Elements of Geometry and Trigonometry |
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Page 12
A theorem is a truth , which becomes evident by means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . A lemma is a subsidiary truth , employed for the demonstra- tion of ...
A theorem is a truth , which becomes evident by means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . A lemma is a subsidiary truth , employed for the demonstra- tion of ...
Page 14
PROPOSITION I. THEOREM . If one straight line meet another straight line , the sum of the two adjacent angles will be equal to two right angles . Let the straight line DC meet the straight line AB at C , then will the angle ACD + the ...
PROPOSITION I. THEOREM . If one straight line meet another straight line , the sum of the two adjacent angles will be equal to two right angles . Let the straight line DC meet the straight line AB at C , then will the angle ACD + the ...
Page 15
THEOREM . If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to twó right angles , the two straight lines which are met , will form one and the same straight line .
THEOREM . If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to twó right angles , the two straight lines which are met , will form one and the same straight line .
Page 18
THEOREM . The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For , the line AB is the shortest dis- ...
THEOREM . The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For , the line AB is the shortest dis- ...
Page 19
... it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . AA B Third Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding theorem , AG + GC < AB + BC ...
... it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . AA B Third Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding theorem , AG + GC < AB + BC ...
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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 |