Elements of Geometry |
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Page 3
A Scholium is a remark upon one or more propositions which have gone before , tending to show their connexion , their restriction , their extension , or the manner of their application . A Hypothesis is a supposition made either in the ...
A Scholium is a remark upon one or more propositions which have gone before , tending to show their connexion , their restriction , their extension , or the manner of their application . A Hypothesis is a supposition made either in the ...
Page 6
Scholium . The four angles , formed about a point by two straight lines which cut each other , are together equal to four right angles ; for the angles ACE , BCE , taken together , are equal to two right angles ; also the other angles ...
Scholium . The four angles , formed about a point by two straight lines which cut each other , are together equal to four right angles ; for the angles ACE , BCE , taken together , are equal to two right angles ; also the other angles ...
Page 9
Scholium . It may be remarked , that equal angles are opposite to equal sides ; thus , the equal angles A and D are opposite to the equal sides B C and EF . THEOREM . 45. In an isosceles triangle , the angles opposite to the equal sides ...
Scholium . It may be remarked , that equal angles are opposite to equal sides ; thus , the equal angles A and D are opposite to the equal sides B C and EF . THEOREM . 45. In an isosceles triangle , the angles opposite to the equal sides ...
Page 10
Scholium . From the equality of the triangles ABD , ACD , it follows , that the angle BAD = DAC , and that the angle BDA = ADC ; therefore these two last are right angles . Hence a straight line , drawn from the vertex of an isosceles ...
Scholium . From the equality of the triangles ABD , ACD , it follows , that the angle BAD = DAC , and that the angle BDA = ADC ; therefore these two last are right angles . Hence a straight line , drawn from the vertex of an isosceles ...
Page 11
Scholium . Through the same point C ( fig . 17 ) , in the Fig . 17 . line AB , it is also impossible to draw two perpendiculars to that line ; for , if CD and CE were these two perpendiculars , the angle DCB would be a right angle as ...
Scholium . Through the same point C ( fig . 17 ) , in the Fig . 17 . line AB , it is also impossible to draw two perpendiculars to that line ; for , if CD and CE were these two perpendiculars , the angle DCB would be a right angle as ...
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Common terms and phrases
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 |