Elements of Geometry and Trigonometry |
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Page 68
The altitude of a parallelogram is the perpendicular which measures the distance between two opposite sides taken as bases . Thus , EF is the altitude of the parallelo- Á gram DB . 7. The altitude of a trapezoid is the perpendicular ...
The altitude of a parallelogram is the perpendicular which measures the distance between two opposite sides taken as bases . Thus , EF is the altitude of the parallelo- Á gram DB . 7. The altitude of a trapezoid is the perpendicular ...
Page 69
Parallelograms which have equal bases and equal altitudes , are equivalent . Let AB be the common base of D CF EDF CE the two parallelograms ABCD , ABEF : and since they are supposed to have the same altitude , their upper bases DC ...
Parallelograms which have equal bases and equal altitudes , are equivalent . Let AB be the common base of D CF EDF CE the two parallelograms ABCD , ABEF : and since they are supposed to have the same altitude , their upper bases DC ...
Page 70
Hence these two parallelograms ABCD , ABEF , which havẽ the same base and altitude , are equivalent Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM .
Hence these two parallelograms ABCD , ABEF , which havẽ the same base and altitude , are equivalent Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM .
Page 71
Let ABCD , AEFD , be two rectan- D gles having the common altitude AD : they are to each other as their bases . AB , AE . A E Suppose , first , that the bases are commensurable , and are to each other , for example , as the numbers 7 ...
Let ABCD , AEFD , be two rectan- D gles having the common altitude AD : they are to each other as their bases . AB , AE . A E Suppose , first , that the bases are commensurable , and are to each other , for example , as the numbers 7 ...
Page 72
Hence , whatever be the ratio of the bases , two rectangles ABCD , AEFD , of the same altitude , are to each other as their bases AB ... Any two rectangles are to each other as the products of their bases multiplied by their altitudes .
Hence , whatever be the ratio of the bases , two rectangles ABCD , AEFD , of the same altitude , are to each other as their bases AB ... Any two rectangles are to each other as the products of their bases multiplied by their altitudes .
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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 |