Elements of Geometry and Trigonometry |
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Page 68
The altitude of a triangle is the per- pendicular let fall from the vertex of an angle on the opposite side , taken as a base . Thus , AD is the altitude of the triangle BAC B 6. The altitude of a parallelogram is the perpendicular ...
The altitude of a triangle is the per- pendicular let fall from the vertex of an angle on the opposite side , taken as a base . Thus , AD is the altitude of the triangle BAC B 6. The altitude of a parallelogram is the perpendicular ...
Page 69
Parallelograms which have equal bases and equal altitudes , are equivalent . D CF EDF CE A B A B Let AB be the common base of the two parallelograms ABCD , ABEF : and since they are sup- posed to have the same altitude , their upper ...
Parallelograms which have equal bases and equal altitudes , are equivalent . D CF EDF CE A B A B Let AB be the common base of the two parallelograms ABCD , ABEF : and since they are sup- posed to have the same altitude , their upper ...
Page 70
Hence these two parallelograms ABCD , ABEF , which have 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 have 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 . E Suppose , first , that the bases are A commensurable , and are to each other , for example , as the numbers 7 and ...
Let ABCD , AEFD , be two rectan- D gles having the common altitude AD : they are to each other as their bases AB , AE . E Suppose , first , that the bases are A commensurable , and are to each other , for example , as the numbers 7 and ...
Page 72
Hence , whatever be the ratio of the bases , two rectangles ABCD , AEFD , of the same altitude , are to each other as their ... Any two rectangles are to each other as the products of their bases multiplied by their altitudes , Let ABCD ...
Hence , whatever be the ratio of the bases , two rectangles ABCD , AEFD , of the same altitude , are to each other as their ... Any two rectangles are to each other as the products of their bases multiplied by their altitudes , Let ABCD ...
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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 |