Elements of Geometry and Trigonometry |
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Page 6
215 Construction and Description of the Tables , 223 Description of Table of Logarithms , - 224 Description of Table of Logarithmic Sines , 228 Principles for the Solution of Rectilineal Triangles , 231 Solution of Rectilineal Triangles ...
215 Construction and Description of the Tables , 223 Description of Table of Logarithms , - 224 Description of Table of Logarithmic Sines , 228 Principles for the Solution of Rectilineal Triangles , 231 Solution of Rectilineal Triangles ...
Page 19
triangle GAC is equal to DEF , since , by construction , they have an equal angle in each , contained by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the ...
triangle GAC is equal to DEF , since , by construction , they have an equal angle in each , contained by equal sides , ( Prop . V. ) ; therefore CG is equal to EF . Now , there may be three cases in the proposition , according as the ...
Page 20
Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to each ; for BA is equal to AC , by hypothesis ; AD is common , and BD is equal to DC by construction : therefore , by the last ...
Then , the triangles BAD , DAC , will have all the sides of the one equal to those of the other , each to each ; for BA is equal to AC , by hypothesis ; AD is common , and BD is equal to DC by construction : therefore , by the last ...
Page 21
Now , in the two triangles BDC , BAC , we have BD - AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the included angle ...
Now , in the two triangles BDC , BAC , we have BD - AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the included angle ...
Page 22
... CBF , will be equal : for , the angles CBA , and CBF are right angles , the side CB is common , and the side AB equal to BF , by construction ; there- fore , the triangles are equal , and the angle ACB = BCF ( Prop . V. Cor . ) .
... CBF , will be equal : for , the angles CBA , and CBF are right angles , the side CB is common , and the side AB equal to BF , by construction ; there- fore , the triangles are equal , and the angle ACB = BCF ( Prop . V. Cor . ) .
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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 |