Elements of Geometry and Trigonometry |
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Page 5
The Circle and the Measurement of Angles , Problems relating to the First and Third Books , BOOK IV . The Proportions of Figures and the Measurement of Areas , - Problems relating to the Fourth Book , 41 57 98 88888 68 BOOK V. Regular ...
The Circle and the Measurement of Angles , Problems relating to the First and Third Books , BOOK IV . The Proportions of Figures and the Measurement of Areas , - Problems relating to the Fourth Book , 41 57 98 88888 68 BOOK V. Regular ...
Page 12
that is to say , when following their perimeters in the same di- rection , the first side of the one is equal to the first side of the other , the second of the one to the second of the other , the third to the third , and so on .
that is to say , when following their perimeters in the same di- rection , the first side of the one is equal to the first side of the other , the second of the one to the second of the other , the third to the third , and so on .
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 18
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- tance between the points A and B ( Def . 3. ) ; hence AC + CB is greater than AB .
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- tance between the points A and B ( Def . 3. ) ; hence AC + CB is greater than AB .
Page 19
Second Case . 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. ) . AA B Third Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding ...
Second Case . 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. ) . AA B Third Case . Lastly , if the point G fall within the triangle BAC , we shall have , by the preceding ...
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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 |