .
Page 4
17 ) , which meets another straight line AB , makes with it two adjacent angles ACD , BCD , which , taken together , are equal to two right angles . Demonstration . At the point C , let CE be PART FIRST. ...
17 ) , which meets another straight line AB , makes with it two adjacent angles ACD , BCD , which , taken together , are equal to two right angles . Demonstration . At the point C , let CE be PART FIRST. ...
Page 5
For , since DE is perpendicular to AB , it follows that the angle ACD is equal to its adjacent angle DCB , and that they are both right angles . But , since the angle ACD is a right angle , it follows that its adjacent angle ACE is also ...
For , since DE is perpendicular to AB , it follows that the angle ACD is equal to its adjacent angle DCB , and that they are both right angles . But , since the angle ACD is a right angle , it follows that its adjacent angle ACE is also ...
Page 6
If two adjacent angles ACD , DCB ( fig . 20 ) , are together equal to two right angles , the two exterior sides AC , CB , are in the same straight line . Demonstration . For if CB is not the line AC produced , let CE be that line ...
If two adjacent angles ACD , DCB ( fig . 20 ) , are together equal to two right angles , the two exterior sides AC , CB , are in the same straight line . Demonstration . For if CB is not the line AC produced , let CE be that line ...
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ABC fig ABCD adjacent altitude applied base called centre chord circ circle circumference circumscribed common cone consequently construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces feet figure follows formed four give given greater half hence inclination inscribed intersection isosceles join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM produced proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment similar solid angle Solution sphere spherical square straight line suppose surface taken tangent THEOREM third triangle ABC 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 |