Elements of Geometry and Trigonometry |
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Page 77
The two rectangles CBIG , GLKD , are each measured by AB × BC ; take them away from the whole figure ABILKEA , which is equivalent to AB2 + BC , and there will evidently remain the square ACDE ; hence the theorem is true . A Scholium .
The two rectangles CBIG , GLKD , are each measured by AB × BC ; take them away from the whole figure ABILKEA , which is equivalent to AB2 + BC , and there will evidently remain the square ACDE ; hence the theorem is true . A Scholium .
Page 78
THEOREM The square described on the hypothenuse of a right angled tr angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be right angled at A. Having described squares on the three sides ...
THEOREM The square described on the hypothenuse of a right angled tr angle is equivalent to the sum of the squares described on the other two sides . Let the triangle ABC be right angled at A. Having described squares on the three sides ...
Page 79
Hence the square of one of the sides of a right angled triangle is equivalent to the square of the hypothenuse diminished by the square of the other side ; which is tas expressed : AB2 - BC - AC2 . Cor . 2. It has just been shown that ...
Hence the square of one of the sides of a right angled triangle is equivalent to the square of the hypothenuse diminished by the square of the other side ; which is tas expressed : AB2 - BC - AC2 . Cor . 2. It has just been shown that ...
Page 81
The right angled triangle is the only one in which the squares described on the two sides are together equivalent to the square described on the third ; for if the angle contained by the two sides is acute , the sum of their squares ...
The right angled triangle is the only one in which the squares described on the two sides are together equivalent to the square described on the third ; for if the angle contained by the two sides is acute , the sum of their squares ...
Page 82
The two triangles BDE , DEC having the same base DE , and the same altitude , since both their vertices lie in a line parallel to the base , are equivalent ( Prop . II . Cor . 2. ) . D The triangles ADE , BDE , whose common vertex is E ...
The two triangles BDE , DEC having the same base DE , and the same altitude , since both their vertices lie in a line parallel to the base , are equivalent ( Prop . II . Cor . 2. ) . D The triangles ADE , BDE , whose common vertex is E ...
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |