Elements of Geometry and Trigonometry |
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Page 69
Figures which have equal areas are called equivalent . The term equal , when applied to figures , designates those which are equal in every respect , and which being applied to each other will coincide in all their parts ( Ax . 13. ) ...
Figures which have equal areas are called equivalent . The term equal , when applied to figures , designates those which are equal in every respect , and which being applied to each other will coincide in all their parts ( Ax . 13. ) ...
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 74
For , the parallelogram ABCD is equivalent F D to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . I. Cor . ) : but this rectangle is measured by AB × BE ( Prop . IV . Sch . ) ; therefore , ABX BE A is ...
For , the parallelogram ABCD is equivalent F D to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . I. Cor . ) : but this rectangle is measured by AB × BE ( Prop . IV . Sch . ) ; therefore , ABX BE A is ...
Page 75
therefore , the trapezoid ABCD is equivalent to the parallelogram ADKL , and is measured by EFX AL . But we have AL - DK ; and since the triangles IBL and KCI are equal , the side BL - CK : hence , AB + CD = AL + DK = 2AL ; hence AL is ...
therefore , the trapezoid ABCD is equivalent to the parallelogram ADKL , and is measured by EFX AL . But we have AL - DK ; and since the triangles IBL and KCI are equal , the side BL - CK : hence , AB + CD = AL + DK = 2AL ; hence AL is ...
Page 76
If a line is divided into two parts , the square described on the whole line is equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . Let AC be the line , and B the ...
If a line is divided into two parts , the square described on the whole line is equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . Let AC be the line , and B the ...
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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 |