Elements of Geometry and Trigonometry |
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Page 6
Division of the Circumference , General Ideas relating to the Trigonometrical Lines , Theorems and Formulas relating to the Sines , Cosines , T'angents , & c . Construction and Description of the Tables , Description of Table of ...
Division of the Circumference , General Ideas relating to the Trigonometrical Lines , Theorems and Formulas relating to the Sines , Cosines , T'angents , & c . Construction and Description of the Tables , Description of Table of ...
Page 215
For the sake of brevity , they are called the cosine , cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , DS = cot AM , or cot ACM , CS cosec AM , or cosec ACM . In general , A being any arc ...
For the sake of brevity , they are called the cosine , cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , DS = cot AM , or cot ACM , CS cosec AM , or cosec ACM . In general , A being any arc ...
Page 216
S MɅT P zero , are zero , and the cosine and secant of this same arc , are each equal to the radius . Hence if R represents the radius of the circle , we have sin 0 = 0 , tang 0 = 0 , cos 0 = R , sec 0 = R . A VIII .
S MɅT P zero , are zero , and the cosine and secant of this same arc , are each equal to the radius . Hence if R represents the radius of the circle , we have sin 0 = 0 , tang 0 = 0 , cos 0 = R , sec 0 = R . A VIII .
Page 217
Hence X. The point M continuing to advance from D towards B , the sines diminish and the cosines increase . Thus M'P ' is the sine of the arc AM ' , and M'Q , or CP ' its cosine . But the arc M'B is the supplement of AM ' , since AM ' + ...
Hence X. The point M continuing to advance from D towards B , the sines diminish and the cosines increase . Thus M'P ' is the sine of the arc AM ' , and M'Q , or CP ' its cosine . But the arc M'B is the supplement of AM ' , since AM ' + ...
Page 218
The versed sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM = R - c -cos AM . Now when the arc AM becomes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot ...
The versed sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM = R - c -cos AM . Now when the arc AM becomes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot ...
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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 |