Elements of Geometry and Trigonometry |
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Page 32
Let ABCD be a parallelogram : then will AB = DC , AD = BC , A = C , and ADC = ABC . For , draw the diagonal BD . The triangles ABD , DBC , have a common side BD ; and since AD , BC , are parallel , they have also the angle ADB = DBC ...
Let ABCD be a parallelogram : then will AB = DC , AD = BC , A = C , and ADC = ABC . For , draw the diagonal BD . The triangles ABD , DBC , have a common side BD ; and since AD , BC , are parallel , they have also the angle ADB = DBC ...
Page 33
For a like reason AB is parallel to CD therefore the quadrilateral ABCD is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and ...
For a like reason AB is parallel to CD therefore the quadrilateral ABCD is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and ...
Page 55
The opposite angles A and C , of an inscribed quadrilateral ABCD , are together equal to two right angles : for the angle BAD is measured by half the arc BCD , the angle BCD is measured by half the arc BAD ; hence the two angles BAD ...
The opposite angles A and C , of an inscribed quadrilateral ABCD , are together equal to two right angles : for the angle BAD is measured by half the arc BCD , the angle BCD is measured by half the arc BAD ; hence the two angles BAD ...
Page 69
Let AB be the common base of the two parallelograms ABCD , ABEF : and since they are supposed to have the same altitude , A B their upper bases DC , FE , will be both situated in one straight line parallel to AB .
Let AB be the common base of the two parallelograms ABCD , ABEF : and since they are supposed to have the same altitude , A B their upper bases DC , FE , will be both situated in one straight line parallel to AB .
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 .
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |
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 produced 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 | Harvard University |
| Digitized | 9 Dec 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |